For 24 ≤ n ≤ 251, An has a unique faithful irreducible of degree at most 250, and this is the deleted permutation representation. We have collated these representations onto this page, along with our definitions of standard generators.
Our standard generators for An with n odd can be taken as (1,2,3) and (3,4,5,...,n). Our standard generators for An with n even can be taken as (1,2,3) and (2,3,4,...n).
| Group | Standard generators | Deleted permutation representation |
|---|---|---|
| A24 | a in 3A, b of order 23 such that ab has order 22 and [a,b] has order 2 | 23-dim |
| A25 | a in 3A, b of order 23 such that ab has order 25 | 24-dim |
| A26 | a in 3A, b of order 25 such that ab has order 24 and [a,b] has order 2 | 25-dim |
| A27 | a in 3A, b of order 25 such that ab has order 27 | 26-dim |
| A28 | a in 3A, b of order 27 such that ab has order 26 and [a,b] has order 2 | 27-dim |
| A29 | a in 3A, b of order 27 such that ab has order 29 | 28-dim |
| A30 | a in 3A, b of order 29 such that ab has order 28 and [a,b] has order 2 | 29-dim |
| A31 | a in 3A, b of order 29 such that ab has order 31 | 30-dim |
| A32 | a in 3A, b of order 31 such that ab has order 30 and [a,b] has order 2 | 31-dim |
| A33 | a in 3A, b of order 31 such that ab has order 33 | 32-dim |
| A34 | a in 3A, b of order 33 such that ab has order 32 and [a,b] has order 2 | 33-dim |
| A35 | a in 3A, b of order 33 such that ab has order 35 | 34-dim |
| A36 | a in 3A, b of order 35 such that ab has order 34 and [a,b] has order 2 | 35-dim |
| A37 | a in 3A, b of order 35 such that ab has order 37 | 36-dim |
| A38 | a in 3A, b of order 37 such that ab has order 36 and [a,b] has order 2 | 37-dim |
| A39 | a in 3A, b of order 37 such that ab has order 39 | 38-dim |
| A40 | a in 3A, b of order 39 such that ab has order 38 and [a,b] has order 2 | 39-dim |
| A41 | a in 3A, b of order 39 such that ab has order 41 | 40-dim |
| A42 | a in 3A, b of order 41 such that ab has order 40 and [a,b] has order 2 | 41-dim |
| A43 | a in 3A, b of order 41 such that ab has order 43 | 42-dim |
| A44 | a in 3A, b of order 43 such that ab has order 42 and [a,b] has order 2 | 43-dim |
| A45 | a in 3A, b of order 43 such that ab has order 45 | 44-dim |
| A46 | a in 3A, b of order 45 such that ab has order 44 and [a,b] has order 2 | 45-dim |
| A47 | a in 3A, b of order 45 such that ab has order 47 | 46-dim |
| A48 | a in 3A, b of order 47 such that ab has order 46 and [a,b] has order 2 | 47-dim |
| A49 | a in 3A, b of order 47 such that ab has order 49 | 48-dim |
| A50 | a in 3A, b of order 49 such that ab has order 48 and [a,b] has order 2 | 49-dim |
| A51 | a in 3A, b of order 49 such that ab has order 51 | 50-dim |
| A52 | a in 3A, b of order 51 such that ab has order 50 and [a,b] has order 2 | 51-dim |
| A53 | a in 3A, b of order 51 such that ab has order 53 | 52-dim |
| A54 | a in 3A, b of order 53 such that ab has order 52 and [a,b] has order 2 | 53-dim |
| A55 | a in 3A, b of order 53 such that ab has order 55 | 54-dim |
| A56 | a in 3A, b of order 55 such that ab has order 54 and [a,b] has order 2 | 55-dim |
| A57 | a in 3A, b of order 55 such that ab has order 57 | 56-dim |
| A58 | a in 3A, b of order 57 such that ab has order 56 and [a,b] has order 2 | 57-dim |
| A59 | a in 3A, b of order 57 such that ab has order 59 | 58-dim |
| A60 | a in 3A, b of order 59 such that ab has order 58 and [a,b] has order 2 | 59-dim |
| A61 | a in 3A, b of order 59 such that ab has order 61 | 60-dim |
| A62 | a in 3A, b of order 61 such that ab has order 60 and [a,b] has order 2 | 61-dim |
| A63 | a in 3A, b of order 61 such that ab has order 63 | 62-dim |
| A64 | a in 3A, b of order 63 such that ab has order 62 and [a,b] has order 2 | 63-dim |
| A65 | a in 3A, b of order 63 such that ab has order 65 | 64-dim |
| A66 | a in 3A, b of order 65 such that ab has order 64 and [a,b] has order 2 | 65-dim |
| A67 | a in 3A, b of order 65 such that ab has order 67 | 66-dim |
| A68 | a in 3A, b of order 67 such that ab has order 66 and [a,b] has order 2 | 67-dim |
| A69 | a in 3A, b of order 67 such that ab has order 69 | 68-dim |
| A70 | a in 3A, b of order 69 such that ab has order 68 and [a,b] has order 2 | 69-dim |
| A71 | a in 3A, b of order 69 such that ab has order 71 | 70-dim |
| A72 | a in 3A, b of order 71 such that ab has order 70 and [a,b] has order 2 | 71-dim |
| A73 | a in 3A, b of order 71 such that ab has order 73 | 72-dim |
| A74 | a in 3A, b of order 73 such that ab has order 72 and [a,b] has order 2 | 73-dim |
| A75 | a in 3A, b of order 73 such that ab has order 75 | 74-dim |
| A76 | a in 3A, b of order 75 such that ab has order 74 and [a,b] has order 2 | 75-dim |
| A77 | a in 3A, b of order 75 such that ab has order 77 | 76-dim |
| A78 | a in 3A, b of order 77 such that ab has order 76 and [a,b] has order 2 | 77-dim |
| A79 | a in 3A, b of order 77 such that ab has order 79 | 78-dim |
| A80 | a in 3A, b of order 79 such that ab has order 78 and [a,b] has order 2 | 79-dim |
| A81 | a in 3A, b of order 79 such that ab has order 81 | 80-dim |
| A82 | a in 3A, b of order 81 such that ab has order 80 and [a,b] has order 2 | 81-dim |
| A83 | a in 3A, b of order 81 such that ab has order 83 | 82-dim |
| A84 | a in 3A, b of order 83 such that ab has order 82 and [a,b] has order 2 | 83-dim |
| A85 | a in 3A, b of order 83 such that ab has order 85 | 84-dim |
| A86 | a in 3A, b of order 85 such that ab has order 84 and [a,b] has order 2 | 85-dim |
| A87 | a in 3A, b of order 85 such that ab has order 87 | 86-dim |
| A88 | a in 3A, b of order 87 such that ab has order 86 and [a,b] has order 2 | 87-dim |
| A89 | a in 3A, b of order 87 such that ab has order 89 | 88-dim |
| A90 | a in 3A, b of order 89 such that ab has order 88 and [a,b] has order 2 | 89-dim |
| A91 | a in 3A, b of order 89 such that ab has order 91 | 90-dim |
| A92 | a in 3A, b of order 91 such that ab has order 90 and [a,b] has order 2 | 91-dim |
| A93 | a in 3A, b of order 91 such that ab has order 93 | 92-dim |
| A94 | a in 3A, b of order 93 such that ab has order 92 and [a,b] has order 2 | 93-dim |
| A95 | a in 3A, b of order 93 such that ab has order 95 | 94-dim |
| A96 | a in 3A, b of order 95 such that ab has order 94 and [a,b] has order 2 | 95-dim |
| A97 | a in 3A, b of order 95 such that ab has order 97 | 96-dim |
| A98 | a in 3A, b of order 97 such that ab has order 96 and [a,b] has order 2 | 97-dim |
| A99 | a in 3A, b of order 97 such that ab has order 99 | 98-dim |
| A100 | a in 3A, b of order 99 such that ab has order 98 and [a,b] has order 2 | 99-dim |
| A101 | a in 3A, b of order 99 such that ab has order 101 | 100-dim |
| A102 | a in 3A, b of order 101 such that ab has order 100 and [a,b] has order 2 | 101-dim |
| A103 | a in 3A, b of order 101 such that ab has order 103 | 102-dim |
| A104 | a in 3A, b of order 103 such that ab has order 102 and [a,b] has order 2 | 103-dim |
| A105 | a in 3A, b of order 103 such that ab has order 105 | 104-dim |
| A106 | a in 3A, b of order 105 such that ab has order 104 and [a,b] has order 2 | 105-dim |
| A107 | a in 3A, b of order 105 such that ab has order 107 | 106-dim |
| A108 | a in 3A, b of order 107 such that ab has order 106 and [a,b] has order 2 | 107-dim |
| A109 | a in 3A, b of order 107 such that ab has order 109 | 108-dim |
| A110 | a in 3A, b of order 109 such that ab has order 108 and [a,b] has order 2 | 109-dim |
| A111 | a in 3A, b of order 109 such that ab has order 111 | 110-dim |
| A112 | a in 3A, b of order 111 such that ab has order 110 and [a,b] has order 2 | 111-dim |
| A113 | a in 3A, b of order 111 such that ab has order 113 | 112-dim |
| A114 | a in 3A, b of order 113 such that ab has order 112 and [a,b] has order 2 | 113-dim |
| A115 | a in 3A, b of order 113 such that ab has order 115 | 114-dim |
| A116 | a in 3A, b of order 115 such that ab has order 114 and [a,b] has order 2 | 115-dim |
| A117 | a in 3A, b of order 115 such that ab has order 117 | 116-dim |
| A118 | a in 3A, b of order 117 such that ab has order 116 and [a,b] has order 2 | 117-dim |
| A119 | a in 3A, b of order 117 such that ab has order 119 | 118-dim |
| A120 | a in 3A, b of order 119 such that ab has order 118 and [a,b] has order 2 | 119-dim |
| A121 | a in 3A, b of order 119 such that ab has order 121 | 120-dim |
| A122 | a in 3A, b of order 121 such that ab has order 120 and [a,b] has order 2 | 121-dim |
| A123 | a in 3A, b of order 121 such that ab has order 123 | 122-dim |
| A124 | a in 3A, b of order 123 such that ab has order 122 and [a,b] has order 2 | 123-dim |
| A125 | a in 3A, b of order 123 such that ab has order 125 | 124-dim |
| A126 | a in 3A, b of order 125 such that ab has order 124 and [a,b] has order 2 | 125-dim |
| A127 | a in 3A, b of order 125 such that ab has order 127 | 126-dim |
| A128 | a in 3A, b of order 127 such that ab has order 126 and [a,b] has order 2 | 127-dim |
| A129 | a in 3A, b of order 127 such that ab has order 129 | 128-dim |
| A130 | a in 3A, b of order 129 such that ab has order 128 and [a,b] has order 2 | 129-dim |
| A131 | a in 3A, b of order 129 such that ab has order 131 | 130-dim |
| A132 | a in 3A, b of order 131 such that ab has order 130 and [a,b] has order 2 | 131-dim |
| A133 | a in 3A, b of order 131 such that ab has order 133 | 132-dim |
| A134 | a in 3A, b of order 133 such that ab has order 132 and [a,b] has order 2 | 133-dim |
| A135 | a in 3A, b of order 133 such that ab has order 135 | 134-dim |
| A136 | a in 3A, b of order 135 such that ab has order 134 and [a,b] has order 2 | 135-dim |
| A137 | a in 3A, b of order 135 such that ab has order 137 | 136-dim |
| A138 | a in 3A, b of order 137 such that ab has order 136 and [a,b] has order 2 | 137-dim |
| A139 | a in 3A, b of order 137 such that ab has order 139 | 138-dim |
| A140 | a in 3A, b of order 139 such that ab has order 138 and [a,b] has order 2 | 139-dim |
| A141 | a in 3A, b of order 139 such that ab has order 141 | 140-dim |
| A142 | a in 3A, b of order 141 such that ab has order 140 and [a,b] has order 2 | 141-dim |
| A143 | a in 3A, b of order 141 such that ab has order 143 | 142-dim |
| A144 | a in 3A, b of order 143 such that ab has order 142 and [a,b] has order 2 | 143-dim |
| A145 | a in 3A, b of order 143 such that ab has order 145 | 144-dim |
| A146 | a in 3A, b of order 145 such that ab has order 144 and [a,b] has order 2 | 145-dim |
| A147 | a in 3A, b of order 145 such that ab has order 147 | 146-dim |
| A148 | a in 3A, b of order 147 such that ab has order 146 and [a,b] has order 2 | 147-dim |
| A149 | a in 3A, b of order 147 such that ab has order 149 | 148-dim |
| A150 | a in 3A, b of order 149 such that ab has order 148 and [a,b] has order 2 | 149-dim |
| A151 | a in 3A, b of order 149 such that ab has order 151 | 150-dim |
| A152 | a in 3A, b of order 151 such that ab has order 150 and [a,b] has order 2 | 151-dim |
| A153 | a in 3A, b of order 151 such that ab has order 153 | 152-dim |
| A154 | a in 3A, b of order 153 such that ab has order 152 and [a,b] has order 2 | 153-dim |
| A155 | a in 3A, b of order 153 such that ab has order 155 | 154-dim |
| A156 | a in 3A, b of order 155 such that ab has order 154 and [a,b] has order 2 | 155-dim |
| A157 | a in 3A, b of order 155 such that ab has order 157 | 156-dim |
| A158 | a in 3A, b of order 157 such that ab has order 156 and [a,b] has order 2 | 157-dim |
| A159 | a in 3A, b of order 157 such that ab has order 159 | 158-dim |
| A160 | a in 3A, b of order 159 such that ab has order 158 and [a,b] has order 2 | 159-dim |
| A161 | a in 3A, b of order 159 such that ab has order 161 | 160-dim |
| A162 | a in 3A, b of order 161 such that ab has order 160 and [a,b] has order 2 | 161-dim |
| A163 | a in 3A, b of order 161 such that ab has order 163 | 162-dim |
| A164 | a in 3A, b of order 163 such that ab has order 162 and [a,b] has order 2 | 163-dim |
| A165 | a in 3A, b of order 163 such that ab has order 165 | 164-dim |
| A166 | a in 3A, b of order 165 such that ab has order 164 and [a,b] has order 2 | 165-dim |
| A167 | a in 3A, b of order 165 such that ab has order 167 | 166-dim |
| A168 | a in 3A, b of order 167 such that ab has order 166 and [a,b] has order 2 | 167-dim |
| A169 | a in 3A, b of order 167 such that ab has order 169 | 168-dim |
| A170 | a in 3A, b of order 169 such that ab has order 168 and [a,b] has order 2 | 169-dim |
| A171 | a in 3A, b of order 169 such that ab has order 171 | 170-dim |
| A172 | a in 3A, b of order 171 such that ab has order 170 and [a,b] has order 2 | 171-dim |
| A173 | a in 3A, b of order 171 such that ab has order 173 | 172-dim |
| A174 | a in 3A, b of order 173 such that ab has order 172 and [a,b] has order 2 | 173-dim |
| A175 | a in 3A, b of order 173 such that ab has order 175 | 174-dim |
| A176 | a in 3A, b of order 175 such that ab has order 174 and [a,b] has order 2 | 175-dim |
| A177 | a in 3A, b of order 175 such that ab has order 177 | 176-dim |
| A178 | a in 3A, b of order 177 such that ab has order 176 and [a,b] has order 2 | 177-dim |
| A179 | a in 3A, b of order 177 such that ab has order 179 | 178-dim |
| A180 | a in 3A, b of order 179 such that ab has order 178 and [a,b] has order 2 | 179-dim |
| A181 | a in 3A, b of order 179 such that ab has order 181 | 180-dim |
| A182 | a in 3A, b of order 181 such that ab has order 180 and [a,b] has order 2 | 181-dim |
| A183 | a in 3A, b of order 181 such that ab has order 183 | 182-dim |
| A184 | a in 3A, b of order 183 such that ab has order 182 and [a,b] has order 2 | 183-dim |
| A185 | a in 3A, b of order 183 such that ab has order 185 | 184-dim |
| A186 | a in 3A, b of order 185 such that ab has order 184 and [a,b] has order 2 | 185-dim |
| A187 | a in 3A, b of order 185 such that ab has order 187 | 186-dim |
| A188 | a in 3A, b of order 187 such that ab has order 186 and [a,b] has order 2 | 187-dim |
| A189 | a in 3A, b of order 187 such that ab has order 189 | 188-dim |
| A190 | a in 3A, b of order 189 such that ab has order 188 and [a,b] has order 2 | 189-dim |
| A191 | a in 3A, b of order 189 such that ab has order 191 | 190-dim |
| A192 | a in 3A, b of order 191 such that ab has order 190 and [a,b] has order 2 | 191-dim |
| A193 | a in 3A, b of order 191 such that ab has order 193 | 192-dim |
| A194 | a in 3A, b of order 193 such that ab has order 192 and [a,b] has order 2 | 193-dim |
| A195 | a in 3A, b of order 193 such that ab has order 195 | 194-dim |
| A196 | a in 3A, b of order 195 such that ab has order 194 and [a,b] has order 2 | 195-dim |
| A197 | a in 3A, b of order 195 such that ab has order 197 | 196-dim |
| A198 | a in 3A, b of order 197 such that ab has order 196 and [a,b] has order 2 | 197-dim |
| A199 | a in 3A, b of order 197 such that ab has order 199 | 198-dim |
| A200 | a in 3A, b of order 199 such that ab has order 198 and [a,b] has order 2 | 199-dim |
| A201 | a in 3A, b of order 199 such that ab has order 201 | 200-dim |
| A202 | a in 3A, b of order 201 such that ab has order 200 and [a,b] has order 2 | 201-dim |
| A203 | a in 3A, b of order 201 such that ab has order 203 | 202-dim |
| A204 | a in 3A, b of order 203 such that ab has order 202 and [a,b] has order 2 | 203-dim |
| A205 | a in 3A, b of order 203 such that ab has order 205 | 204-dim |
| A206 | a in 3A, b of order 205 such that ab has order 204 and [a,b] has order 2 | 205-dim |
| A207 | a in 3A, b of order 205 such that ab has order 207 | 206-dim |
| A208 | a in 3A, b of order 207 such that ab has order 206 and [a,b] has order 2 | 207-dim |
| A209 | a in 3A, b of order 207 such that ab has order 209 | 208-dim |
| A210 | a in 3A, b of order 209 such that ab has order 208 and [a,b] has order 2 | 209-dim |
| A211 | a in 3A, b of order 209 such that ab has order 211 | 210-dim |
| A212 | a in 3A, b of order 211 such that ab has order 210 and [a,b] has order 2 | 211-dim |
| A213 | a in 3A, b of order 211 such that ab has order 213 | 212-dim |
| A214 | a in 3A, b of order 213 such that ab has order 212 and [a,b] has order 2 | 213-dim |
| A215 | a in 3A, b of order 213 such that ab has order 215 | 214-dim |
| A216 | a in 3A, b of order 215 such that ab has order 214 and [a,b] has order 2 | 215-dim |
| A217 | a in 3A, b of order 215 such that ab has order 217 | 216-dim |
| A218 | a in 3A, b of order 217 such that ab has order 216 and [a,b] has order 2 | 217-dim |
| A219 | a in 3A, b of order 217 such that ab has order 219 | 218-dim |
| A220 | a in 3A, b of order 219 such that ab has order 218 and [a,b] has order 2 | 219-dim |
| A221 | a in 3A, b of order 219 such that ab has order 221 | 220-dim |
| A222 | a in 3A, b of order 221 such that ab has order 220 and [a,b] has order 2 | 221-dim |
| A223 | a in 3A, b of order 221 such that ab has order 223 | 222-dim |
| A224 | a in 3A, b of order 223 such that ab has order 222 and [a,b] has order 2 | 223-dim |
| A225 | a in 3A, b of order 223 such that ab has order 225 | 224-dim |
| A226 | a in 3A, b of order 225 such that ab has order 224 and [a,b] has order 2 | 225-dim |
| A227 | a in 3A, b of order 225 such that ab has order 227 | 226-dim |
| A228 | a in 3A, b of order 227 such that ab has order 226 and [a,b] has order 2 | 227-dim |
| A229 | a in 3A, b of order 227 such that ab has order 229 | 228-dim |
| A230 | a in 3A, b of order 229 such that ab has order 228 and [a,b] has order 2 | 229-dim |
| A231 | a in 3A, b of order 229 such that ab has order 231 | 230-dim |
| A232 | a in 3A, b of order 231 such that ab has order 230 and [a,b] has order 2 | 231-dim |
| A233 | a in 3A, b of order 231 such that ab has order 233 | 232-dim |
| A234 | a in 3A, b of order 233 such that ab has order 232 and [a,b] has order 2 | 233-dim |
| A235 | a in 3A, b of order 233 such that ab has order 235 | 234-dim |
| A236 | a in 3A, b of order 235 such that ab has order 234 and [a,b] has order 2 | 235-dim |
| A237 | a in 3A, b of order 235 such that ab has order 237 | 236-dim |
| A238 | a in 3A, b of order 237 such that ab has order 236 and [a,b] has order 2 | 237-dim |
| A239 | a in 3A, b of order 237 such that ab has order 239 | 238-dim |
| A240 | a in 3A, b of order 239 such that ab has order 238 and [a,b] has order 2 | 239-dim |
| A241 | a in 3A, b of order 239 such that ab has order 241 | 240-dim |
| A242 | a in 3A, b of order 241 such that ab has order 240 and [a,b] has order 2 | 241-dim |
| A243 | a in 3A, b of order 241 such that ab has order 243 | 242-dim |
| A244 | a in 3A, b of order 243 such that ab has order 242 and [a,b] has order 2 | 243-dim |
| A245 | a in 3A, b of order 243 such that ab has order 245 | 244-dim |
| A246 | a in 3A, b of order 245 such that ab has order 244 and [a,b] has order 2 | 245-dim |
| A247 | a in 3A, b of order 245 such that ab has order 247 | 246-dim |
| A248 | a in 3A, b of order 247 such that ab has order 246 and [a,b] has order 2 | 247-dim |
| A249 | a in 3A, b of order 247 such that ab has order 249 | 248-dim |
| A250 | a in 3A, b of order 249 such that ab has order 248 and [a,b] has order 2 | 249-dim |
| A251 | a in 3A, b of order 249 such that ab has order 251 | 250-dim |
Last updated on 3rd September, 2005.