Straight line programs for some maximal subgroups

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We give straight line programs for generating the (non-trivial) maximal subgroups of the following groups in terms of their standard generators:

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Tables of straight line programs

Maximal subgroups of M12.2

i Ki Programs
(1) (2)
2 L2(11):2 Program 1 (Atlas/GAP) length 6
Standard generators		 Program 2 (Atlas/GAP) length 4
3 L2(11):2 Program 1 (Atlas/GAP) length 7
Standard generators		 Program 2 (Atlas/GAP) length 2
4 (22 × A5):2 Program 1 (Atlas/GAP) length 8
5 21+4.S3.2 Program 1 (Atlas/GAP) length 8
6 42:D12.2 Program 1 (Atlas/GAP) length 16
7 31+2:D8 Program 1 (Atlas/GAP) length 7
8 S4 × S3 Program 1 (Atlas/GAP) length 8
9 S5 Program 1 (Atlas/GAP) length 5
Standard generators

Maximal subgroups of M22.2

i Ki Programs
(1) (2)
2 L3(4):2 Program 1 (Atlas/GAP) length 9
Standard generators		 Program 2 (Atlas/GAP) length 6
3 24:A6:2 Program 1 (Atlas/GAP) length 8
4 25:S5 Program 1 (Atlas/GAP) length 8
5 23:L3(2) × 2 Program 1 (Atlas/GAP) length 15
Generators mapping onto standard generators for L3(2) 		Program 2 (Atlas/GAP) length 6
6 A6:22 Program 1 (Atlas/GAP) length 4
Standard generators
7 L2(11):2 Program 1 (Atlas/GAP) length 10
Standard generators		 Program 2 (Atlas/GAP) length 3

Maximal subgroups of HS.2

i Ki Programs
(1) (2)
2 M22:2 Program 1 (Atlas/GAP) length 11
Standard generators		 Program 2 (Atlas/GAP) length 4
3 L3(4).2.2 Program 1 (Atlas/GAP) length 6
4 S8 × 2 Program 1 (Atlas/GAP) length 9
Generators mapping onto standard generators for S8 		Program 2 (Atlas/GAP) length 2
5 26:S6 Program 1 (Atlas/GAP) length 11
Generators mapping onto standard generators for S6
6 43.(2 × L3(2)) Program 1 (Atlas/GAP) length 12
Generators mapping onto standard generators for L3(2) 		Program 2 (Atlas/GAP) length 5
7 21+6.S5 Program 1 (Atlas/GAP) length 14
Generators mapping onto standard generators for S5
8 (2 × A6.2.2).2 Program 1 (Atlas/GAP) length 26
Three generators
9 51+2.[25] Program 1 (Atlas/GAP) length 13
10 5:4 × S5 Program 1 (Atlas/GAP) length 17
Generators mapping onto standard generators for S5

Maximal subgroups of Suz.2

i Ki Programs
(1) (2)
2 G2(4):2 Program 1 (Atlas/GAP) length 14
Standard generators		 Program 2 (Atlas/GAP) length 7
3 3.U4(3).2.2 Program 1 (Atlas/GAP) length 6
4 U5(2):2 Program 1 (Atlas/GAP) length 25
Standard generators
5 21+6.U4(2).2 Program 1 (Atlas/GAP) length 11
Generators mapping onto standard generators for U4(2).2 		Program 2 (Atlas/GAP) length 7
6 35:(M11 × 2) Program 1 (Atlas/GAP) length 22
Generators mapping onto standard generators for M11
7 J2:2 × 2 Program 1 (Atlas/GAP) length 13
Generators mapping onto standard generators for J2:2 		Program 2 (Atlas/GAP) length 6
8 24+6:3.S6 Program 1 (Atlas/GAP) length 16
Generators mapping onto standard generators for S6 		Program 2 (Atlas/GAP) length 7
9 (A4 × L3(4):2):2 Program 1 (Atlas/GAP) length 9
10 22+8:(S5 × S3) Program 1 (Atlas/GAP) length 8
11 M12:2 × 2 Program 1 (Atlas/GAP) length 20
Generators mapping onto standard generators for M12:2 		Program 2 (Atlas/GAP) length 4
12 32+4:2.(S4 × D8) Program 1 (Atlas/GAP) length 32
Three generators
13 (PGL2(9) × A5).2 Program 1 (Atlas/GAP) length 12
Generators mapping onto standard generators for PGL2(9).2 		Program 2 (Atlas/GAP) length 11
14 (A6 × 32:8).2 Program 1 (Atlas/GAP) length 18
Generators mapping onto standard generators for S6
15 L2(25):2 Program 1 (Atlas/GAP) length 8
16 S7 Program 1 (Atlas/GAP) length 23
Standard generators		 Program 2 (Atlas/GAP) length 7

Maximal subgroups of McL.2

i Ki Programs
(1) (2)
2 U4(3):2 Program 1 (Atlas/GAP) length 7
3 U3(5):2 Program 1 (Atlas/GAP) length 6
4 31+4:4.S5 Program 1 (Atlas/GAP) length 8
5 34:(M10 × 2) Program 1 (Atlas/GAP) length 9
6 L3(4):2:2 Program 1 (Atlas/GAP) length 5
7 2.S8 Program 1 (Atlas/GAP) length 22
Standard generators		 Program 2 (Atlas/GAP) length 6
8 M11 × 2 Program 1 (Atlas/GAP) length 14
Generators mapping onto standard generators for M11 		Program 2 (Atlas/GAP) length 6
9 51+2:3:8.2 Program 1 (Atlas/GAP) length 19
10 22+4:(S3 × S3) Program 1 (Atlas/GAP) length 14

Maximal subgroups of He.2

i Ki Programs
(1) (2)
2 S4(4):4 Program 1 (Atlas/GAP) length 14
Standard generators		 Program 2 (Atlas/GAP) length 6
3 22.L3(4).D12 Program 1 (Atlas/GAP) length 13
Generators mapping onto standard generators for L3(4).D12 		Program 2 (Atlas/GAP) length 9
4 21+6.L3(2).2 Program 1 (Atlas/GAP) length 18
Generators mapping onto standard generators for L3(2).2 		Program 2 (Atlas/GAP) length 7
5 72:2L2(7).2 Program 1 (Atlas/GAP) length 16
Generators mapping onto standard generators for 2.L2(7).2
6 3.S7 × 2 Program 1 (Atlas/GAP) length 9
Generators mapping onto standard generators for 3.S7 		Program 2 (Atlas/GAP) length 5
7 (S5 × S5):2 Program 1 (Atlas/GAP) length 9
8 24+4.(S3 × S3).2 Program 1 (Atlas/GAP) length 9
9 71+2:(S3 × 6) Program 1 (Atlas/GAP) length 16
10 S4 × L3(2):2 Program 1 (Atlas/GAP) length 14
Generators mapping onto standard generators for L3(2):2 		Program 2 (Atlas/GAP) length 11
11 7:6 × L3(2) Program 1 (Atlas/GAP) length 14
Generators mapping onto standard generators for L3(2)
12 52:4S4 Program 1 (Atlas/GAP) length 15

Maximal subgroups of J2.2

i Ki Programs
(1) (2)
2 U3(3):2 Program 1 (Atlas/GAP) length 10
Standard generators		 Program 2 (Atlas/GAP) length 5
3 3.A6.2.2 Program 1 (Atlas/GAP) length 10
Standard generators		 Program 2 (Atlas/GAP) length 6
4 21+4.A5.2 Program 1 (Atlas/GAP) length 3
5 22+4:(3 × S3).2 Program 1 (Atlas/GAP) length 6
6 (A4 × A5):2 Program 1 (Atlas/GAP) length 4
7 (A5 × D10).2 Program 1 (Atlas/GAP) length 6
8 L3(2):2 × 2 Program 1 (Atlas/GAP) length 11
Generators mapping onto standard generators for L3(2):2 		Program 2 (Atlas/GAP) length 7
9 52:(4 × S3) Program 1 (Atlas/GAP) length 10
10 S5 Program 1 (Atlas/GAP) length 12
Standard generators		 Program 2 (Atlas/GAP) length 5

Maximal subgroups of J3.2

i Ki Programs
(1) (2)
2 L2(16):4 Program 1 (Atlas/GAP) length 13
Standard generators
3 24:(3 × A5).2 Program 1 (Atlas/GAP) length 8
4 L2(17) × 2 Program 1 (Atlas/GAP) length 11
Generators mapping onto standard generators for L2(17) 		Program 2 (Atlas/GAP) length 6
5 (3 × M10):2 Program 1 (Atlas/GAP) length 10
6 32.(3 × 32):8.2 Program 1 (Atlas/GAP) length 8
7 21+4.S5 Program 1 (Atlas/GAP) length 7
8 22+4:(S3 × S3) Program 1 (Atlas/GAP) length 8
9 19:18 Program 1 (Atlas/GAP) length 12

Maximal subgroups of F22.2

i Ki Programs
(1) (2)
2 2.U6(2).2 Program 1 (Atlas/GAP) length 17
Standard generators		 Program 2 (Atlas/GAP) length 2
3 O8+(2):S3 × 2 Program 1 (Atlas/GAP) length 5
4 210:M22:2 Program 1 (Atlas/GAP) length 16
Generators mapping onto standard generators for M22:2
5 27:S6(2) Program 1 (Atlas/GAP) length 6
6 (2 × 21+8:U4(2):2):2 Program 1 (Atlas/GAP) length 25
7 S3 × U4(3).(22) Program 1 (Atlas/GAP) length 32
Three generators
8 2F4(2) Program 1 (Atlas/GAP) length 15
Standard generators
9 25+8:(S3 × S6) Program 1 (Atlas/GAP) length 20
10 35:(2 × U4(2):2) Program 1 (Atlas/GAP) length 6
11 31+6:23+4:32.2.2 Program 1 (Atlas/GAP) length 18
12 G2(3):2 Program 1 (Atlas/GAP) length 15
Standard generators
13 M12:2 Program 1 (Atlas/GAP) length 15
Standard generators

Maximal subgroups of O'N.2

i Ki Programs
(1) (2)
2 71+2:(3 × D16) Program 1 (Atlas/GAP) length 17
3 J1 × 2 Program 1 (Atlas/GAP) length 14
4 4.L3(4).22 Program 1 (Atlas/GAP) length 11
5 (32:4 × A6).22 Program 1 (Atlas/GAP) length 15
6 34:21+4D10.2 Program 1 (Atlas/GAP) length 16
7 31:30 Program 1 (Atlas/GAP) length 13
8 43.L3(2) × 2 Program 1 (Atlas/GAP) length 13
9 L2(7):2 Program 1 (Atlas/GAP) length 13
10 A6:22 Program 1 (Atlas/GAP) length 15

Maximal subgroups of HN.2

i Ki Programs
(1) (2)
2 S12 Program 1 (Atlas/GAP) length 17
Standard generators
3 4.HS.2 Program 1 (Atlas/GAP) length 29
4 U3(8):6 Program 1 (Atlas/GAP) length 11
Standard generators
5 21+8.(A5 × A5).22 Program 1 (Atlas/GAP) length 21
6 5:4 × U3(5):2 Program 1 (Atlas/GAP) length 82
7 51+4:21+4.5.4.2 Program 1 (Atlas/GAP) length 64
8 26.U4(2).2 Program 1 (Atlas/GAP) length 12
Generators mapping onto standard generators for U4(2).2
9 (S6 × S6):22 Program 1 (Atlas/GAP) length 37
Three generators
10 23.22.26.(3 × L3(2)).2 Program 1 (Atlas/GAP) length 52
11 52.5.52.4A5.2 Program 1 (Atlas/GAP) length 110
12 34:2(S4 × S4).2 Program 1 (Atlas/GAP) length 91
13 31+4:4S5 Program 1 (Atlas/GAP) length 61

Maximal subgroups of F24

i Ki Programs
(1) (2)
2 F23 × 2 Program 1 (Atlas/GAP) length 4
3 (2 × 2.F22):2 Program 1 (Atlas/GAP) length 11
4 S3 × O8+(3):S3 Program 1 (Atlas/GAP) length 27
5 O10-(2):2 Program 1 (Atlas/GAP) length 13
6 37.O7(3):2 Program 1 (Atlas/GAP) length 13
7 31+10:(2 × U5(2):2) Program 1 (Atlas/GAP) length 13
8 212.M24 Program 1 (Atlas/GAP) length 45
9 (2 × 22.U6(2)):S3 Program 1 (Atlas/GAP) length 19
10 21+12.3U4(3).22 Program 1 (Atlas/GAP) length 24
11 33.[310].(L3(2) × 22) Program 1 (Atlas/GAP) length 46
12 32.34.38.(S5 × 2S4) Program 1 (Atlas/GAP) length 46
13 S4 × O8+(2):S3 Program 1 (Atlas/GAP) length 56
14 23+12.(L3(2) × S6) Program 1 (Atlas/GAP) length 79
15 27+8.(S3 × A8) Program 1 (Atlas/GAP) length 82
16 (S3 × S3 × G2(3)):2 Program 1 (Atlas/GAP) length 72
17 S5 × S9 Program 1 (Atlas/GAP) length 76
18 S6 × L2(8):3 Program 1 (Atlas/GAP) length 65
19 7:6 × S7 Program 1 (Atlas/GAP) length 102
20 71+2:(6 × S3).2 Program 1 (Atlas/GAP) length 75
21 29:28 Program 1 (Atlas/GAP) length 56