Order = 42305421312000 = 218.36.53.7.11.23.
Mult = 1.
Out = 1.


Porting notes

Porting incomplete.

Standard generators

Standard generators of Co2 are a, b where a is in class 2A, b is in class 5A and ab has order 28.


Black box algorithms

Finding generators

Group Algorithm File
Co2
Download

Checking generators (semi-presentations)

Group Semi-presentation File
Co2 〈〈 a, b | o(a) = 2, o(b) = 5, o(ab) = 28, o(a(ab)14) = 3 〉〉 Download

Presentations

Group Presentation Link
Co2 a, b | a2 = b5 = (abb)9 = [a, b]4 = [a, b2]4 = [a, bab]3 = [a, bab2ab]2 = [a, bab−2]3 = [a, b−2abab−2]2 = [a, b2ab2]3 = (abab2ab−1ab−2)7 = 1 〉 Details

Representations

Representations of Co2


Maximal subgroups

Maximal subgroups of Co2

Subgroup Order Index Programs/reps
U6(2):2 18 393 661 440 2 300 Program: Generators
Program: Much shorter!
210:M22:2 908 328 960 46 575 Program: Generators
McL 898 128 000 47 104 Program: Generators
21+8:S6(2) 743 178 240 56 925 Program: Generators
HS:2 88 704 000 476 928 Program: Generators
(24 × 21+6).A8 41 287 680 1 024 650 Program: Generators
U4(3):D8 26 127 360 1 619 200 Program: Generators
24+10.(S5 × S3) 11 796 480 3 586 275 Program: Generators
M23 10 200 960 4 147 200 Program: Standard generators
31+4}.2{1+4.S5 933 120 45 337 600 Program: Generators
51+2:4S4 12 000 3 525 451 776 Program: Generators

Conjugacy classes

Conjugacy classes of Co2

Conjugacy class Centraliser order Power up Class rep(s)
1A42 305 421 312 000 (ababbabbabababbabbbababbabababbabababbabbb)8
2A743 178 240 4A 4D 6B 6C 6D 8A 8C 8D 10B 12A 12C 12E 14A 16A 16B 18A 24A 28A 30A (ababbabababbabbbabababbabababbabbb)8
2B41 287 680 4B 4C 4E 4F 6A 6E 8B 8E 8F 10A 12B 12D 12F 12G 12H 14B 14C 20A 24B 30B 30C (ababbabbabababbabbbababbabababbabababbabbb)4
2C1 474 560 4G 6F 10C 20B (abbababbabbababbabbbabbababbabb)3
3A466 560 6A 6B 9A 12A 12B 12E 12G 15B 15C 18A 24B 30B 30C (babababbabbbabababbabababbabbb)4
3B155 520 6C 6D 6E 6F 12C 12D 12F 12H 15A 24A 30A (abbababbabbababbabbbabbababbabb)2
4A3 096 576 8A 12A 12C 24A 28A (babababbabbbabababbabababbabbb)3
4B122 880 12F 20A (bababb)3
4C73 728 8B 8E 12B 12D 24B (abababbabbbabababbabababbabbb)2
4D49 152 8C 8D 12E 16A 16B (ababbabababbabbbabababbabababbabbb)4
4E6 144 8F 12G (ababbabbabababbabbbababbabababbabababbabbb)2
4F6 144 12H (ababbabb)3
4G1 280 20B (abababbabababbabbb)5
5A3 000 10A 15B 15C 20A 30B 30C (abbababbabb)4
5B600 10B 10C 15A 20B 30A (abababbabababbabbb)4
6A5 760 12B 12G 24B 30B 30C (ababbabbabababbabbb)2
6B5 184 12A 12E 18A (babababbabbbabababbabababbabbb)2
6C4 320 30A (abababb)5
6D3 456 12C 24A (ababb)4
6E576 12D 12F 12H (abababbabababbababbabbabababbabbb)2
6F288 abbababbabbababbabbbabbababbabb
7A56 14A 14B 14C 28A (abababbabbbababbababbabb)2
8A768 24A (ababb)3
8B768 24B (ababbabababbabababbabbb)3
8C512 16B (ababbabababbabbbabababbabababbabbb)2
8D512 16A (ababbabbbabbababbabb)2
8E256 abababbabbbabababbabababbabbb
8F64 ababbabbabababbabbbababbabababbabababbabbb
9A54 18A (abababbabbb)2
10A120 20A 30B 30C (abbababbabb)2
10B60 30A (abababb)3
10C40 20B (abababbabababbabbb)2
11A11 ababbababbabb
12A864 babababbabbbabababbabababbabbb
12B288 24B (ababbabababbabababbabbb)2
12C288 24A (ababb)2
12D288 abababbabababbababbabbabababbabbb
12E96 ababbabbababbabbb
12F96 bababb
12G48 ababbabbabababbabbb
12H48 ababbabb
14A56 28A (ab)2
14B28 14C3 abababbabbbababbababbabb
14C28 14B3 (abababbabbbababbababbabb)3
15A30 30A (abababb)2
15B30 15C7 30B 30C (ababbababbabbb)14
15C30 15B7 30B 30C (ababbababbabbb)2
16A32 ababbabbbabbababbabb
16B32 ababbabababbabbbabababbabababbabbb
18A18 abababbabbb
20A20 abbababbabb
20B20 abababbabababbabbb
23A23 23B5 ababbabbb
23B23 23A5 (ababbabbb)5
24A24 ababb
24B24 ababbabababbabababbabbb
28A28 ab
30A30 abababb
30B30 30C7 (ababbababbabbb)7
30C30 30B7 ababbababbabbb

Download words for class representatives.