Order = 495766656000 = 210.37.53.7.11.23.
Mult = 1.
Out = 1.

Porting notes

Fully copied from version 2. 30/7/06.

Standard generators

Standard generators of Co3 are a, b where a is in class 3A, b is in class 4A and ab has order 14.

Black box algorithms

Finding generators

Group Algorithm File
Co3 Download

Checking generators (semi-presentations)

Group Semi-presentation File
Co3 〈〈 a, b | o(a) = 3, o(b) = 4, o(ab) = 14, o(w) = 5, o([w,y]) = 1; t = abab3a2, u = (b2(b2)abb)3, v = t(b2(b2)t)2, w = (uvv)3(uv)6 〉〉 Download

Representations

Representations of Co3

Maximal subgroups

Maximal subgroups of Co3

Subgroup Order Index Programs/reps
McL:2 1 796 256 000 276 Program: Generators
HS 44 352 000 11 178 Program: Generators
U4(3).(22)133 13 063 680 37 950 Program: Generators
M23 10 200 960 48 600 Program: Generators
35:(2 × M11) 3 849 120 128 800 Program: Generators
2.S6(2) 2 903 040 170 775 Program: Generators
U3(5):S3 756 000 655 776 Program: Generators
31+4:4S6 699 840 708 400 Program: Generators
24.A8 322 560 1 536 975 Program: Generators
L3(4):D12 241 920 2 049 300 Program: Generators
2 × M12 190 080 2 608 200 Program: Generators
[210.33] 27 648 17 931 375 Program: Generators
Program: Generators
S3 × L2(8):3 9 072 54 648 000 Program: Generators
A4 × S5 1 440 344 282 400 Program: Generators
Program: Generators

Conjugacy classes

Conjugacy classes of Co3

Conjugacy class Centraliser order Power up Class rep(s)
1A 495 766 656 000 (baababbaabaabbaababbabbaabaabb)8
2A 2 903 040 4A 4B 6A 6B 6C 8A 8B 8C 10A 12A 12B 12C 14A 18A 20A 20B 24A 24B 30A (baababbaabaabbaababbabbaabaabb)4
2B 190 080 6D 6E 10B 22A 22B (abbabbaabaabb)3
3A 349 920 6A 6B 9A 9B 12A 12B 15A 18A 24A 24B 30A (baababbaabaabbbabbaababbaabaabbaabb)4
3B 29 160 6C 6D 12C 15B (aababbabbaabaabb)2
3C 4 536 6E 21A (abbabbaabaabb)2
4A 23 040 12A 12C 20A 20B (baababbaabaabbbabbaababbaabaabbaabb)3
4B 1 536 8A 8B 8C 12B 24A 24B (baababbaabaabbaababbabbaabaabb)2
5A 1 500 10A 15A 20A 20B 30A (babbaababbaabaabb)4
5B 300 10B 15B (ababbaababbaabaabb)2
6A 4 320 12A 12B 24A 24B 30A (baababbaabaabbbabbaababbaabaabbaabb)2
6B 1 296 18A (baababbaabaabb)3
6C 216 12C (aababbaabaabbaabbabbaabaabb)2
6D 108 aababbabbaabaabb
6E 72 abbabbaabaabb
7A 42 14A 21A (ab)2
8A 192 24A (abb)3
8B 192 24B (aabbabbaabaabb)3
8C 32 baababbaabaabbaababbabbaabaabb
9A 162 18A (baababbaabaabb)2
9B 81 babbaababbaabaabbaabb
10A 60 20A 20B 30A (babbaababbaabaabb)2
10B 20 ababbaababbaabaabb
11A 22 11B2 22A 22B (abbaababbaabaabb)4
11B 22 11A2 22A 22B (abbaababbaabaabb)2
12A 144 baababbaabaabbbabbaababbaabaabbaabb
12B 48 24A 24B (abb)2
12C 36 aababbaabaabbaabbabbaabaabb
14A 14 ab
15A 30 30A (aabaabbaababbaabaabb)2
15B 15 aabaabb
18A 18 baababbaabaabb
20A 20 20B11 babbaababbaabaabb
20B 20 20A11 (babbaababbaabaabb)11
21A 21 abbaabaabb
22A 22 22B7 abbaababbaabaabb
22B 22 22A7 (abbaababbaabaabb)7
23A 23 23B5 aababbaabaabb
23B 23 23A5 (aababbaabaabb)5
24A 24 abb
24B 24 aabbabbaabaabb
30A 30 aabaabbaababbaabaabb

Download words for class representatives.