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

### 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

## Maximal subgroups

### Maximal subgroups of Co3

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

## Conjugacy classes

### Conjugacy classes of Co3

Conjugacy class Centraliser order Power up Class rep(s)
1A495 766 656 000 (baababbaabaabbaababbabbaabaabb)8
2A2 903 040 4A 4B 6A 6B 6C 8A 8B 8C 10A 12A 12B 12C 14A 18A 20A 20B 24A 24B 30A (baababbaabaabbaababbabbaabaabb)4
2B190 080 6D 6E 10B 22A 22B (abbabbaabaabb)3
3A349 920 6A 6B 9A 9B 12A 12B 15A 18A 24A 24B 30A (baababbaabaabbbabbaababbaabaabbaabb)4
3B29 160 6C 6D 12C 15B (aababbabbaabaabb)2
3C4 536 6E 21A (abbabbaabaabb)2
4A23 040 12A 12C 20A 20B (baababbaabaabbbabbaababbaabaabbaabb)3
4B1 536 8A 8B 8C 12B 24A 24B (baababbaabaabbaababbabbaabaabb)2
5A1 500 10A 15A 20A 20B 30A (babbaababbaabaabb)4
5B300 10B 15B (ababbaababbaabaabb)2
6A4 320 12A 12B 24A 24B 30A (baababbaabaabbbabbaababbaabaabbaabb)2
6B1 296 18A (baababbaabaabb)3
6C216 12C (aababbaabaabbaabbabbaabaabb)2
6D108 aababbabbaabaabb
6E72 abbabbaabaabb
7A42 14A 21A (ab)2
8A192 24A (abb)3
8B192 24B (aabbabbaabaabb)3
8C32 baababbaabaabbaababbabbaabaabb
9A162 18A (baababbaabaabb)2
9B81 babbaababbaabaabbaabb
10A60 20A 20B 30A (babbaababbaabaabb)2
10B20 ababbaababbaabaabb
11A22 11B2 22A 22B (abbaababbaabaabb)4
11B22 11A2 22A 22B (abbaababbaabaabb)2
12A144 baababbaabaabbbabbaababbaabaabbaabb
12B48 24A 24B (abb)2
12C36 aababbaabaabbaabbabbaabaabb
14A14 ab
15A30 30A (aabaabbaababbaabaabb)2
15B15 aabaabb
18A18 baababbaabaabb
20A20 20B11 babbaababbaabaabb
20B20 20A11 (babbaababbaabaabb)11
21A21 abbaabaabb
22A22 22B7 abbaababbaabaabb
22B22 22A7 (abbaababbaabaabb)7
23A23 23B5 aababbaabaabb
23B23 23A5 (aababbaabaabb)5
24A24 abb
24B24 aabbabbaabaabb
30A30 aabaabbaababbaabaabb