Order = 211341312 = 212.34.72.13.
Mult = 1.
Out = 3.

Porting notes

Porting incomplete.

Standard generators

Standard generators of 3D4(2) are a, b where a is in class 2A, b has order 9, ab has order 13 and abb has order 8. Alternatively: a is in class 2A, b has order 9 and ab has order 13.

Standard generators of 3D4(2).3 are c, d where c has order 2 (necessarily in class 2B), d is in class 3D, cd has order 21, cdcdd has order 7 and cdcdcdcddcdcddcddcdd has order 6.

Representations

Representations of 3D4(2)

Representations of 3D4(2).3

Maximal subgroups

Maximal subgroups of 3D4(2)

Subgroup Order Index Programs/reps
21+8:L2(8) Program: Generators
[211]:(7 × S3) Program: Generators
U3(3):2 Program: Generators
S3 × L2(8) Program: Generators
(7 × L2(7)):2 Program: Generators
31+2.2S4 Program: Generators
72:2A4 Program: Generators
32:2A4 Program: Generators
13:4 Program: Generators

Maximal subgroups of 3D4(2).3

Subgroup Order Index Programs/reps
3D4(2)
21+8:L2(8):3
[211]:(7:3 × S3)
3 × U3(3):2 Program: Generators
S3 × L2(8):3
(7:3 × L2(7)):2
31+2.2S4.3
72:(2A4 × 3)
32:2A4 × 3
13:12

Conjugacy classes

Conjugacy classes of 3D4(2)

Conjugacy class Centraliser order Power up Class rep(s)
1A 211 341 312 abbabbbabbbabbabbbabbbabbabbbabbbabbabbbabbb
2A 258 048 ababbbababbbababbbababbb
2B 3 072 abbabbbabbbabbabbbabbb
3A 1 512 abbabbabbbabbbabbabbabbbabbb
3B 648 abbbbabbbbabbbbabbbb
4A 3 584 ababbbababbb
4B 1 536 abbabb
4C 64 abbabbbabbb
6A 72 abbbbabbbb
6B 24 abbabbabbbabbb
7A 1 176 ababbbbababbbbababbbbababbbbababbbbababbbbababbbbababbbb
7B 1 176 Omitted owing to length.
7C 1 176 ababbbbababbbbababbbbababbbb
7D 49 abababbb
8A 32 ababbb
8B 32 abb
9A 54 abbbabbb
9B 54 abbbabbbabbbabbb
9C 54 abbbabbbabbbabbbabbbabbbabbbabbb
12A 12 abbbb
13A 13 ab
13B 13 abab
13C 13 abababab
14A 56 (ababbbbababbbb)3
14B 56 ababbbbababbbb
14C 56 (ababbbbababbbb)9
18A 18 (abbb)7
18B 18 (abbb)49
18C 18 abbb
21A 21 abbabbbabbabbb
21B 21 abbabbbabbabbbabbabbbabbabbb
21C 21 abbabbb
28A 28 ababbbb
28B 28 (ababbbb)9
28C 28 (ababbbb)3

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Conjugacy classes of 3D4(2).3

Conjugacy class Centraliser order Power up Class rep(s)
1A 634 023 936 (cdcdcddcdcdcddcdcdcdcddcdcdcddcd)3
2A 774 144 (cdcdcddcddcdcdcddcdcdcddcdcdcdcddcddcdcdcddcdcdcddcd)3
2B 9 216 (cdcdcddcdcdcddcd)3
3A 4 536 cdcdcddcdcdcddcdcdcdcddcdcdcddcd
3B 1 944 Omitted owing to length.
4A 10 752 (cdcdcddcdcddcdcdcddcdcdd)3
4B 4 608 (cdcdcddcddcdcdcddcdcdcddcd)3
4C 192 (cdcdcdd)3
6A 216 cdcdcddcddcdcdcddcdcdcddcdcdcdcddcddcdcdcddcdcdcddcd
6B 72 cdcdcddcdcdcddcd
7A 1 176 Omitted owing to length.
7D 147 (cd)3
8A 96 (cdcdcddcdcdd)3
8B 96 (cdcdcdcdcddcd)3
9A 54 cddcdcdcdcdcddcdcddcdcdcdcdcddcd
12A 36 cdcdcddcddcdcdcddcdcdcddcd
13A 13 cdcdcddcdcdcdcddcdcdd
14A 56 ccdcdcddcddcdcdcddcdcdcddcdccdcdcddcddcdcdcddcdcdcddcd
18A 18 cddcdcdcdcdcddcd
21A 21 cdcdcdcddcd
28A 28 ccdcdcddcddcdcdcddcdcdcddcd
3C 36 288 Omitted owing to length.
3C' 36 288 dcdcdcddcdcdcddcddcdcdcddcdcdcddcd
3D 648 cdcdcddcdcdcddcdcdcddcdcdcdd
3D' 648 cdcdcddcdcdcddcdcdcddcdcdcddcdcdcddcdcdcddcdcdcddcdcdcdd
6C 576 dcdcdcddcdcdcddcdcdcdcdcdcddcddcdcdcddcdcdcddcdcdcdcdcdcddcd
6C' 576 Omitted owing to length.
6D 144 dcdcdcddcdcdcddcd
6D' 144 (dcdcdcddcdcdcddcd)5
6E 72 (cdcdcddcdcdcdd)5
6E' 72 cdcdcddcdcdcdd
9D 54 cdcdcddcdcdcdcddcd
9D' 54 cdcdcddcdcdcdcddcdcdcdcddcdcdcdcddcd
12B 288 (cdcdcdcdcddcdcdcdcdcdcddcd)5
12B' 288 cdcdcdcdcddcdcdcdcdcdcddcd
12C 144 (dcdcdcddcdcdcddcdcdcdcdcdcddcd)5
12C' 144 dcdcdcddcdcdcddcdcdcdcdcdcddcd
12D 96 (cdcdcddcdcddcdcdcddcdcdd)5
12D' 96 cdcdcddcdcddcdcdcddcdcdd
12E 12 cdcdcdd
12E' 12 (cdcdcdd)5
18D 18 (cdcdcddcd)5
18D' 18 cdcdcddcd
21D 21 cd
21D' 21 cdcd
24A 24 cdcdcdcdcddcd
24A' 24 (cdcdcdcdcddcd)5
24B 24 cdcdcddcdcdd
24B' 24 (cdcdcddcdcdd)5

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