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)
1A211 341 312 abbabbbabbbabbabbbabbbabbabbbabbbabbabbbabbb
2A258 048 ababbbababbbababbbababbb
2B3 072 abbabbbabbbabbabbbabbb
3A1 512 abbabbabbbabbbabbabbabbbabbb
3B648 abbbbabbbbabbbbabbbb
4A3 584 ababbbababbb
4B1 536 abbabb
4C64 abbabbbabbb
6A72 abbbbabbbb
6B24 abbabbabbbabbb
7A1 176 ababbbbababbbbababbbbababbbbababbbbababbbbababbbbababbbb
7B1 176 Omitted owing to length.
7C1 176 ababbbbababbbbababbbbababbbb
7D49 abababbb
8A32 ababbb
8B32 abb
9A54 abbbabbb
9B54 abbbabbbabbbabbb
9C54 abbbabbbabbbabbbabbbabbbabbbabbb
12A12 abbbb
13A13 ab
13B13 abab
13C13 abababab
14A56 (ababbbbababbbb)3
14B56 ababbbbababbbb
14C56 (ababbbbababbbb)9
18A18 (abbb)7
18B18 (abbb)49
18C18 abbb
21A21 abbabbbabbabbb
21B21 abbabbbabbabbbabbabbbabbabbb
21C21 abbabbb
28A28 ababbbb
28B28 (ababbbb)9
28C28 (ababbbb)3

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Conjugacy classes of 3D4(2).3

Conjugacy class Centraliser order Power up Class rep(s)
1A634 023 936 (cdcdcddcdcdcddcdcdcdcddcdcdcddcd)3
2A774 144 (cdcdcddcddcdcdcddcdcdcddcdcdcdcddcddcdcdcddcdcdcddcd)3
2B9 216 (cdcdcddcdcdcddcd)3
3A4 536 cdcdcddcdcdcddcdcdcdcddcdcdcddcd
3B1 944 Omitted owing to length.
4A10 752 (cdcdcddcdcddcdcdcddcdcdd)3
4B4 608 (cdcdcddcddcdcdcddcdcdcddcd)3
4C192 (cdcdcdd)3
6A216 cdcdcddcddcdcdcddcdcdcddcdcdcdcddcddcdcdcddcdcdcddcd
6B72 cdcdcddcdcdcddcd
7A1 176 Omitted owing to length.
7D147 (cd)3
8A96 (cdcdcddcdcdd)3
8B96 (cdcdcdcdcddcd)3
9A54 cddcdcdcdcdcddcdcddcdcdcdcdcddcd
12A36 cdcdcddcddcdcdcddcdcdcddcd
13A13 cdcdcddcdcdcdcddcdcdd
14A56 ccdcdcddcddcdcdcddcdcdcddcdccdcdcddcddcdcdcddcdcdcddcd
18A18 cddcdcdcdcdcddcd
21A21 cdcdcdcddcd
28A28 ccdcdcddcddcdcdcddcdcdcddcd
3C36 288 Omitted owing to length.
3C'36 288 dcdcdcddcdcdcddcddcdcdcddcdcdcddcd
3D648 cdcdcddcdcdcddcdcdcddcdcdcdd
3D'648 cdcdcddcdcdcddcdcdcddcdcdcddcdcdcddcdcdcddcdcdcddcdcdcdd
6C576 dcdcdcddcdcdcddcdcdcdcdcdcddcddcdcdcddcdcdcddcdcdcdcdcdcddcd
6C'576 Omitted owing to length.
6D144 dcdcdcddcdcdcddcd
6D'144 (dcdcdcddcdcdcddcd)5
6E72 (cdcdcddcdcdcdd)5
6E'72 cdcdcddcdcdcdd
9D54 cdcdcddcdcdcdcddcd
9D'54 cdcdcddcdcdcdcddcdcdcdcddcdcdcdcddcd
12B288 (cdcdcdcdcddcdcdcdcdcdcddcd)5
12B'288 cdcdcdcdcddcdcdcdcdcdcddcd
12C144 (dcdcdcddcdcdcddcdcdcdcdcdcddcd)5
12C'144 dcdcdcddcdcdcddcdcdcdcdcdcddcd
12D96 (cdcdcddcdcddcdcdcddcdcdd)5
12D'96 cdcdcddcdcddcdcdcddcdcdd
12E12 cdcdcdd
12E'12 (cdcdcdd)5
18D18 (cdcdcddcd)5
18D'18 cdcdcddcd
21D21 cd
21D'21 cdcd
24A24 cdcdcdcdcddcd
24A'24 (cdcdcdcdcddcd)5
24B24 cdcdcddcdcdd
24B'24 (cdcdcddcdcdd)5

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