GAP Package AtlasRep

AtlasRep Info for ³D₄(2)

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Representations for G = ³D₄(2): (all refer to std. generators 1)

1	G ≤ Sym(819)	rank 4, on cosets of 21+8+:L2(8) (1st max.)
2	G ≤ GL(26,2)	character 26a
3	G ≤ GL(25,3)	character 25a
4	G ≤ GL(52,3)	character 52a
5	G ≤ GL(196,3)	character 196a
6	G ≤ GL(324,3)	character 324a
7	G ≤ GL(441,3)	character 441a
8	G ≤ GL(1053,3)	character 1053a
9	G ≤ GL(26,7)	character 26a
10	G ≤ GL(298,7)	character 298a
11	G ≤ GL(8a,8)	character 8a
12	G ≤ GL(26,13)	character 26a
13	G ≤ GL(351a,27)	character 351a
14	G ≤ GL(351b,27)	character 351b
15	G ≤ GL(351c,27)	character 351c
16	G ≤ GL(26,ℤ)	character 26a
17	G ≤ GL(52,ℤ)	character 52a
18	G ≤ GL(196,ℤ)	character 196a

Programs for G = ³D₄(2): (all refer to std. generators 1)

• class repres.:
• repr. cyc. subg.:
• automorphisms:

  3

• maxes (all 9):

  1	21+8+:L2(8)
  2	22.[29]:(7 × S3)
  3	U3(3).2
  4	S3 × L2(8)
  5	(7 × L2(7)):2
  6	3(1+2)+.2S4
  7	72:2A4
  8	32:2A4
  9	13:4

File created automatically by GAP on 22-Apr-2022.