GAP Package AtlasRep

AtlasRep Info for HN

→ ATLAS page for HN

→ Overview of Groups

Representations for G = HN: (all refer to std. generators 1)

1	G ≤ Sym(1140000)	rank 12, on cosets of A12 (1st max.)
5	G ≤ GL(760,2)	character 760a
6	G ≤ GL(760,3)	character 760a
7	G ≤ GL(132a,4)	character 132a
8	G ≤ GL(132b,4)	character 132b
9	G ≤ GL(133,4)	character 1a+132a
10	G ≤ GL(2650a,4)	character 2650b
11	G ≤ GL(133,5)	character 133a
12	G ≤ GL(626,5)	character 626a
13	G ≤ GL(627,5)	character 1a+626a
14	G ≤ GL(760,7)	character 760a
15	G ≤ GL(133a,9)	character 133a
16	G ≤ GL(133b,9)	character 133b
17	G ≤ GL(133a,11)	character 133a
18	G ≤ GL(133b,11)	character 133b
19	G ≤ GL(760,11)	character 760a
20	G ≤ GL(133a,19)	character 133a
21	G ≤ GL(133b,19)	character 133b
22	G ≤ GL(760,19)	character 760a
23	G ≤ GL(133a,49)	character 133a
24	G ≤ GL(133b,49)	character 133b

Programs for G = HN: (all refer to std. generators 1)

• class repres.:
• repr. cyc. subg.:
• std. gen. checker:
• std. gen. finder:
• automorphisms:

  2

• maxes (11 out of 14):

  1	A12
  1	A12
  2	2.HS.2
  3	U3(8).31
  3	U3(8).31
  4	21+8.(A5 × A5).2
  5	(D10 × U3(5)).2
  6	51+4:21+4.5.4
  7	26.U4(2)
  10	52.5.52.4A5
  11	M12.2
  12	M12.2
  14	31+4:4A5

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