GAP Package AtlasRep

AtlasRep Info for U₃(3)

→ ATLAS page for U₃(3)

→ Overview of Groups

Representations for G = U₃(3): (all refer to std. generators 1)

1	G ≤ Sym(28)	2-trans., on cosets of 31+2+:8 (1st max.)
2	G ≤ Sym(36)	rank 4, on cosets of L2(7) (2nd max.)
3	G ≤ Sym(63a)	rank 4, on cosets of 4.S4 (3rd max.)
4	G ≤ Sym(63b)	rank 5, on cosets of 42:S3 (4th max.)
5	G ≤ GL(6,2)
6	G ≤ GL(14,2)
7	G ≤ GL(32a,2)
8	G ≤ GL(32b,2)
9	G ≤ GL(7,3)
10	G ≤ GL(27,3)
11	G ≤ GL(6,7)
12	G ≤ GL(7a,7)
13	G ≤ GL(14,7)
14	G ≤ GL(21a,7)
15	G ≤ GL(26,7)
16	G ≤ GL(3b,9)
17	G ≤ GL(6b,9)
18	G ≤ GL(15b,9)
19	G ≤ GL(7b,49)
20	G ≤ GL(21b,49)
21	G ≤ GL(28a,49)
22	G ≤ GL(7a,ℤ)
23	G ≤ GL(14a,ℤ)
24	G ≤ GL(14b,ℤ)
25	G ≤ GL(21a,ℤ)
26	G ≤ GL(27,ℤ)
27	G ≤ GL(42,ℤ)
28	G ≤ GL(56,ℤ)
29	G ≤ GL(64,ℤ)
30	G ≤ GL(6,Field([Sqrt(-1)]))
31	G ≤ GL(7b,Field([Sqrt(-1)]))
32	G ≤ GL(7c,Field([Sqrt(-1)]))
33	G ≤ GL(21b,Field([Sqrt(-1)]))
34	G ≤ GL(21c,Field([Sqrt(-1)]))
35	G ≤ GL(28a,Field([Sqrt(-1)]))
36	G ≤ GL(28b,Field([Sqrt(-1)]))

Programs for G = U₃(3): (all refer to std. generators 1)

• maxes (3 out of 4):

  1	31+2:8
  2	L3(2)
  4	42:S3

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