direct product, non-abelian, not soluble, A-group
Aliases: C8×A5, C2.1(C4×A5), C4.4(C2×A5), (C2×A5).2C4, (C4×A5).4C2, SmallGroup(480,220)
Series: Chief►Derived ►Lower central ►Upper central
| A5 — C8×A5 |
| A5 — C8×A5 |
15C2
15C2
10C3
6C5
5C22
15C22
15C4
15C22
10C6
10S3
10S3
6D5
6D5
6C10
5C23
15C2×C4
15C2×C4
15C8
5A4
10C12
10D6
10Dic3
6Dic5
6C20
6D10
15C2×C8
15C2×C8
10C24
10C4×S3
10C3⋊C8
6C40
10S3×C8
Smallest permutation representation of C8×A5
►On 40 points
Generators in S40
(1 33 6 38 11 23 16 28)(2 26 7 31 12 36 17 21)(3 35 8 40 13 25 18 30)(4 32 9 37 14 22 19 27)(5 29 10 34 15 39 20 24)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)(21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40)
G:=sub<Sym(40)| (1,33,6,38,11,23,16,28)(2,26,7,31,12,36,17,21)(3,35,8,40,13,25,18,30)(4,32,9,37,14,22,19,27)(5,29,10,34,15,39,20,24), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)>;
G:=Group( (1,33,6,38,11,23,16,28)(2,26,7,31,12,36,17,21)(3,35,8,40,13,25,18,30)(4,32,9,37,14,22,19,27)(5,29,10,34,15,39,20,24), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40) );
G=PermutationGroup([[(1,33,6,38,11,23,16,28),(2,26,7,31,12,36,17,21),(3,35,8,40,13,25,18,30),(4,32,9,37,14,22,19,27),(5,29,10,34,15,39,20,24)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)]])
40 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 5A | 5B | 6 | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 10A | 10B | 12A | 12B | 20A | 20B | 20C | 20D | 24A | 24B | 24C | 24D | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 12 | 12 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 40 | ··· | 40 |
| size | 1 | 1 | 15 | 15 | 20 | 1 | 1 | 15 | 15 | 12 | 12 | 20 | 1 | 1 | 1 | 1 | 15 | 15 | 15 | 15 | 12 | 12 | 20 | 20 | 12 | 12 | 12 | 12 | 20 | 20 | 20 | 20 | 12 | ··· | 12 |
40 irreducible representations
| dim | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 |
| type | + | + | + | + | + | + | + | + | ||||||||
| image | C1 | C2 | C4 | C8 | A5 | C2×A5 | C4×A5 | C8×A5 | A5 | C2×A5 | C4×A5 | C8×A5 | A5 | C2×A5 | C4×A5 | C8×A5 |
| kernel | C8×A5 | C4×A5 | C2×A5 | A5 | C8 | C4 | C2 | C1 | C8 | C4 | C2 | C1 | C8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 2 | 2 | 4 | 8 | 1 | 1 | 2 | 4 | 1 | 1 | 2 | 4 |
Matrix representation of C8×A5 ►in GL4(𝔽241) generated by
| 211 | 0 | 0 | 0 |
| 0 | 64 | 0 | 0 |
| 0 | 188 | 34 | 10 |
| 0 | 182 | 53 | 207 |
| 177 | 0 | 0 | 0 |
| 0 | 182 | 210 | 97 |
| 0 | 233 | 0 | 0 |
| 0 | 97 | 231 | 7 |
G:=sub<GL(4,GF(241))| [211,0,0,0,0,64,188,182,0,0,34,53,0,0,10,207],[177,0,0,0,0,182,233,97,0,210,0,231,0,97,0,7] >;
C8×A5 in GAP, Magma, Sage, TeX
C_8\times A_5
% in TeX
G:=Group("C8xA5"); // GroupNames label
G:=SmallGroup(480,220);
// by ID
G=gap.SmallGroup(480,220);
# by ID
Export