direct product, non-abelian, not soluble, A-group
Aliases: C8xA5, C2.1(C4xA5), C4.4(C2xA5), (C2xA5).2C4, (C4xA5).4C2, SmallGroup(480,220)
Series: Chief►Derived ►Lower central ►Upper central
| A5 — C8xA5 |
| A5 — C8xA5 |
Quotients: C1, C2, C4, C8, A5, C2xA5, C4xA5, C8xA5
15C2
15C2
10C3
6C5
5C22
15C22
15C4
15C22
10C6
10S3
10S3
6D5
6D5
6C10
5C23
15C2xC4
15C2xC4
15C8
5A4
10C12
10D6
10Dic3
6Dic5
6C20
6D10
15C2xC8
15C2xC8
10C24
10C4xS3
10C3:C8
6C40
10S3xC8
Smallest permutation representation of C8xA5
►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 | C2xA5 | C4xA5 | C8xA5 | A5 | C2xA5 | C4xA5 | C8xA5 | A5 | C2xA5 | C4xA5 | C8xA5 |
| kernel | C8xA5 | C4xA5 | C2xA5 | 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 C8xA5 ►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] >;
C8xA5 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