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G = C2xC4xA5order 480 = 25·3·5

Direct product of C2xC4 and A5

direct product, non-abelian, not soluble, A-group

Aliases: C2xC4xA5, C2.1(C22xA5), C22.3(C2xA5), (C2xA5).6C22, (C22xA5).2C2, SmallGroup(480,954)

Series: ChiefDerived Lower central Upper central

C1C2C22C2xC4 — C2xC4xA5
A5 — C2xC4xA5
A5 — C2xC4xA5
C1C2xC4

Subgroups: 1038 in 120 conjugacy classes, 16 normal (8 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, C5, S3, C6, C2xC4, C2xC4, C23, D5, C10, Dic3, C12, A4, D6, C2xC6, C22xC4, C24, Dic5, C20, D10, C2xC10, C4xS3, C2xDic3, C2xC12, C2xA4, C22xS3, C23xC4, C4xD5, C2xDic5, C2xC20, C22xD5, C4xA4, S3xC2xC4, C22xA4, A5, C2xC4xD5, C2xC4xA4, C2xA5, C2xA5, C4xA5, C22xA5, C2xC4xA5
Quotients: C1, C2, C4, C22, C2xC4, A5, C2xA5, C4xA5, C22xA5, C2xC4xA5

Smallest permutation representation of C2xC4xA5
On 40 points
Generators in S40
(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)
(1 33 15 27 17 25 19 39 13 21 11 23 5 37 7 35 9 29 3 31)(2 30 4 24 18 26 16 28 10 22 12 40 14 34 8 36 6 38 20 32)

G:=sub<Sym(40)| (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), (1,33,15,27,17,25,19,39,13,21,11,23,5,37,7,35,9,29,3,31)(2,30,4,24,18,26,16,28,10,22,12,40,14,34,8,36,6,38,20,32)>;

G:=Group( (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), (1,33,15,27,17,25,19,39,13,21,11,23,5,37,7,35,9,29,3,31)(2,30,4,24,18,26,16,28,10,22,12,40,14,34,8,36,6,38,20,32) );

G=PermutationGroup([[(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)], [(1,33,15,27,17,25,19,39,13,21,11,23,5,37,7,35,9,29,3,31),(2,30,4,24,18,26,16,28,10,22,12,40,14,34,8,36,6,38,20,32)]])

40 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A4B4C4D4E4F4G4H5A5B6A6B6C10A···10F12A12B12C12D20A···20H
order122222223444444445566610···101212121220···20
size11111515151520111115151515121220202012···122020202012···12

40 irreducible representations

dim1111333344445555
type++++++++++++
imageC1C2C2C4A5C2xA5C2xA5C4xA5A5C2xA5C2xA5C4xA5A5C2xA5C2xA5C4xA5
kernelC2xC4xA5C4xA5C22xA5C2xA5C2xC4C4C22C2C2xC4C4C22C2C2xC4C4C22C2
# reps1214242812141214

Matrix representation of C2xC4xA5 in GL5(F61)

600000
011000
0013922
0022309
000600
,
10000
011000
0039139
006000
0030939

G:=sub<GL(5,GF(61))| [60,0,0,0,0,0,11,0,0,0,0,0,13,22,0,0,0,9,30,60,0,0,22,9,0],[1,0,0,0,0,0,11,0,0,0,0,0,39,60,30,0,0,13,0,9,0,0,9,0,39] >;

C2xC4xA5 in GAP, Magma, Sage, TeX

C_2\times C_4\times A_5
% in TeX

G:=Group("C2xC4xA5");
// GroupNames label

G:=SmallGroup(480,954);
// by ID

G=gap.SmallGroup(480,954);
# by ID

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