direct product, abelian, monomial, 2-elementary
Aliases: C2×C24, SmallGroup(48,23)
Series: Derived ►Chief ►Lower central ►Upper central
C1 — C2×C24 |
C1 — C2×C24 |
C1 — C2×C24 |
Generators and relations for C2×C24
G = < a,b | a2=b24=1, ab=ba >
(1 35)(2 36)(3 37)(4 38)(5 39)(6 40)(7 41)(8 42)(9 43)(10 44)(11 45)(12 46)(13 47)(14 48)(15 25)(16 26)(17 27)(18 28)(19 29)(20 30)(21 31)(22 32)(23 33)(24 34)
(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 41 42 43 44 45 46 47 48)
G:=sub<Sym(48)| (1,35)(2,36)(3,37)(4,38)(5,39)(6,40)(7,41)(8,42)(9,43)(10,44)(11,45)(12,46)(13,47)(14,48)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(21,31)(22,32)(23,33)(24,34), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)>;
G:=Group( (1,35)(2,36)(3,37)(4,38)(5,39)(6,40)(7,41)(8,42)(9,43)(10,44)(11,45)(12,46)(13,47)(14,48)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(21,31)(22,32)(23,33)(24,34), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48) );
G=PermutationGroup([[(1,35),(2,36),(3,37),(4,38),(5,39),(6,40),(7,41),(8,42),(9,43),(10,44),(11,45),(12,46),(13,47),(14,48),(15,25),(16,26),(17,27),(18,28),(19,29),(20,30),(21,31),(22,32),(23,33),(24,34)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24),(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)]])
C2×C24 is a maximal subgroup of
C12.C8 Dic3⋊C8 C24⋊C4 C2.Dic12 C8⋊Dic3 C24⋊1C4 C24.C4 D6⋊C8 C2.D24 C8○D12 C4○D24 He3⋊2(C2×C8)
48 conjugacy classes
class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | 4B | 4C | 4D | 6A | ··· | 6F | 8A | ··· | 8H | 12A | ··· | 12H | 24A | ··· | 24P |
order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 8 | ··· | 8 | 12 | ··· | 12 | 24 | ··· | 24 |
size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
48 irreducible representations
dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
type | + | + | + | |||||||||
image | C1 | C2 | C2 | C3 | C4 | C4 | C6 | C6 | C8 | C12 | C12 | C24 |
kernel | C2×C24 | C24 | C2×C12 | C2×C8 | C12 | C2×C6 | C8 | C2×C4 | C6 | C4 | C22 | C2 |
# reps | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 2 | 8 | 4 | 4 | 16 |
Matrix representation of C2×C24 ►in GL2(𝔽73) generated by
72 | 0 |
0 | 1 |
51 | 0 |
0 | 17 |
G:=sub<GL(2,GF(73))| [72,0,0,1],[51,0,0,17] >;
C2×C24 in GAP, Magma, Sage, TeX
C_2\times C_{24}
% in TeX
G:=Group("C2xC24");
// GroupNames label
G:=SmallGroup(48,23);
// by ID
G=gap.SmallGroup(48,23);
# by ID
G:=PCGroup([5,-2,-2,-3,-2,-2,60,58]);
// Polycyclic
G:=Group<a,b|a^2=b^24=1,a*b=b*a>;
// generators/relations
Export