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G = C2×C24order 48 = 24·3

Abelian group of type [2,24]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C24, SmallGroup(48,23)

Series: Derived Chief Lower central Upper central

C1 — C2×C24
C1C2C4C12C24 — C2×C24
C1 — C2×C24
C1 — C2×C24

Generators and relations for C2×C24
 G = < a,b | a2=b24=1, ab=ba >


Smallest permutation representation of C2×C24
Regular action on 48 points
Generators in S48
(1 32)(2 33)(3 34)(4 35)(5 36)(6 37)(7 38)(8 39)(9 40)(10 41)(11 42)(12 43)(13 44)(14 45)(15 46)(16 47)(17 48)(18 25)(19 26)(20 27)(21 28)(22 29)(23 30)(24 31)
(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)| (1,32)(2,33)(3,34)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,25)(19,26)(20,27)(21,28)(22,29)(23,30)(24,31), (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( (1,32)(2,33)(3,34)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,25)(19,26)(20,27)(21,28)(22,29)(23,30)(24,31), (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([(1,32),(2,33),(3,34),(4,35),(5,36),(6,37),(7,38),(8,39),(9,40),(10,41),(11,42),(12,43),(13,44),(14,45),(15,46),(16,47),(17,48),(18,25),(19,26),(20,27),(21,28),(22,29),(23,30),(24,31)], [(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)])

48 conjugacy classes

class 1 2A2B2C3A3B4A4B4C4D6A···6F8A···8H12A···12H24A···24P
order12223344446···68···812···1224···24
size11111111111···11···11···11···1

48 irreducible representations

dim111111111111
type+++
imageC1C2C2C3C4C4C6C6C8C12C12C24
kernelC2×C24C24C2×C12C2×C8C12C2×C6C8C2×C4C6C4C22C2
# reps1212224284416

Matrix representation of C2×C24 in GL2(𝔽73) generated by

720
01
,
510
017
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

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