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G = C48order 48 = 24·3

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C48, also denoted Z48, SmallGroup(48,2)

Series: Derived Chief Lower central Upper central

C1 — C48
C1C2C4C8C24 — C48
C1 — C48
C1 — C48

Generators and relations for C48
 G = < a | a48=1 >


Smallest permutation representation of C48
Regular action on 48 points
Generators in S48
(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)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)])

48 conjugacy classes

class 1  2 3A3B4A4B6A6B8A8B8C8D12A12B12C12D16A···16H24A···24H48A···48P
order1233446688881212121216···1624···2448···48
size11111111111111111···11···11···1

48 irreducible representations

dim1111111111
type++
imageC1C2C3C4C6C8C12C16C24C48
kernelC48C24C16C12C8C6C4C3C2C1
# reps11222448816

Matrix representation of C48 in GL2(𝔽7) generated by

02
25
G:=sub<GL(2,GF(7))| [0,2,2,5] >;

C48 in GAP, Magma, Sage, TeX

C_{48}
% in TeX

G:=Group("C48");
// GroupNames label

G:=SmallGroup(48,2);
// by ID

G=gap.SmallGroup(48,2);
# by ID

G:=PCGroup([5,-2,-3,-2,-2,-2,30,42,58]);
// Polycyclic

G:=Group<a|a^48=1>;
// generators/relations

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