Copied to
clipboard

G = C46order 46 = 2·23

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C46, also denoted Z46, SmallGroup(46,2)

Series: Derived Chief Lower central Upper central

C1 — C46
C1C23 — C46
C1 — C46
C1 — C46

Generators and relations for C46
 G = < a | a46=1 >


Smallest permutation representation of C46
Regular action on 46 points
Generators in S46
(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)

G:=sub<Sym(46)| (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)>;

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) );

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)])

46 conjugacy classes

class 1  2 23A···23V46A···46V
order1223···2346···46
size111···11···1

46 irreducible representations

dim1111
type++
imageC1C2C23C46
kernelC46C23C2C1
# reps112222

Matrix representation of C46 in GL1(𝔽47) generated by

19
G:=sub<GL(1,GF(47))| [19] >;

C46 in GAP, Magma, Sage, TeX

C_{46}
% in TeX

G:=Group("C46");
// GroupNames label

G:=SmallGroup(46,2);
// by ID

G=gap.SmallGroup(46,2);
# by ID

G:=PCGroup([2,-2,-23]);
// Polycyclic

G:=Group<a|a^46=1>;
// generators/relations

׿
×
𝔽