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G = C58order 58 = 2·29

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C58, also denoted Z58, SmallGroup(58,2)

Series: Derived Chief Lower central Upper central

C1 — C58
C1C29 — C58
C1 — C58
C1 — C58

Generators and relations for C58
 G = < a | a58=1 >


Smallest permutation representation of C58
Regular action on 58 points
Generators in S58
(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 49 50 51 52 53 54 55 56 57 58)

G:=sub<Sym(58)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)])

58 conjugacy classes

class 1  2 29A···29AB58A···58AB
order1229···2958···58
size111···11···1

58 irreducible representations

dim1111
type++
imageC1C2C29C58
kernelC58C29C2C1
# reps112828

Matrix representation of C58 in GL1(𝔽59) generated by

11
G:=sub<GL(1,GF(59))| [11] >;

C58 in GAP, Magma, Sage, TeX

C_{58}
% in TeX

G:=Group("C58");
// GroupNames label

G:=SmallGroup(58,2);
// by ID

G=gap.SmallGroup(58,2);
# by ID

G:=PCGroup([2,-2,-29]);
// Polycyclic

G:=Group<a|a^58=1>;
// generators/relations

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