Copied to
clipboard

## G = C58order 58 = 2·29

### Cyclic group

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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C58
 Chief series C1 — C29 — C58
 Lower central C1 — C58
 Upper central 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)]])`

C58 is a maximal subgroup of   Dic29

58 conjugacy classes

 class 1 2 29A ··· 29AB 58A ··· 58AB order 1 2 29 ··· 29 58 ··· 58 size 1 1 1 ··· 1 1 ··· 1

58 irreducible representations

 dim 1 1 1 1 type + + image C1 C2 C29 C58 kernel C58 C29 C2 C1 # reps 1 1 28 28

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`

Export

׿
×
𝔽