Copied to
clipboard

## G = C34order 34 = 2·17

### Cyclic group

Aliases: C34, also denoted Z34, SmallGroup(34,2)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C34
 Chief series C1 — C17 — C34
 Lower central C1 — C34
 Upper central C1 — C34

Generators and relations for C34
G = < a | a34=1 >

Smallest permutation representation of C34
Regular action on 34 points
Generators in S34
`(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)`

`G:=sub<Sym(34)| (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)>;`

`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) );`

`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)]])`

C34 is a maximal subgroup of   Dic17

34 conjugacy classes

 class 1 2 17A ··· 17P 34A ··· 34P order 1 2 17 ··· 17 34 ··· 34 size 1 1 1 ··· 1 1 ··· 1

34 irreducible representations

 dim 1 1 1 1 type + + image C1 C2 C17 C34 kernel C34 C17 C2 C1 # reps 1 1 16 16

Matrix representation of C34 in GL1(𝔽103) generated by

 90
`G:=sub<GL(1,GF(103))| [90] >;`

C34 in GAP, Magma, Sage, TeX

`C_{34}`
`% in TeX`

`G:=Group("C34");`
`// GroupNames label`

`G:=SmallGroup(34,2);`
`// by ID`

`G=gap.SmallGroup(34,2);`
`# by ID`

`G:=PCGroup([2,-2,-17]);`
`// Polycyclic`

`G:=Group<a|a^34=1>;`
`// generators/relations`

Export

׿
×
𝔽