Copied to
clipboard

## G = C97order 97

### Cyclic group

Aliases: C97, also denoted Z97, SmallGroup(97,1)

Series: Derived Chief Lower central Upper central Jennings

 Derived series C1 — C97
 Chief series C1 — C97
 Lower central C1 — C97
 Upper central C1 — C97
 Jennings C1 — C97

Generators and relations for C97
G = < a | a97=1 >

Smallest permutation representation of C97
Regular action on 97 points
Generators in S97
`(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 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97)`

`G:=sub<Sym(97)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97)>;`

`G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97) );`

`G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97)]])`

C97 is a maximal subgroup of   D97  C97⋊C3

97 conjugacy classes

 class 1 97A ··· 97CR order 1 97 ··· 97 size 1 1 ··· 1

97 irreducible representations

 dim 1 1 type + image C1 C97 kernel C97 C1 # reps 1 96

Matrix representation of C97 in GL1(𝔽389) generated by

 119
`G:=sub<GL(1,GF(389))| [119] >;`

C97 in GAP, Magma, Sage, TeX

`C_{97}`
`% in TeX`

`G:=Group("C97");`
`// GroupNames label`

`G:=SmallGroup(97,1);`
`// by ID`

`G=gap.SmallGroup(97,1);`
`# by ID`

`G:=PCGroup([1,-97]:ExponentLimit:=1);`
`// Polycyclic`

`G:=Group<a|a^97=1>;`
`// generators/relations`

Export

׿
×
𝔽