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G = C35order 35 = 5·7

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C35, also denoted Z35, SmallGroup(35,1)

Series: Derived Chief Lower central Upper central

C1 — C35
C1C7 — C35
C1 — C35
C1 — C35

Generators and relations for C35
 G = < a | a35=1 >


Smallest permutation representation of C35
Regular action on 35 points
Generators in S35
(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)

G:=sub<Sym(35)| (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)>;

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) );

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)])

35 conjugacy classes

class 1 5A5B5C5D7A···7F35A···35X
order155557···735···35
size111111···11···1

35 irreducible representations

dim1111
type+
imageC1C5C7C35
kernelC35C7C5C1
# reps14624

Matrix representation of C35 in GL1(𝔽71) generated by

58
G:=sub<GL(1,GF(71))| [58] >;

C35 in GAP, Magma, Sage, TeX

C_{35}
% in TeX

G:=Group("C35");
// GroupNames label

G:=SmallGroup(35,1);
// by ID

G=gap.SmallGroup(35,1);
# by ID

G:=PCGroup([2,-5,-7]);
// Polycyclic

G:=Group<a|a^35=1>;
// generators/relations

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