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G = C34order 34 = 2·17

Cyclic group

direct product, cyclic, abelian, monomial

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

Series: Derived Chief Lower central Upper central

C1 — C34
C1C17 — C34
C1 — C34
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)])

34 conjugacy classes

class 1  2 17A···17P34A···34P
order1217···1734···34
size111···11···1

34 irreducible representations

dim1111
type++
imageC1C2C17C34
kernelC34C17C2C1
# reps111616

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

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