Copied to
clipboard

G = C33order 33 = 3·11

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C33, also denoted Z33, SmallGroup(33,1)

Series: Derived Chief Lower central Upper central

C1 — C33
C1C11 — C33
C1 — C33
C1 — C33

Generators and relations for C33
 G = < a | a33=1 >


Smallest permutation representation of C33
Regular action on 33 points
Generators in S33
(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)

G:=sub<Sym(33)| (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)>;

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) );

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)])

33 conjugacy classes

class 1 3A3B11A···11J33A···33T
order13311···1133···33
size1111···11···1

33 irreducible representations

dim1111
type+
imageC1C3C11C33
kernelC33C11C3C1
# reps121020

Matrix representation of C33 in GL1(𝔽67) generated by

65
G:=sub<GL(1,GF(67))| [65] >;

C33 in GAP, Magma, Sage, TeX

C_{33}
% in TeX

G:=Group("C33");
// GroupNames label

G:=SmallGroup(33,1);
// by ID

G=gap.SmallGroup(33,1);
# by ID

G:=PCGroup([2,-3,-11]);
// Polycyclic

G:=Group<a|a^33=1>;
// generators/relations

׿
×
𝔽