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G = C66order 66 = 2·3·11

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C66, also denoted Z66, SmallGroup(66,4)

Series: Derived Chief Lower central Upper central

C1 — C66
C1C11C33 — C66
C1 — C66
C1 — C66

Generators and relations for C66
 G = < a | a66=1 >


Smallest permutation representation of C66
Regular action on 66 points
Generators in S66
(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)

G:=sub<Sym(66)| (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)>;

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) );

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)])

C66 is a maximal subgroup of   Dic33

66 conjugacy classes

class 1  2 3A3B6A6B11A···11J22A···22J33A···33T66A···66T
order12336611···1122···2233···3366···66
size1111111···11···11···11···1

66 irreducible representations

dim11111111
type++
imageC1C2C3C6C11C22C33C66
kernelC66C33C22C11C6C3C2C1
# reps112210102020

Matrix representation of C66 in GL2(𝔽23) generated by

014
13
G:=sub<GL(2,GF(23))| [0,1,14,3] >;

C66 in GAP, Magma, Sage, TeX

C_{66}
% in TeX

G:=Group("C66");
// GroupNames label

G:=SmallGroup(66,4);
// by ID

G=gap.SmallGroup(66,4);
# by ID

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

G:=Group<a|a^66=1>;
// generators/relations

Export

Subgroup lattice of C66 in TeX

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