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G = C62order 36 = 22·32

Abelian group of type [6,6]

direct product, abelian, monomial

Aliases: C62, SmallGroup(36,14)

Series: Derived Chief Lower central Upper central

C1 — C62
C1C3C32C3×C6 — C62
C1 — C62
C1 — C62

Generators and relations for C62
 G = < a,b | a6=b6=1, ab=ba >


Smallest permutation representation of C62
Regular action on 36 points
Generators in S36
(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)
(1 32 30 13 8 23)(2 33 25 14 9 24)(3 34 26 15 10 19)(4 35 27 16 11 20)(5 36 28 17 12 21)(6 31 29 18 7 22)

G:=sub<Sym(36)| (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), (1,32,30,13,8,23)(2,33,25,14,9,24)(3,34,26,15,10,19)(4,35,27,16,11,20)(5,36,28,17,12,21)(6,31,29,18,7,22)>;

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), (1,32,30,13,8,23)(2,33,25,14,9,24)(3,34,26,15,10,19)(4,35,27,16,11,20)(5,36,28,17,12,21)(6,31,29,18,7,22) );

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)], [(1,32,30,13,8,23),(2,33,25,14,9,24),(3,34,26,15,10,19),(4,35,27,16,11,20),(5,36,28,17,12,21),(6,31,29,18,7,22)])

36 conjugacy classes

class 1 2A2B2C3A···3H6A···6X
order12223···36···6
size11111···11···1

36 irreducible representations

dim1111
type++
imageC1C2C3C6
kernelC62C3×C6C2×C6C6
# reps13824

Matrix representation of C62 in GL2(𝔽7) generated by

50
01
,
60
03
G:=sub<GL(2,GF(7))| [5,0,0,1],[6,0,0,3] >;

C62 in GAP, Magma, Sage, TeX

C_6^2
% in TeX

G:=Group("C6^2");
// GroupNames label

G:=SmallGroup(36,14);
// by ID

G=gap.SmallGroup(36,14);
# by ID

G:=PCGroup([4,-2,-2,-3,-3]);
// Polycyclic

G:=Group<a,b|a^6=b^6=1,a*b=b*a>;
// generators/relations

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