Copied to
clipboard

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

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

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

C62 is a maximal subgroup of   C327D4  C32.A4  C32⋊A4

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

Export

Subgroup lattice of C62 in TeX

׿
×
𝔽