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G = C62order 62 = 2·31

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C62, also denoted Z62, SmallGroup(62,2)

Series: Derived Chief Lower central Upper central

C1 — C62
C1C31 — C62
C1 — C62
C1 — C62

Generators and relations for C62
 G = < a | a62=1 >


Smallest permutation representation of C62
Regular action on 62 points
Generators in S62
(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)

G:=sub<Sym(62)| (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)>;

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) );

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)])

C62 is a maximal subgroup of   Dic31

62 conjugacy classes

class 1  2 31A···31AD62A···62AD
order1231···3162···62
size111···11···1

62 irreducible representations

dim1111
type++
imageC1C2C31C62
kernelC62C31C2C1
# reps113030

Matrix representation of C62 in GL1(𝔽311) generated by

298
G:=sub<GL(1,GF(311))| [298] >;

C62 in GAP, Magma, Sage, TeX

C_{62}
% in TeX

G:=Group("C62");
// GroupNames label

G:=SmallGroup(62,2);
// by ID

G=gap.SmallGroup(62,2);
# by ID

G:=PCGroup([2,-2,-31]);
// Polycyclic

G:=Group<a|a^62=1>;
// generators/relations

Export

Subgroup lattice of C62 in TeX

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