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G = C82order 82 = 2·41

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C82, also denoted Z82, SmallGroup(82,2)

Series: Derived Chief Lower central Upper central

C1 — C82
C1C41 — C82
C1 — C82
C1 — C82

Generators and relations for C82
 G = < a | a82=1 >


Smallest permutation representation of C82
Regular action on 82 points
Generators in S82
(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 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82)

G:=sub<Sym(82)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82)])

C82 is a maximal subgroup of   Dic41

82 conjugacy classes

class 1  2 41A···41AN82A···82AN
order1241···4182···82
size111···11···1

82 irreducible representations

dim1111
type++
imageC1C2C41C82
kernelC82C41C2C1
# reps114040

Matrix representation of C82 in GL1(𝔽83) generated by

67
G:=sub<GL(1,GF(83))| [67] >;

C82 in GAP, Magma, Sage, TeX

C_{82}
% in TeX

G:=Group("C82");
// GroupNames label

G:=SmallGroup(82,2);
// by ID

G=gap.SmallGroup(82,2);
# by ID

G:=PCGroup([2,-2,-41]);
// Polycyclic

G:=Group<a|a^82=1>;
// generators/relations

Export

Subgroup lattice of C82 in TeX

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