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G = C102order 102 = 2·3·17

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C102, also denoted Z102, SmallGroup(102,4)

Series: Derived Chief Lower central Upper central

C1 — C102
C1C17C51 — C102
C1 — C102
C1 — C102

Generators and relations for C102
 G = < a | a102=1 >


Smallest permutation representation of C102
Regular action on 102 points
Generators in S102
(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 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102)

G:=sub<Sym(102)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102)])

C102 is a maximal subgroup of   Dic51

102 conjugacy classes

class 1  2 3A3B6A6B17A···17P34A···34P51A···51AF102A···102AF
order12336617···1734···3451···51102···102
size1111111···11···11···11···1

102 irreducible representations

dim11111111
type++
imageC1C2C3C6C17C34C51C102
kernelC102C51C34C17C6C3C2C1
# reps112216163232

Matrix representation of C102 in GL1(𝔽103) generated by

21
G:=sub<GL(1,GF(103))| [21] >;

C102 in GAP, Magma, Sage, TeX

C_{102}
% in TeX

G:=Group("C102");
// GroupNames label

G:=SmallGroup(102,4);
// by ID

G=gap.SmallGroup(102,4);
# by ID

G:=PCGroup([3,-2,-3,-17]);
// Polycyclic

G:=Group<a|a^102=1>;
// generators/relations

Export

Subgroup lattice of C102 in TeX

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