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G = C130order 130 = 2·5·13

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C130, also denoted Z130, SmallGroup(130,4)

Series: Derived Chief Lower central Upper central

C1 — C130
C1C13C65 — C130
C1 — C130
C1 — C130

Generators and relations for C130
 G = < a | a130=1 >


Smallest permutation representation of C130
Regular action on 130 points
Generators in S130
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130)

G:=sub<Sym(130)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130)])

C130 is a maximal subgroup of   Dic65

130 conjugacy classes

class 1  2 5A5B5C5D10A10B10C10D13A···13L26A···26L65A···65AV130A···130AV
order1255551010101013···1326···2665···65130···130
size11111111111···11···11···11···1

130 irreducible representations

dim11111111
type++
imageC1C2C5C10C13C26C65C130
kernelC130C65C26C13C10C5C2C1
# reps114412124848

Matrix representation of C130 in GL2(𝔽131) generated by

710
065
G:=sub<GL(2,GF(131))| [71,0,0,65] >;

C130 in GAP, Magma, Sage, TeX

C_{130}
% in TeX

G:=Group("C130");
// GroupNames label

G:=SmallGroup(130,4);
// by ID

G=gap.SmallGroup(130,4);
# by ID

G:=PCGroup([3,-2,-5,-13]);
// Polycyclic

G:=Group<a|a^130=1>;
// generators/relations

Export

Subgroup lattice of C130 in TeX

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