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G = C132order 132 = 22·3·11

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C132, also denoted Z132, SmallGroup(132,4)

Series: Derived Chief Lower central Upper central

C1 — C132
C1C2C22C66 — C132
C1 — C132
C1 — C132

Generators and relations for C132
 G = < a | a132=1 >


Smallest permutation representation of C132
Regular action on 132 points
Generators in S132
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132)

G:=sub<Sym(132)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132)])

C132 is a maximal subgroup of   C33⋊C8  Dic66  D132

132 conjugacy classes

class 1  2 3A3B4A4B6A6B11A···11J12A12B12C12D22A···22J33A···33T44A···44T66A···66T132A···132AN
order1233446611···111212121222···2233···3344···4466···66132···132
size111111111···111111···11···11···11···11···1

132 irreducible representations

dim111111111111
type++
imageC1C2C3C4C6C11C12C22C33C44C66C132
kernelC132C66C44C33C22C12C11C6C4C3C2C1
# reps112221041020202040

Matrix representation of C132 in GL2(𝔽23) generated by

07
118
G:=sub<GL(2,GF(23))| [0,1,7,18] >;

C132 in GAP, Magma, Sage, TeX

C_{132}
% in TeX

G:=Group("C132");
// GroupNames label

G:=SmallGroup(132,4);
// by ID

G=gap.SmallGroup(132,4);
# by ID

G:=PCGroup([4,-2,-3,-11,-2,264]);
// Polycyclic

G:=Group<a|a^132=1>;
// generators/relations

Export

Subgroup lattice of C132 in TeX

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