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## G = C143order 143 = 11·13

### Cyclic group

Aliases: C143, also denoted Z143, SmallGroup(143,1)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C143
 Chief series C1 — C13 — C143
 Lower central C1 — C143
 Upper central C1 — C143

Generators and relations for C143
G = < a | a143=1 >

Smallest permutation representation of C143
Regular action on 143 points
Generators in S143
`(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143)`

`G:=sub<Sym(143)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143)>;`

`G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143) );`

`G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143)]])`

C143 is a maximal subgroup of   D143

143 conjugacy classes

 class 1 11A ··· 11J 13A ··· 13L 143A ··· 143DP order 1 11 ··· 11 13 ··· 13 143 ··· 143 size 1 1 ··· 1 1 ··· 1 1 ··· 1

143 irreducible representations

 dim 1 1 1 1 type + image C1 C11 C13 C143 kernel C143 C13 C11 C1 # reps 1 10 12 120

Matrix representation of C143 in GL1(𝔽859) generated by

 406
`G:=sub<GL(1,GF(859))| [406] >;`

C143 in GAP, Magma, Sage, TeX

`C_{143}`
`% in TeX`

`G:=Group("C143");`
`// GroupNames label`

`G:=SmallGroup(143,1);`
`// by ID`

`G=gap.SmallGroup(143,1);`
`# by ID`

`G:=PCGroup([2,-11,-13]);`
`// Polycyclic`

`G:=Group<a|a^143=1>;`
`// generators/relations`

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