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## G = C145order 145 = 5·29

### Cyclic group

Aliases: C145, also denoted Z145, SmallGroup(145,1)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C145
 Chief series C1 — C29 — C145
 Lower central C1 — C145
 Upper central C1 — C145

Generators and relations for C145
G = < a | a145=1 >

Smallest permutation representation of C145
Regular action on 145 points
Generators in S145
`(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145)`

`G:=sub<Sym(145)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145)>;`

`G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145) );`

`G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145)])`

C145 is a maximal subgroup of   D145

145 conjugacy classes

 class 1 5A 5B 5C 5D 29A ··· 29AB 145A ··· 145DH order 1 5 5 5 5 29 ··· 29 145 ··· 145 size 1 1 1 1 1 1 ··· 1 1 ··· 1

145 irreducible representations

 dim 1 1 1 1 type + image C1 C5 C29 C145 kernel C145 C29 C5 C1 # reps 1 4 28 112

Matrix representation of C145 in GL1(𝔽1451) generated by

 1113
`G:=sub<GL(1,GF(1451))| [1113] >;`

C145 in GAP, Magma, Sage, TeX

`C_{145}`
`% in TeX`

`G:=Group("C145");`
`// GroupNames label`

`G:=SmallGroup(145,1);`
`// by ID`

`G=gap.SmallGroup(145,1);`
`# by ID`

`G:=PCGroup([2,-5,-29]);`
`// Polycyclic`

`G:=Group<a|a^145=1>;`
`// generators/relations`

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