Copied to
clipboard

G = C154order 154 = 2·7·11

Cyclic group

Aliases: C154, also denoted Z154, SmallGroup(154,4)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C154
 Chief series C1 — C11 — C77 — C154
 Lower central C1 — C154
 Upper central C1 — C154

Generators and relations for C154
G = < a | a154=1 >

Smallest permutation representation of C154
Regular action on 154 points
Generators in S154
`(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154)`

`G:=sub<Sym(154)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154)>;`

`G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154) );`

`G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154)]])`

C154 is a maximal subgroup of   Dic77

154 conjugacy classes

 class 1 2 7A ··· 7F 11A ··· 11J 14A ··· 14F 22A ··· 22J 77A ··· 77BH 154A ··· 154BH order 1 2 7 ··· 7 11 ··· 11 14 ··· 14 22 ··· 22 77 ··· 77 154 ··· 154 size 1 1 1 ··· 1 1 ··· 1 1 ··· 1 1 ··· 1 1 ··· 1 1 ··· 1

154 irreducible representations

 dim 1 1 1 1 1 1 1 1 type + + image C1 C2 C7 C11 C14 C22 C77 C154 kernel C154 C77 C22 C14 C11 C7 C2 C1 # reps 1 1 6 10 6 10 60 60

Matrix representation of C154 in GL1(𝔽463) generated by

 363
`G:=sub<GL(1,GF(463))| [363] >;`

C154 in GAP, Magma, Sage, TeX

`C_{154}`
`% in TeX`

`G:=Group("C154");`
`// GroupNames label`

`G:=SmallGroup(154,4);`
`// by ID`

`G=gap.SmallGroup(154,4);`
`# by ID`

`G:=PCGroup([3,-2,-7,-11]);`
`// Polycyclic`

`G:=Group<a|a^154=1>;`
`// generators/relations`

Export

׿
×
𝔽