direct product, cyclic, abelian, monomial
Aliases: C146, also denoted Z146, SmallGroup(146,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C146 |
| C1 — C146 |
| C1 — C146 |
Generators and relations for C146
G = < a | a146=1 >
Smallest permutation representation of C146
►Regular action on 146 points
Generators in S146
(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)
G:=sub<Sym(146)| (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)>;
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) );
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)]])
C146 is a maximal subgroup of
Dic73
146 conjugacy classes
| class | 1 | 2 | 73A | ··· | 73BT | 146A | ··· | 146BT |
| order | 1 | 2 | 73 | ··· | 73 | 146 | ··· | 146 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
146 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C73 | C146 |
| kernel | C146 | C73 | C2 | C1 |
| # reps | 1 | 1 | 72 | 72 |
Matrix representation of C146 ►in GL1(𝔽293) generated by
| 202 |
G:=sub<GL(1,GF(293))| [202] >;
C146 in GAP, Magma, Sage, TeX
C_{146} % in TeX
G:=Group("C146"); // GroupNames label
G:=SmallGroup(146,2);
// by ID
G=gap.SmallGroup(146,2);
# by ID
G:=PCGroup([2,-2,-73]);
// Polycyclic
G:=Group<a|a^146=1>;
// generators/relations
Export