metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: Dic46, C23⋊Q8, C4.D23, C92.1C2, C2.3D46, Dic23.C2, C46.1C22, SmallGroup(184,3)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic46
G = < a,b | a92=1, b2=a46, bab-1=a-1 >
Smallest permutation representation of Dic46
►Regular action on 184 points
Generators in S184
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184)
(1 106 47 152)(2 105 48 151)(3 104 49 150)(4 103 50 149)(5 102 51 148)(6 101 52 147)(7 100 53 146)(8 99 54 145)(9 98 55 144)(10 97 56 143)(11 96 57 142)(12 95 58 141)(13 94 59 140)(14 93 60 139)(15 184 61 138)(16 183 62 137)(17 182 63 136)(18 181 64 135)(19 180 65 134)(20 179 66 133)(21 178 67 132)(22 177 68 131)(23 176 69 130)(24 175 70 129)(25 174 71 128)(26 173 72 127)(27 172 73 126)(28 171 74 125)(29 170 75 124)(30 169 76 123)(31 168 77 122)(32 167 78 121)(33 166 79 120)(34 165 80 119)(35 164 81 118)(36 163 82 117)(37 162 83 116)(38 161 84 115)(39 160 85 114)(40 159 86 113)(41 158 87 112)(42 157 88 111)(43 156 89 110)(44 155 90 109)(45 154 91 108)(46 153 92 107)
G:=sub<Sym(184)| (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)(93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184), (1,106,47,152)(2,105,48,151)(3,104,49,150)(4,103,50,149)(5,102,51,148)(6,101,52,147)(7,100,53,146)(8,99,54,145)(9,98,55,144)(10,97,56,143)(11,96,57,142)(12,95,58,141)(13,94,59,140)(14,93,60,139)(15,184,61,138)(16,183,62,137)(17,182,63,136)(18,181,64,135)(19,180,65,134)(20,179,66,133)(21,178,67,132)(22,177,68,131)(23,176,69,130)(24,175,70,129)(25,174,71,128)(26,173,72,127)(27,172,73,126)(28,171,74,125)(29,170,75,124)(30,169,76,123)(31,168,77,122)(32,167,78,121)(33,166,79,120)(34,165,80,119)(35,164,81,118)(36,163,82,117)(37,162,83,116)(38,161,84,115)(39,160,85,114)(40,159,86,113)(41,158,87,112)(42,157,88,111)(43,156,89,110)(44,155,90,109)(45,154,91,108)(46,153,92,107)>;
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)(93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184), (1,106,47,152)(2,105,48,151)(3,104,49,150)(4,103,50,149)(5,102,51,148)(6,101,52,147)(7,100,53,146)(8,99,54,145)(9,98,55,144)(10,97,56,143)(11,96,57,142)(12,95,58,141)(13,94,59,140)(14,93,60,139)(15,184,61,138)(16,183,62,137)(17,182,63,136)(18,181,64,135)(19,180,65,134)(20,179,66,133)(21,178,67,132)(22,177,68,131)(23,176,69,130)(24,175,70,129)(25,174,71,128)(26,173,72,127)(27,172,73,126)(28,171,74,125)(29,170,75,124)(30,169,76,123)(31,168,77,122)(32,167,78,121)(33,166,79,120)(34,165,80,119)(35,164,81,118)(36,163,82,117)(37,162,83,116)(38,161,84,115)(39,160,85,114)(40,159,86,113)(41,158,87,112)(42,157,88,111)(43,156,89,110)(44,155,90,109)(45,154,91,108)(46,153,92,107) );
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),(93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184)], [(1,106,47,152),(2,105,48,151),(3,104,49,150),(4,103,50,149),(5,102,51,148),(6,101,52,147),(7,100,53,146),(8,99,54,145),(9,98,55,144),(10,97,56,143),(11,96,57,142),(12,95,58,141),(13,94,59,140),(14,93,60,139),(15,184,61,138),(16,183,62,137),(17,182,63,136),(18,181,64,135),(19,180,65,134),(20,179,66,133),(21,178,67,132),(22,177,68,131),(23,176,69,130),(24,175,70,129),(25,174,71,128),(26,173,72,127),(27,172,73,126),(28,171,74,125),(29,170,75,124),(30,169,76,123),(31,168,77,122),(32,167,78,121),(33,166,79,120),(34,165,80,119),(35,164,81,118),(36,163,82,117),(37,162,83,116),(38,161,84,115),(39,160,85,114),(40,159,86,113),(41,158,87,112),(42,157,88,111),(43,156,89,110),(44,155,90,109),(45,154,91,108),(46,153,92,107)]])
Dic46 is a maximal subgroup of
C184⋊C2 Dic92 D4.D23 C23⋊Q16 D92⋊5C2 D4⋊2D23 Q8×D23
Dic46 is a maximal quotient of Dic23⋊C4 C92⋊C4
49 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 23A | ··· | 23K | 46A | ··· | 46K | 92A | ··· | 92V |
| order | 1 | 2 | 4 | 4 | 4 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 |
| size | 1 | 1 | 2 | 46 | 46 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
49 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | + | - |
| image | C1 | C2 | C2 | Q8 | D23 | D46 | Dic46 |
| kernel | Dic46 | Dic23 | C92 | C23 | C4 | C2 | C1 |
| # reps | 1 | 2 | 1 | 1 | 11 | 11 | 22 |
Matrix representation of Dic46 ►in GL2(𝔽277) generated by
| 162 | 58 |
| 219 | 128 |
| 54 | 13 |
| 10 | 223 |
G:=sub<GL(2,GF(277))| [162,219,58,128],[54,10,13,223] >;
Dic46 in GAP, Magma, Sage, TeX
{\rm Dic}_{46} % in TeX
G:=Group("Dic46"); // GroupNames label
G:=SmallGroup(184,3);
// by ID
G=gap.SmallGroup(184,3);
# by ID
G:=PCGroup([4,-2,-2,-2,-23,16,49,21,2819]);
// Polycyclic
G:=Group<a,b|a^92=1,b^2=a^46,b*a*b^-1=a^-1>;
// generators/relations
Export