metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: Dic47, C47⋊C4, C94.C2, C2.D47, SmallGroup(188,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C47 — Dic47 |
Generators and relations for Dic47
G = < a,b | a94=1, b2=a47, bab-1=a-1 >
Smallest permutation representation of Dic47
►Regular action on 188 points
Generators in S188
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188)
(1 165 48 118)(2 164 49 117)(3 163 50 116)(4 162 51 115)(5 161 52 114)(6 160 53 113)(7 159 54 112)(8 158 55 111)(9 157 56 110)(10 156 57 109)(11 155 58 108)(12 154 59 107)(13 153 60 106)(14 152 61 105)(15 151 62 104)(16 150 63 103)(17 149 64 102)(18 148 65 101)(19 147 66 100)(20 146 67 99)(21 145 68 98)(22 144 69 97)(23 143 70 96)(24 142 71 95)(25 141 72 188)(26 140 73 187)(27 139 74 186)(28 138 75 185)(29 137 76 184)(30 136 77 183)(31 135 78 182)(32 134 79 181)(33 133 80 180)(34 132 81 179)(35 131 82 178)(36 130 83 177)(37 129 84 176)(38 128 85 175)(39 127 86 174)(40 126 87 173)(41 125 88 172)(42 124 89 171)(43 123 90 170)(44 122 91 169)(45 121 92 168)(46 120 93 167)(47 119 94 166)
G:=sub<Sym(188)| (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)(95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188), (1,165,48,118)(2,164,49,117)(3,163,50,116)(4,162,51,115)(5,161,52,114)(6,160,53,113)(7,159,54,112)(8,158,55,111)(9,157,56,110)(10,156,57,109)(11,155,58,108)(12,154,59,107)(13,153,60,106)(14,152,61,105)(15,151,62,104)(16,150,63,103)(17,149,64,102)(18,148,65,101)(19,147,66,100)(20,146,67,99)(21,145,68,98)(22,144,69,97)(23,143,70,96)(24,142,71,95)(25,141,72,188)(26,140,73,187)(27,139,74,186)(28,138,75,185)(29,137,76,184)(30,136,77,183)(31,135,78,182)(32,134,79,181)(33,133,80,180)(34,132,81,179)(35,131,82,178)(36,130,83,177)(37,129,84,176)(38,128,85,175)(39,127,86,174)(40,126,87,173)(41,125,88,172)(42,124,89,171)(43,123,90,170)(44,122,91,169)(45,121,92,168)(46,120,93,167)(47,119,94,166)>;
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)(95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188), (1,165,48,118)(2,164,49,117)(3,163,50,116)(4,162,51,115)(5,161,52,114)(6,160,53,113)(7,159,54,112)(8,158,55,111)(9,157,56,110)(10,156,57,109)(11,155,58,108)(12,154,59,107)(13,153,60,106)(14,152,61,105)(15,151,62,104)(16,150,63,103)(17,149,64,102)(18,148,65,101)(19,147,66,100)(20,146,67,99)(21,145,68,98)(22,144,69,97)(23,143,70,96)(24,142,71,95)(25,141,72,188)(26,140,73,187)(27,139,74,186)(28,138,75,185)(29,137,76,184)(30,136,77,183)(31,135,78,182)(32,134,79,181)(33,133,80,180)(34,132,81,179)(35,131,82,178)(36,130,83,177)(37,129,84,176)(38,128,85,175)(39,127,86,174)(40,126,87,173)(41,125,88,172)(42,124,89,171)(43,123,90,170)(44,122,91,169)(45,121,92,168)(46,120,93,167)(47,119,94,166) );
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),(95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188)], [(1,165,48,118),(2,164,49,117),(3,163,50,116),(4,162,51,115),(5,161,52,114),(6,160,53,113),(7,159,54,112),(8,158,55,111),(9,157,56,110),(10,156,57,109),(11,155,58,108),(12,154,59,107),(13,153,60,106),(14,152,61,105),(15,151,62,104),(16,150,63,103),(17,149,64,102),(18,148,65,101),(19,147,66,100),(20,146,67,99),(21,145,68,98),(22,144,69,97),(23,143,70,96),(24,142,71,95),(25,141,72,188),(26,140,73,187),(27,139,74,186),(28,138,75,185),(29,137,76,184),(30,136,77,183),(31,135,78,182),(32,134,79,181),(33,133,80,180),(34,132,81,179),(35,131,82,178),(36,130,83,177),(37,129,84,176),(38,128,85,175),(39,127,86,174),(40,126,87,173),(41,125,88,172),(42,124,89,171),(43,123,90,170),(44,122,91,169),(45,121,92,168),(46,120,93,167),(47,119,94,166)]])
Dic47 is a maximal subgroup of
Dic94 C4×D47 C47⋊D4
Dic47 is a maximal quotient of C47⋊C8
50 conjugacy classes
| class | 1 | 2 | 4A | 4B | 47A | ··· | 47W | 94A | ··· | 94W |
| order | 1 | 2 | 4 | 4 | 47 | ··· | 47 | 94 | ··· | 94 |
| size | 1 | 1 | 47 | 47 | 2 | ··· | 2 | 2 | ··· | 2 |
50 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | - | |
| image | C1 | C2 | C4 | D47 | Dic47 |
| kernel | Dic47 | C94 | C47 | C2 | C1 |
| # reps | 1 | 1 | 2 | 23 | 23 |
Matrix representation of Dic47 ►in GL2(𝔽941) generated by
| 176 | 1 |
| 940 | 0 |
| 253 | 739 |
| 438 | 688 |
G:=sub<GL(2,GF(941))| [176,940,1,0],[253,438,739,688] >;
Dic47 in GAP, Magma, Sage, TeX
{\rm Dic}_{47} % in TeX
G:=Group("Dic47"); // GroupNames label
G:=SmallGroup(188,1);
// by ID
G=gap.SmallGroup(188,1);
# by ID
G:=PCGroup([3,-2,-2,-47,6,1658]);
// Polycyclic
G:=Group<a,b|a^94=1,b^2=a^47,b*a*b^-1=a^-1>;
// generators/relations
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