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G = D191order 382 = 2·191

Dihedral group

metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: D191, C191⋊C2, sometimes denoted D382 or Dih191 or Dih382, SmallGroup(382,1)

Series: Derived Chief Lower central Upper central

C1C191 — D191
C1C191 — D191
C191 — D191
C1

Generators and relations for D191
 G = < a,b | a191=b2=1, bab=a-1 >

191C2

Smallest permutation representation of D191
On 191 points: primitive
Generators in S191
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191)
(1 191)(2 190)(3 189)(4 188)(5 187)(6 186)(7 185)(8 184)(9 183)(10 182)(11 181)(12 180)(13 179)(14 178)(15 177)(16 176)(17 175)(18 174)(19 173)(20 172)(21 171)(22 170)(23 169)(24 168)(25 167)(26 166)(27 165)(28 164)(29 163)(30 162)(31 161)(32 160)(33 159)(34 158)(35 157)(36 156)(37 155)(38 154)(39 153)(40 152)(41 151)(42 150)(43 149)(44 148)(45 147)(46 146)(47 145)(48 144)(49 143)(50 142)(51 141)(52 140)(53 139)(54 138)(55 137)(56 136)(57 135)(58 134)(59 133)(60 132)(61 131)(62 130)(63 129)(64 128)(65 127)(66 126)(67 125)(68 124)(69 123)(70 122)(71 121)(72 120)(73 119)(74 118)(75 117)(76 116)(77 115)(78 114)(79 113)(80 112)(81 111)(82 110)(83 109)(84 108)(85 107)(86 106)(87 105)(88 104)(89 103)(90 102)(91 101)(92 100)(93 99)(94 98)(95 97)

G:=sub<Sym(191)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191), (1,191)(2,190)(3,189)(4,188)(5,187)(6,186)(7,185)(8,184)(9,183)(10,182)(11,181)(12,180)(13,179)(14,178)(15,177)(16,176)(17,175)(18,174)(19,173)(20,172)(21,171)(22,170)(23,169)(24,168)(25,167)(26,166)(27,165)(28,164)(29,163)(30,162)(31,161)(32,160)(33,159)(34,158)(35,157)(36,156)(37,155)(38,154)(39,153)(40,152)(41,151)(42,150)(43,149)(44,148)(45,147)(46,146)(47,145)(48,144)(49,143)(50,142)(51,141)(52,140)(53,139)(54,138)(55,137)(56,136)(57,135)(58,134)(59,133)(60,132)(61,131)(62,130)(63,129)(64,128)(65,127)(66,126)(67,125)(68,124)(69,123)(70,122)(71,121)(72,120)(73,119)(74,118)(75,117)(76,116)(77,115)(78,114)(79,113)(80,112)(81,111)(82,110)(83,109)(84,108)(85,107)(86,106)(87,105)(88,104)(89,103)(90,102)(91,101)(92,100)(93,99)(94,98)(95,97)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191), (1,191)(2,190)(3,189)(4,188)(5,187)(6,186)(7,185)(8,184)(9,183)(10,182)(11,181)(12,180)(13,179)(14,178)(15,177)(16,176)(17,175)(18,174)(19,173)(20,172)(21,171)(22,170)(23,169)(24,168)(25,167)(26,166)(27,165)(28,164)(29,163)(30,162)(31,161)(32,160)(33,159)(34,158)(35,157)(36,156)(37,155)(38,154)(39,153)(40,152)(41,151)(42,150)(43,149)(44,148)(45,147)(46,146)(47,145)(48,144)(49,143)(50,142)(51,141)(52,140)(53,139)(54,138)(55,137)(56,136)(57,135)(58,134)(59,133)(60,132)(61,131)(62,130)(63,129)(64,128)(65,127)(66,126)(67,125)(68,124)(69,123)(70,122)(71,121)(72,120)(73,119)(74,118)(75,117)(76,116)(77,115)(78,114)(79,113)(80,112)(81,111)(82,110)(83,109)(84,108)(85,107)(86,106)(87,105)(88,104)(89,103)(90,102)(91,101)(92,100)(93,99)(94,98)(95,97) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191)], [(1,191),(2,190),(3,189),(4,188),(5,187),(6,186),(7,185),(8,184),(9,183),(10,182),(11,181),(12,180),(13,179),(14,178),(15,177),(16,176),(17,175),(18,174),(19,173),(20,172),(21,171),(22,170),(23,169),(24,168),(25,167),(26,166),(27,165),(28,164),(29,163),(30,162),(31,161),(32,160),(33,159),(34,158),(35,157),(36,156),(37,155),(38,154),(39,153),(40,152),(41,151),(42,150),(43,149),(44,148),(45,147),(46,146),(47,145),(48,144),(49,143),(50,142),(51,141),(52,140),(53,139),(54,138),(55,137),(56,136),(57,135),(58,134),(59,133),(60,132),(61,131),(62,130),(63,129),(64,128),(65,127),(66,126),(67,125),(68,124),(69,123),(70,122),(71,121),(72,120),(73,119),(74,118),(75,117),(76,116),(77,115),(78,114),(79,113),(80,112),(81,111),(82,110),(83,109),(84,108),(85,107),(86,106),(87,105),(88,104),(89,103),(90,102),(91,101),(92,100),(93,99),(94,98),(95,97)])

97 conjugacy classes

class 1  2 191A···191CQ
order12191···191
size11912···2

97 irreducible representations

dim112
type+++
imageC1C2D191
kernelD191C191C1
# reps1195

Matrix representation of D191 in GL2(𝔽383) generated by

70382
120343
,
88250
231295
G:=sub<GL(2,GF(383))| [70,120,382,343],[88,231,250,295] >;

D191 in GAP, Magma, Sage, TeX

D_{191}
% in TeX

G:=Group("D191");
// GroupNames label

G:=SmallGroup(382,1);
// by ID

G=gap.SmallGroup(382,1);
# by ID

G:=PCGroup([2,-2,-191,1521]);
// Polycyclic

G:=Group<a,b|a^191=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D191 in TeX

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