Copied to
clipboard

G = D187order 374 = 2·11·17

Dihedral group

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

Aliases: D187, C17⋊D11, C11⋊D17, C1871C2, sometimes denoted D374 or Dih187 or Dih374, SmallGroup(374,3)

Series: Derived Chief Lower central Upper central

C1C187 — D187
C1C17C187 — D187
C187 — D187
C1

Generators and relations for D187
 G = < a,b | a187=b2=1, bab=a-1 >

187C2
17D11
11D17

Smallest permutation representation of D187
On 187 points
Generators in S187
(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)
(1 187)(2 186)(3 185)(4 184)(5 183)(6 182)(7 181)(8 180)(9 179)(10 178)(11 177)(12 176)(13 175)(14 174)(15 173)(16 172)(17 171)(18 170)(19 169)(20 168)(21 167)(22 166)(23 165)(24 164)(25 163)(26 162)(27 161)(28 160)(29 159)(30 158)(31 157)(32 156)(33 155)(34 154)(35 153)(36 152)(37 151)(38 150)(39 149)(40 148)(41 147)(42 146)(43 145)(44 144)(45 143)(46 142)(47 141)(48 140)(49 139)(50 138)(51 137)(52 136)(53 135)(54 134)(55 133)(56 132)(57 131)(58 130)(59 129)(60 128)(61 127)(62 126)(63 125)(64 124)(65 123)(66 122)(67 121)(68 120)(69 119)(70 118)(71 117)(72 116)(73 115)(74 114)(75 113)(76 112)(77 111)(78 110)(79 109)(80 108)(81 107)(82 106)(83 105)(84 104)(85 103)(86 102)(87 101)(88 100)(89 99)(90 98)(91 97)(92 96)(93 95)

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

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

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

95 conjugacy classes

class 1  2 11A···11E17A···17H187A···187CB
order1211···1117···17187···187
size11872···22···22···2

95 irreducible representations

dim11222
type+++++
imageC1C2D11D17D187
kernelD187C187C17C11C1
# reps115880

Matrix representation of D187 in GL2(𝔽1123) generated by

1021292
831935
,
1021292
922102
G:=sub<GL(2,GF(1123))| [1021,831,292,935],[1021,922,292,102] >;

D187 in GAP, Magma, Sage, TeX

D_{187}
% in TeX

G:=Group("D187");
// GroupNames label

G:=SmallGroup(374,3);
// by ID

G=gap.SmallGroup(374,3);
# by ID

G:=PCGroup([3,-2,-11,-17,121,3170]);
// Polycyclic

G:=Group<a,b|a^187=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D187 in TeX

׿
×
𝔽