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G = D193order 386 = 2·193

Dihedral group

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

Aliases: D193, C193⋊C2, sometimes denoted D386 or Dih193 or Dih386, SmallGroup(386,1)

Series: Derived Chief Lower central Upper central

C1C193 — D193
C1C193 — D193
C193 — D193
C1

Generators and relations for D193
 G = < a,b | a193=b2=1, bab=a-1 >

193C2

Smallest permutation representation of D193
On 193 points: primitive
Generators in S193
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193)
(1 193)(2 192)(3 191)(4 190)(5 189)(6 188)(7 187)(8 186)(9 185)(10 184)(11 183)(12 182)(13 181)(14 180)(15 179)(16 178)(17 177)(18 176)(19 175)(20 174)(21 173)(22 172)(23 171)(24 170)(25 169)(26 168)(27 167)(28 166)(29 165)(30 164)(31 163)(32 162)(33 161)(34 160)(35 159)(36 158)(37 157)(38 156)(39 155)(40 154)(41 153)(42 152)(43 151)(44 150)(45 149)(46 148)(47 147)(48 146)(49 145)(50 144)(51 143)(52 142)(53 141)(54 140)(55 139)(56 138)(57 137)(58 136)(59 135)(60 134)(61 133)(62 132)(63 131)(64 130)(65 129)(66 128)(67 127)(68 126)(69 125)(70 124)(71 123)(72 122)(73 121)(74 120)(75 119)(76 118)(77 117)(78 116)(79 115)(80 114)(81 113)(82 112)(83 111)(84 110)(85 109)(86 108)(87 107)(88 106)(89 105)(90 104)(91 103)(92 102)(93 101)(94 100)(95 99)(96 98)

G:=sub<Sym(193)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193), (1,193)(2,192)(3,191)(4,190)(5,189)(6,188)(7,187)(8,186)(9,185)(10,184)(11,183)(12,182)(13,181)(14,180)(15,179)(16,178)(17,177)(18,176)(19,175)(20,174)(21,173)(22,172)(23,171)(24,170)(25,169)(26,168)(27,167)(28,166)(29,165)(30,164)(31,163)(32,162)(33,161)(34,160)(35,159)(36,158)(37,157)(38,156)(39,155)(40,154)(41,153)(42,152)(43,151)(44,150)(45,149)(46,148)(47,147)(48,146)(49,145)(50,144)(51,143)(52,142)(53,141)(54,140)(55,139)(56,138)(57,137)(58,136)(59,135)(60,134)(61,133)(62,132)(63,131)(64,130)(65,129)(66,128)(67,127)(68,126)(69,125)(70,124)(71,123)(72,122)(73,121)(74,120)(75,119)(76,118)(77,117)(78,116)(79,115)(80,114)(81,113)(82,112)(83,111)(84,110)(85,109)(86,108)(87,107)(88,106)(89,105)(90,104)(91,103)(92,102)(93,101)(94,100)(95,99)(96,98)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193), (1,193)(2,192)(3,191)(4,190)(5,189)(6,188)(7,187)(8,186)(9,185)(10,184)(11,183)(12,182)(13,181)(14,180)(15,179)(16,178)(17,177)(18,176)(19,175)(20,174)(21,173)(22,172)(23,171)(24,170)(25,169)(26,168)(27,167)(28,166)(29,165)(30,164)(31,163)(32,162)(33,161)(34,160)(35,159)(36,158)(37,157)(38,156)(39,155)(40,154)(41,153)(42,152)(43,151)(44,150)(45,149)(46,148)(47,147)(48,146)(49,145)(50,144)(51,143)(52,142)(53,141)(54,140)(55,139)(56,138)(57,137)(58,136)(59,135)(60,134)(61,133)(62,132)(63,131)(64,130)(65,129)(66,128)(67,127)(68,126)(69,125)(70,124)(71,123)(72,122)(73,121)(74,120)(75,119)(76,118)(77,117)(78,116)(79,115)(80,114)(81,113)(82,112)(83,111)(84,110)(85,109)(86,108)(87,107)(88,106)(89,105)(90,104)(91,103)(92,102)(93,101)(94,100)(95,99)(96,98) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193)], [(1,193),(2,192),(3,191),(4,190),(5,189),(6,188),(7,187),(8,186),(9,185),(10,184),(11,183),(12,182),(13,181),(14,180),(15,179),(16,178),(17,177),(18,176),(19,175),(20,174),(21,173),(22,172),(23,171),(24,170),(25,169),(26,168),(27,167),(28,166),(29,165),(30,164),(31,163),(32,162),(33,161),(34,160),(35,159),(36,158),(37,157),(38,156),(39,155),(40,154),(41,153),(42,152),(43,151),(44,150),(45,149),(46,148),(47,147),(48,146),(49,145),(50,144),(51,143),(52,142),(53,141),(54,140),(55,139),(56,138),(57,137),(58,136),(59,135),(60,134),(61,133),(62,132),(63,131),(64,130),(65,129),(66,128),(67,127),(68,126),(69,125),(70,124),(71,123),(72,122),(73,121),(74,120),(75,119),(76,118),(77,117),(78,116),(79,115),(80,114),(81,113),(82,112),(83,111),(84,110),(85,109),(86,108),(87,107),(88,106),(89,105),(90,104),(91,103),(92,102),(93,101),(94,100),(95,99),(96,98)])

98 conjugacy classes

class 1  2 193A···193CR
order12193···193
size11932···2

98 irreducible representations

dim112
type+++
imageC1C2D193
kernelD193C193C1
# reps1196

Matrix representation of D193 in GL2(𝔽773) generated by

524772
10
,
524772
160249
G:=sub<GL(2,GF(773))| [524,1,772,0],[524,160,772,249] >;

D193 in GAP, Magma, Sage, TeX

D_{193}
% in TeX

G:=Group("D193");
// GroupNames label

G:=SmallGroup(386,1);
// by ID

G=gap.SmallGroup(386,1);
# by ID

G:=PCGroup([2,-2,-193,1537]);
// Polycyclic

G:=Group<a,b|a^193=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D193 in TeX

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