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G = C19×D13order 494 = 2·13·19

Direct product of C19 and D13

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

Aliases: C19×D13, C13⋊C38, C2473C2, SmallGroup(494,1)

Series: Derived Chief Lower central Upper central

C1C13 — C19×D13
C1C13C247 — C19×D13
C13 — C19×D13
C1C19

Generators and relations for C19×D13
 G = < a,b,c | a19=b13=c2=1, ab=ba, ac=ca, cbc=b-1 >

13C2
13C38

Smallest permutation representation of C19×D13
On 247 points
Generators in S247
(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)(191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209)(210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228)(229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247)
(1 173 157 230 223 122 192 90 57 74 100 34 149)(2 174 158 231 224 123 193 91 39 75 101 35 150)(3 175 159 232 225 124 194 92 40 76 102 36 151)(4 176 160 233 226 125 195 93 41 58 103 37 152)(5 177 161 234 227 126 196 94 42 59 104 38 134)(6 178 162 235 228 127 197 95 43 60 105 20 135)(7 179 163 236 210 128 198 77 44 61 106 21 136)(8 180 164 237 211 129 199 78 45 62 107 22 137)(9 181 165 238 212 130 200 79 46 63 108 23 138)(10 182 166 239 213 131 201 80 47 64 109 24 139)(11 183 167 240 214 132 202 81 48 65 110 25 140)(12 184 168 241 215 133 203 82 49 66 111 26 141)(13 185 169 242 216 115 204 83 50 67 112 27 142)(14 186 170 243 217 116 205 84 51 68 113 28 143)(15 187 171 244 218 117 206 85 52 69 114 29 144)(16 188 153 245 219 118 207 86 53 70 96 30 145)(17 189 154 246 220 119 208 87 54 71 97 31 146)(18 190 155 247 221 120 209 88 55 72 98 32 147)(19 172 156 229 222 121 191 89 56 73 99 33 148)
(1 149)(2 150)(3 151)(4 152)(5 134)(6 135)(7 136)(8 137)(9 138)(10 139)(11 140)(12 141)(13 142)(14 143)(15 144)(16 145)(17 146)(18 147)(19 148)(20 178)(21 179)(22 180)(23 181)(24 182)(25 183)(26 184)(27 185)(28 186)(29 187)(30 188)(31 189)(32 190)(33 172)(34 173)(35 174)(36 175)(37 176)(38 177)(39 224)(40 225)(41 226)(42 227)(43 228)(44 210)(45 211)(46 212)(47 213)(48 214)(49 215)(50 216)(51 217)(52 218)(53 219)(54 220)(55 221)(56 222)(57 223)(58 233)(59 234)(60 235)(61 236)(62 237)(63 238)(64 239)(65 240)(66 241)(67 242)(68 243)(69 244)(70 245)(71 246)(72 247)(73 229)(74 230)(75 231)(76 232)(77 128)(78 129)(79 130)(80 131)(81 132)(82 133)(83 115)(84 116)(85 117)(86 118)(87 119)(88 120)(89 121)(90 122)(91 123)(92 124)(93 125)(94 126)(95 127)(96 153)(97 154)(98 155)(99 156)(100 157)(101 158)(102 159)(103 160)(104 161)(105 162)(106 163)(107 164)(108 165)(109 166)(110 167)(111 168)(112 169)(113 170)(114 171)

G:=sub<Sym(247)| (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)(191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209)(210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228)(229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247), (1,173,157,230,223,122,192,90,57,74,100,34,149)(2,174,158,231,224,123,193,91,39,75,101,35,150)(3,175,159,232,225,124,194,92,40,76,102,36,151)(4,176,160,233,226,125,195,93,41,58,103,37,152)(5,177,161,234,227,126,196,94,42,59,104,38,134)(6,178,162,235,228,127,197,95,43,60,105,20,135)(7,179,163,236,210,128,198,77,44,61,106,21,136)(8,180,164,237,211,129,199,78,45,62,107,22,137)(9,181,165,238,212,130,200,79,46,63,108,23,138)(10,182,166,239,213,131,201,80,47,64,109,24,139)(11,183,167,240,214,132,202,81,48,65,110,25,140)(12,184,168,241,215,133,203,82,49,66,111,26,141)(13,185,169,242,216,115,204,83,50,67,112,27,142)(14,186,170,243,217,116,205,84,51,68,113,28,143)(15,187,171,244,218,117,206,85,52,69,114,29,144)(16,188,153,245,219,118,207,86,53,70,96,30,145)(17,189,154,246,220,119,208,87,54,71,97,31,146)(18,190,155,247,221,120,209,88,55,72,98,32,147)(19,172,156,229,222,121,191,89,56,73,99,33,148), (1,149)(2,150)(3,151)(4,152)(5,134)(6,135)(7,136)(8,137)(9,138)(10,139)(11,140)(12,141)(13,142)(14,143)(15,144)(16,145)(17,146)(18,147)(19,148)(20,178)(21,179)(22,180)(23,181)(24,182)(25,183)(26,184)(27,185)(28,186)(29,187)(30,188)(31,189)(32,190)(33,172)(34,173)(35,174)(36,175)(37,176)(38,177)(39,224)(40,225)(41,226)(42,227)(43,228)(44,210)(45,211)(46,212)(47,213)(48,214)(49,215)(50,216)(51,217)(52,218)(53,219)(54,220)(55,221)(56,222)(57,223)(58,233)(59,234)(60,235)(61,236)(62,237)(63,238)(64,239)(65,240)(66,241)(67,242)(68,243)(69,244)(70,245)(71,246)(72,247)(73,229)(74,230)(75,231)(76,232)(77,128)(78,129)(79,130)(80,131)(81,132)(82,133)(83,115)(84,116)(85,117)(86,118)(87,119)(88,120)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,153)(97,154)(98,155)(99,156)(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)(111,168)(112,169)(113,170)(114,171)>;

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)(191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209)(210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228)(229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247), (1,173,157,230,223,122,192,90,57,74,100,34,149)(2,174,158,231,224,123,193,91,39,75,101,35,150)(3,175,159,232,225,124,194,92,40,76,102,36,151)(4,176,160,233,226,125,195,93,41,58,103,37,152)(5,177,161,234,227,126,196,94,42,59,104,38,134)(6,178,162,235,228,127,197,95,43,60,105,20,135)(7,179,163,236,210,128,198,77,44,61,106,21,136)(8,180,164,237,211,129,199,78,45,62,107,22,137)(9,181,165,238,212,130,200,79,46,63,108,23,138)(10,182,166,239,213,131,201,80,47,64,109,24,139)(11,183,167,240,214,132,202,81,48,65,110,25,140)(12,184,168,241,215,133,203,82,49,66,111,26,141)(13,185,169,242,216,115,204,83,50,67,112,27,142)(14,186,170,243,217,116,205,84,51,68,113,28,143)(15,187,171,244,218,117,206,85,52,69,114,29,144)(16,188,153,245,219,118,207,86,53,70,96,30,145)(17,189,154,246,220,119,208,87,54,71,97,31,146)(18,190,155,247,221,120,209,88,55,72,98,32,147)(19,172,156,229,222,121,191,89,56,73,99,33,148), (1,149)(2,150)(3,151)(4,152)(5,134)(6,135)(7,136)(8,137)(9,138)(10,139)(11,140)(12,141)(13,142)(14,143)(15,144)(16,145)(17,146)(18,147)(19,148)(20,178)(21,179)(22,180)(23,181)(24,182)(25,183)(26,184)(27,185)(28,186)(29,187)(30,188)(31,189)(32,190)(33,172)(34,173)(35,174)(36,175)(37,176)(38,177)(39,224)(40,225)(41,226)(42,227)(43,228)(44,210)(45,211)(46,212)(47,213)(48,214)(49,215)(50,216)(51,217)(52,218)(53,219)(54,220)(55,221)(56,222)(57,223)(58,233)(59,234)(60,235)(61,236)(62,237)(63,238)(64,239)(65,240)(66,241)(67,242)(68,243)(69,244)(70,245)(71,246)(72,247)(73,229)(74,230)(75,231)(76,232)(77,128)(78,129)(79,130)(80,131)(81,132)(82,133)(83,115)(84,116)(85,117)(86,118)(87,119)(88,120)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,153)(97,154)(98,155)(99,156)(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)(111,168)(112,169)(113,170)(114,171) );

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),(191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209),(210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228),(229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247)], [(1,173,157,230,223,122,192,90,57,74,100,34,149),(2,174,158,231,224,123,193,91,39,75,101,35,150),(3,175,159,232,225,124,194,92,40,76,102,36,151),(4,176,160,233,226,125,195,93,41,58,103,37,152),(5,177,161,234,227,126,196,94,42,59,104,38,134),(6,178,162,235,228,127,197,95,43,60,105,20,135),(7,179,163,236,210,128,198,77,44,61,106,21,136),(8,180,164,237,211,129,199,78,45,62,107,22,137),(9,181,165,238,212,130,200,79,46,63,108,23,138),(10,182,166,239,213,131,201,80,47,64,109,24,139),(11,183,167,240,214,132,202,81,48,65,110,25,140),(12,184,168,241,215,133,203,82,49,66,111,26,141),(13,185,169,242,216,115,204,83,50,67,112,27,142),(14,186,170,243,217,116,205,84,51,68,113,28,143),(15,187,171,244,218,117,206,85,52,69,114,29,144),(16,188,153,245,219,118,207,86,53,70,96,30,145),(17,189,154,246,220,119,208,87,54,71,97,31,146),(18,190,155,247,221,120,209,88,55,72,98,32,147),(19,172,156,229,222,121,191,89,56,73,99,33,148)], [(1,149),(2,150),(3,151),(4,152),(5,134),(6,135),(7,136),(8,137),(9,138),(10,139),(11,140),(12,141),(13,142),(14,143),(15,144),(16,145),(17,146),(18,147),(19,148),(20,178),(21,179),(22,180),(23,181),(24,182),(25,183),(26,184),(27,185),(28,186),(29,187),(30,188),(31,189),(32,190),(33,172),(34,173),(35,174),(36,175),(37,176),(38,177),(39,224),(40,225),(41,226),(42,227),(43,228),(44,210),(45,211),(46,212),(47,213),(48,214),(49,215),(50,216),(51,217),(52,218),(53,219),(54,220),(55,221),(56,222),(57,223),(58,233),(59,234),(60,235),(61,236),(62,237),(63,238),(64,239),(65,240),(66,241),(67,242),(68,243),(69,244),(70,245),(71,246),(72,247),(73,229),(74,230),(75,231),(76,232),(77,128),(78,129),(79,130),(80,131),(81,132),(82,133),(83,115),(84,116),(85,117),(86,118),(87,119),(88,120),(89,121),(90,122),(91,123),(92,124),(93,125),(94,126),(95,127),(96,153),(97,154),(98,155),(99,156),(100,157),(101,158),(102,159),(103,160),(104,161),(105,162),(106,163),(107,164),(108,165),(109,166),(110,167),(111,168),(112,169),(113,170),(114,171)])

152 conjugacy classes

class 1  2 13A···13F19A···19R38A···38R247A···247DD
order1213···1319···1938···38247···247
size1132···21···113···132···2

152 irreducible representations

dim111122
type+++
imageC1C2C19C38D13C19×D13
kernelC19×D13C247D13C13C19C1
# reps1118186108

Matrix representation of C19×D13 in GL2(𝔽1483) generated by

7920
0792
,
111
238561
,
560237
967923
G:=sub<GL(2,GF(1483))| [792,0,0,792],[11,238,1,561],[560,967,237,923] >;

C19×D13 in GAP, Magma, Sage, TeX

C_{19}\times D_{13}
% in TeX

G:=Group("C19xD13");
// GroupNames label

G:=SmallGroup(494,1);
// by ID

G=gap.SmallGroup(494,1);
# by ID

G:=PCGroup([3,-2,-19,-13,4106]);
// Polycyclic

G:=Group<a,b,c|a^19=b^13=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C19×D13 in TeX

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