metabelian, supersoluble, monomial, A-group
Aliases: C92⋊8S3, C9⋊(C9⋊S3), C3⋊(C9⋊D9), (C3×C9)⋊11D9, (C3×C92)⋊5C2, (C32×C9).27S3, C32.18(C9⋊S3), C33.49(C3⋊S3), C3.1(C32⋊4D9), C32.9(C33⋊C2), (C3×C9).20(C3⋊S3), SmallGroup(486,180)
Series: Derived ►Chief ►Lower central ►Upper central
| C3×C92 — C92⋊8S3 |
Generators and relations for C92⋊8S3
G = < a,b,c,d | a9=b9=c3=d2=1, ab=ba, ac=ca, dad=a-1, bc=cb, dbd=b-1, dcd=c-1 >
Subgroups: 3226 in 252 conjugacy classes, 127 normal (5 characteristic)
C1, C2, C3, S3, C9, C32, C32, D9, C3⋊S3, C3×C9, C33, C9⋊S3, C33⋊C2, C92, C32×C9, C9⋊D9, C32⋊4D9, C3×C92, C92⋊8S3
Quotients: C1, C2, S3, D9, C3⋊S3, C9⋊S3, C33⋊C2, C9⋊D9, C32⋊4D9, C92⋊8S3
►On 243 points
Generators in S243
(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)
(1 53 143 34 149 185 59 236 74)(2 54 144 35 150 186 60 237 75)(3 46 136 36 151 187 61 238 76)(4 47 137 28 152 188 62 239 77)(5 48 138 29 153 189 63 240 78)(6 49 139 30 145 181 55 241 79)(7 50 140 31 146 182 56 242 80)(8 51 141 32 147 183 57 243 81)(9 52 142 33 148 184 58 235 73)(10 154 101 115 195 26 229 40 208)(11 155 102 116 196 27 230 41 209)(12 156 103 117 197 19 231 42 210)(13 157 104 109 198 20 232 43 211)(14 158 105 110 190 21 233 44 212)(15 159 106 111 191 22 234 45 213)(16 160 107 112 192 23 226 37 214)(17 161 108 113 193 24 227 38 215)(18 162 100 114 194 25 228 39 216)(64 127 82 124 223 179 202 93 164)(65 128 83 125 224 180 203 94 165)(66 129 84 126 225 172 204 95 166)(67 130 85 118 217 173 205 96 167)(68 131 86 119 218 174 206 97 168)(69 132 87 120 219 175 207 98 169)(70 133 88 121 220 176 199 99 170)(71 134 89 122 221 177 200 91 171)(72 135 90 123 222 178 201 92 163)
(1 193 97)(2 194 98)(3 195 99)(4 196 91)(5 197 92)(6 198 93)(7 190 94)(8 191 95)(9 192 96)(10 121 187)(11 122 188)(12 123 189)(13 124 181)(14 125 182)(15 126 183)(16 118 184)(17 119 185)(18 120 186)(19 163 48)(20 164 49)(21 165 50)(22 166 51)(23 167 52)(24 168 53)(25 169 54)(26 170 46)(27 171 47)(28 41 134)(29 42 135)(30 43 127)(31 44 128)(32 45 129)(33 37 130)(34 38 131)(35 39 132)(36 40 133)(55 157 223)(56 158 224)(57 159 225)(58 160 217)(59 161 218)(60 162 219)(61 154 220)(62 155 221)(63 156 222)(64 139 232)(65 140 233)(66 141 234)(67 142 226)(68 143 227)(69 144 228)(70 136 229)(71 137 230)(72 138 231)(73 112 205)(74 113 206)(75 114 207)(76 115 199)(77 116 200)(78 117 201)(79 109 202)(80 110 203)(81 111 204)(82 145 211)(83 146 212)(84 147 213)(85 148 214)(86 149 215)(87 150 216)(88 151 208)(89 152 209)(90 153 210)(100 175 237)(101 176 238)(102 177 239)(103 178 240)(104 179 241)(105 180 242)(106 172 243)(107 173 235)(108 174 236)
(2 9)(3 8)(4 7)(5 6)(10 84)(11 83)(12 82)(13 90)(14 89)(15 88)(16 87)(17 86)(18 85)(19 202)(20 201)(21 200)(22 199)(23 207)(24 206)(25 205)(26 204)(27 203)(28 56)(29 55)(30 63)(31 62)(32 61)(33 60)(34 59)(35 58)(36 57)(37 219)(38 218)(39 217)(40 225)(41 224)(42 223)(43 222)(44 221)(45 220)(46 81)(47 80)(48 79)(49 78)(50 77)(51 76)(52 75)(53 74)(54 73)(64 103)(65 102)(66 101)(67 100)(68 108)(69 107)(70 106)(71 105)(72 104)(91 190)(92 198)(93 197)(94 196)(95 195)(96 194)(97 193)(98 192)(99 191)(109 163)(110 171)(111 170)(112 169)(113 168)(114 167)(115 166)(116 165)(117 164)(118 216)(119 215)(120 214)(121 213)(122 212)(123 211)(124 210)(125 209)(126 208)(127 156)(128 155)(129 154)(130 162)(131 161)(132 160)(133 159)(134 158)(135 157)(136 243)(137 242)(138 241)(139 240)(140 239)(141 238)(142 237)(143 236)(144 235)(145 189)(146 188)(147 187)(148 186)(149 185)(150 184)(151 183)(152 182)(153 181)(172 229)(173 228)(174 227)(175 226)(176 234)(177 233)(178 232)(179 231)(180 230)
G:=sub<Sym(243)| (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), (1,53,143,34,149,185,59,236,74)(2,54,144,35,150,186,60,237,75)(3,46,136,36,151,187,61,238,76)(4,47,137,28,152,188,62,239,77)(5,48,138,29,153,189,63,240,78)(6,49,139,30,145,181,55,241,79)(7,50,140,31,146,182,56,242,80)(8,51,141,32,147,183,57,243,81)(9,52,142,33,148,184,58,235,73)(10,154,101,115,195,26,229,40,208)(11,155,102,116,196,27,230,41,209)(12,156,103,117,197,19,231,42,210)(13,157,104,109,198,20,232,43,211)(14,158,105,110,190,21,233,44,212)(15,159,106,111,191,22,234,45,213)(16,160,107,112,192,23,226,37,214)(17,161,108,113,193,24,227,38,215)(18,162,100,114,194,25,228,39,216)(64,127,82,124,223,179,202,93,164)(65,128,83,125,224,180,203,94,165)(66,129,84,126,225,172,204,95,166)(67,130,85,118,217,173,205,96,167)(68,131,86,119,218,174,206,97,168)(69,132,87,120,219,175,207,98,169)(70,133,88,121,220,176,199,99,170)(71,134,89,122,221,177,200,91,171)(72,135,90,123,222,178,201,92,163), (1,193,97)(2,194,98)(3,195,99)(4,196,91)(5,197,92)(6,198,93)(7,190,94)(8,191,95)(9,192,96)(10,121,187)(11,122,188)(12,123,189)(13,124,181)(14,125,182)(15,126,183)(16,118,184)(17,119,185)(18,120,186)(19,163,48)(20,164,49)(21,165,50)(22,166,51)(23,167,52)(24,168,53)(25,169,54)(26,170,46)(27,171,47)(28,41,134)(29,42,135)(30,43,127)(31,44,128)(32,45,129)(33,37,130)(34,38,131)(35,39,132)(36,40,133)(55,157,223)(56,158,224)(57,159,225)(58,160,217)(59,161,218)(60,162,219)(61,154,220)(62,155,221)(63,156,222)(64,139,232)(65,140,233)(66,141,234)(67,142,226)(68,143,227)(69,144,228)(70,136,229)(71,137,230)(72,138,231)(73,112,205)(74,113,206)(75,114,207)(76,115,199)(77,116,200)(78,117,201)(79,109,202)(80,110,203)(81,111,204)(82,145,211)(83,146,212)(84,147,213)(85,148,214)(86,149,215)(87,150,216)(88,151,208)(89,152,209)(90,153,210)(100,175,237)(101,176,238)(102,177,239)(103,178,240)(104,179,241)(105,180,242)(106,172,243)(107,173,235)(108,174,236), (2,9)(3,8)(4,7)(5,6)(10,84)(11,83)(12,82)(13,90)(14,89)(15,88)(16,87)(17,86)(18,85)(19,202)(20,201)(21,200)(22,199)(23,207)(24,206)(25,205)(26,204)(27,203)(28,56)(29,55)(30,63)(31,62)(32,61)(33,60)(34,59)(35,58)(36,57)(37,219)(38,218)(39,217)(40,225)(41,224)(42,223)(43,222)(44,221)(45,220)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(64,103)(65,102)(66,101)(67,100)(68,108)(69,107)(70,106)(71,105)(72,104)(91,190)(92,198)(93,197)(94,196)(95,195)(96,194)(97,193)(98,192)(99,191)(109,163)(110,171)(111,170)(112,169)(113,168)(114,167)(115,166)(116,165)(117,164)(118,216)(119,215)(120,214)(121,213)(122,212)(123,211)(124,210)(125,209)(126,208)(127,156)(128,155)(129,154)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(136,243)(137,242)(138,241)(139,240)(140,239)(141,238)(142,237)(143,236)(144,235)(145,189)(146,188)(147,187)(148,186)(149,185)(150,184)(151,183)(152,182)(153,181)(172,229)(173,228)(174,227)(175,226)(176,234)(177,233)(178,232)(179,231)(180,230)>;
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), (1,53,143,34,149,185,59,236,74)(2,54,144,35,150,186,60,237,75)(3,46,136,36,151,187,61,238,76)(4,47,137,28,152,188,62,239,77)(5,48,138,29,153,189,63,240,78)(6,49,139,30,145,181,55,241,79)(7,50,140,31,146,182,56,242,80)(8,51,141,32,147,183,57,243,81)(9,52,142,33,148,184,58,235,73)(10,154,101,115,195,26,229,40,208)(11,155,102,116,196,27,230,41,209)(12,156,103,117,197,19,231,42,210)(13,157,104,109,198,20,232,43,211)(14,158,105,110,190,21,233,44,212)(15,159,106,111,191,22,234,45,213)(16,160,107,112,192,23,226,37,214)(17,161,108,113,193,24,227,38,215)(18,162,100,114,194,25,228,39,216)(64,127,82,124,223,179,202,93,164)(65,128,83,125,224,180,203,94,165)(66,129,84,126,225,172,204,95,166)(67,130,85,118,217,173,205,96,167)(68,131,86,119,218,174,206,97,168)(69,132,87,120,219,175,207,98,169)(70,133,88,121,220,176,199,99,170)(71,134,89,122,221,177,200,91,171)(72,135,90,123,222,178,201,92,163), (1,193,97)(2,194,98)(3,195,99)(4,196,91)(5,197,92)(6,198,93)(7,190,94)(8,191,95)(9,192,96)(10,121,187)(11,122,188)(12,123,189)(13,124,181)(14,125,182)(15,126,183)(16,118,184)(17,119,185)(18,120,186)(19,163,48)(20,164,49)(21,165,50)(22,166,51)(23,167,52)(24,168,53)(25,169,54)(26,170,46)(27,171,47)(28,41,134)(29,42,135)(30,43,127)(31,44,128)(32,45,129)(33,37,130)(34,38,131)(35,39,132)(36,40,133)(55,157,223)(56,158,224)(57,159,225)(58,160,217)(59,161,218)(60,162,219)(61,154,220)(62,155,221)(63,156,222)(64,139,232)(65,140,233)(66,141,234)(67,142,226)(68,143,227)(69,144,228)(70,136,229)(71,137,230)(72,138,231)(73,112,205)(74,113,206)(75,114,207)(76,115,199)(77,116,200)(78,117,201)(79,109,202)(80,110,203)(81,111,204)(82,145,211)(83,146,212)(84,147,213)(85,148,214)(86,149,215)(87,150,216)(88,151,208)(89,152,209)(90,153,210)(100,175,237)(101,176,238)(102,177,239)(103,178,240)(104,179,241)(105,180,242)(106,172,243)(107,173,235)(108,174,236), (2,9)(3,8)(4,7)(5,6)(10,84)(11,83)(12,82)(13,90)(14,89)(15,88)(16,87)(17,86)(18,85)(19,202)(20,201)(21,200)(22,199)(23,207)(24,206)(25,205)(26,204)(27,203)(28,56)(29,55)(30,63)(31,62)(32,61)(33,60)(34,59)(35,58)(36,57)(37,219)(38,218)(39,217)(40,225)(41,224)(42,223)(43,222)(44,221)(45,220)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(64,103)(65,102)(66,101)(67,100)(68,108)(69,107)(70,106)(71,105)(72,104)(91,190)(92,198)(93,197)(94,196)(95,195)(96,194)(97,193)(98,192)(99,191)(109,163)(110,171)(111,170)(112,169)(113,168)(114,167)(115,166)(116,165)(117,164)(118,216)(119,215)(120,214)(121,213)(122,212)(123,211)(124,210)(125,209)(126,208)(127,156)(128,155)(129,154)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(136,243)(137,242)(138,241)(139,240)(140,239)(141,238)(142,237)(143,236)(144,235)(145,189)(146,188)(147,187)(148,186)(149,185)(150,184)(151,183)(152,182)(153,181)(172,229)(173,228)(174,227)(175,226)(176,234)(177,233)(178,232)(179,231)(180,230) );
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)], [(1,53,143,34,149,185,59,236,74),(2,54,144,35,150,186,60,237,75),(3,46,136,36,151,187,61,238,76),(4,47,137,28,152,188,62,239,77),(5,48,138,29,153,189,63,240,78),(6,49,139,30,145,181,55,241,79),(7,50,140,31,146,182,56,242,80),(8,51,141,32,147,183,57,243,81),(9,52,142,33,148,184,58,235,73),(10,154,101,115,195,26,229,40,208),(11,155,102,116,196,27,230,41,209),(12,156,103,117,197,19,231,42,210),(13,157,104,109,198,20,232,43,211),(14,158,105,110,190,21,233,44,212),(15,159,106,111,191,22,234,45,213),(16,160,107,112,192,23,226,37,214),(17,161,108,113,193,24,227,38,215),(18,162,100,114,194,25,228,39,216),(64,127,82,124,223,179,202,93,164),(65,128,83,125,224,180,203,94,165),(66,129,84,126,225,172,204,95,166),(67,130,85,118,217,173,205,96,167),(68,131,86,119,218,174,206,97,168),(69,132,87,120,219,175,207,98,169),(70,133,88,121,220,176,199,99,170),(71,134,89,122,221,177,200,91,171),(72,135,90,123,222,178,201,92,163)], [(1,193,97),(2,194,98),(3,195,99),(4,196,91),(5,197,92),(6,198,93),(7,190,94),(8,191,95),(9,192,96),(10,121,187),(11,122,188),(12,123,189),(13,124,181),(14,125,182),(15,126,183),(16,118,184),(17,119,185),(18,120,186),(19,163,48),(20,164,49),(21,165,50),(22,166,51),(23,167,52),(24,168,53),(25,169,54),(26,170,46),(27,171,47),(28,41,134),(29,42,135),(30,43,127),(31,44,128),(32,45,129),(33,37,130),(34,38,131),(35,39,132),(36,40,133),(55,157,223),(56,158,224),(57,159,225),(58,160,217),(59,161,218),(60,162,219),(61,154,220),(62,155,221),(63,156,222),(64,139,232),(65,140,233),(66,141,234),(67,142,226),(68,143,227),(69,144,228),(70,136,229),(71,137,230),(72,138,231),(73,112,205),(74,113,206),(75,114,207),(76,115,199),(77,116,200),(78,117,201),(79,109,202),(80,110,203),(81,111,204),(82,145,211),(83,146,212),(84,147,213),(85,148,214),(86,149,215),(87,150,216),(88,151,208),(89,152,209),(90,153,210),(100,175,237),(101,176,238),(102,177,239),(103,178,240),(104,179,241),(105,180,242),(106,172,243),(107,173,235),(108,174,236)], [(2,9),(3,8),(4,7),(5,6),(10,84),(11,83),(12,82),(13,90),(14,89),(15,88),(16,87),(17,86),(18,85),(19,202),(20,201),(21,200),(22,199),(23,207),(24,206),(25,205),(26,204),(27,203),(28,56),(29,55),(30,63),(31,62),(32,61),(33,60),(34,59),(35,58),(36,57),(37,219),(38,218),(39,217),(40,225),(41,224),(42,223),(43,222),(44,221),(45,220),(46,81),(47,80),(48,79),(49,78),(50,77),(51,76),(52,75),(53,74),(54,73),(64,103),(65,102),(66,101),(67,100),(68,108),(69,107),(70,106),(71,105),(72,104),(91,190),(92,198),(93,197),(94,196),(95,195),(96,194),(97,193),(98,192),(99,191),(109,163),(110,171),(111,170),(112,169),(113,168),(114,167),(115,166),(116,165),(117,164),(118,216),(119,215),(120,214),(121,213),(122,212),(123,211),(124,210),(125,209),(126,208),(127,156),(128,155),(129,154),(130,162),(131,161),(132,160),(133,159),(134,158),(135,157),(136,243),(137,242),(138,241),(139,240),(140,239),(141,238),(142,237),(143,236),(144,235),(145,189),(146,188),(147,187),(148,186),(149,185),(150,184),(151,183),(152,182),(153,181),(172,229),(173,228),(174,227),(175,226),(176,234),(177,233),(178,232),(179,231),(180,230)]])
123 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3M | 9A | ··· | 9DD |
| order | 1 | 2 | 3 | ··· | 3 | 9 | ··· | 9 |
| size | 1 | 243 | 2 | ··· | 2 | 2 | ··· | 2 |
123 irreducible representations
| dim | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | S3 | S3 | D9 |
| kernel | C92⋊8S3 | C3×C92 | C92 | C32×C9 | C3×C9 |
| # reps | 1 | 1 | 9 | 4 | 108 |
Matrix representation of C92⋊8S3 ►in GL6(𝔽19)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 18 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 12 | 0 | 0 |
| 0 | 0 | 7 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 12 | 17 | 0 | 0 | 0 | 0 |
| 2 | 14 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 14 | 0 | 0 |
| 0 | 0 | 5 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 7 |
| 0 | 0 | 0 | 0 | 12 | 17 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 18 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 18 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 18 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 18 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(19))| [0,18,0,0,0,0,1,18,0,0,0,0,0,0,17,7,0,0,0,0,12,5,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[12,2,0,0,0,0,17,14,0,0,0,0,0,0,2,5,0,0,0,0,14,7,0,0,0,0,0,0,5,12,0,0,0,0,7,17],[0,18,0,0,0,0,1,18,0,0,0,0,0,0,18,1,0,0,0,0,18,0,0,0,0,0,0,0,18,1,0,0,0,0,18,0],[1,18,0,0,0,0,0,18,0,0,0,0,0,0,18,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
C92⋊8S3 in GAP, Magma, Sage, TeX
C_9^2\rtimes_8S_3
% in TeX
G:=Group("C9^2:8S3"); // GroupNames label
G:=SmallGroup(486,180);
// by ID
G=gap.SmallGroup(486,180);
# by ID
G:=PCGroup([6,-2,-3,-3,-3,-3,-3,697,655,3134,986,867,3244,11669]);
// Polycyclic
G:=Group<a,b,c,d|a^9=b^9=c^3=d^2=1,a*b=b*a,a*c=c*a,d*a*d=a^-1,b*c=c*b,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations