direct product, metabelian, supersoluble, monomial, A-group
Aliases: C2×C3⋊D39, C6⋊D39, C78⋊1S3, C3⋊2D78, C39⋊6D6, C32⋊6D26, C26⋊(C3⋊S3), (C3×C78)⋊1C2, (C3×C6)⋊2D13, (C3×C39)⋊6C22, C13⋊2(C2×C3⋊S3), SmallGroup(468,54)
Series: Derived ►Chief ►Lower central ►Upper central
| C3×C39 — C2×C3⋊D39 |
Generators and relations for C2×C3⋊D39
G = < a,b,c,d | a2=b3=c39=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >
Subgroups: 948 in 60 conjugacy classes, 27 normal (9 characteristic)
C1, C2, C2, C3, C22, S3, C6, C32, D6, C13, C3⋊S3, C3×C6, D13, C26, C2×C3⋊S3, C39, D26, D39, C78, C3×C39, D78, C3⋊D39, C3×C78, C2×C3⋊D39
Quotients: C1, C2, C22, S3, D6, C3⋊S3, D13, C2×C3⋊S3, D26, D39, D78, C3⋊D39, C2×C3⋊D39
►On 234 points
Generators in S234
(1 126)(2 127)(3 128)(4 129)(5 130)(6 131)(7 132)(8 133)(9 134)(10 135)(11 136)(12 137)(13 138)(14 139)(15 140)(16 141)(17 142)(18 143)(19 144)(20 145)(21 146)(22 147)(23 148)(24 149)(25 150)(26 151)(27 152)(28 153)(29 154)(30 155)(31 156)(32 118)(33 119)(34 120)(35 121)(36 122)(37 123)(38 124)(39 125)(40 172)(41 173)(42 174)(43 175)(44 176)(45 177)(46 178)(47 179)(48 180)(49 181)(50 182)(51 183)(52 184)(53 185)(54 186)(55 187)(56 188)(57 189)(58 190)(59 191)(60 192)(61 193)(62 194)(63 195)(64 157)(65 158)(66 159)(67 160)(68 161)(69 162)(70 163)(71 164)(72 165)(73 166)(74 167)(75 168)(76 169)(77 170)(78 171)(79 208)(80 209)(81 210)(82 211)(83 212)(84 213)(85 214)(86 215)(87 216)(88 217)(89 218)(90 219)(91 220)(92 221)(93 222)(94 223)(95 224)(96 225)(97 226)(98 227)(99 228)(100 229)(101 230)(102 231)(103 232)(104 233)(105 234)(106 196)(107 197)(108 198)(109 199)(110 200)(111 201)(112 202)(113 203)(114 204)(115 205)(116 206)(117 207)
(1 103 69)(2 104 70)(3 105 71)(4 106 72)(5 107 73)(6 108 74)(7 109 75)(8 110 76)(9 111 77)(10 112 78)(11 113 40)(12 114 41)(13 115 42)(14 116 43)(15 117 44)(16 79 45)(17 80 46)(18 81 47)(19 82 48)(20 83 49)(21 84 50)(22 85 51)(23 86 52)(24 87 53)(25 88 54)(26 89 55)(27 90 56)(28 91 57)(29 92 58)(30 93 59)(31 94 60)(32 95 61)(33 96 62)(34 97 63)(35 98 64)(36 99 65)(37 100 66)(38 101 67)(39 102 68)(118 224 193)(119 225 194)(120 226 195)(121 227 157)(122 228 158)(123 229 159)(124 230 160)(125 231 161)(126 232 162)(127 233 163)(128 234 164)(129 196 165)(130 197 166)(131 198 167)(132 199 168)(133 200 169)(134 201 170)(135 202 171)(136 203 172)(137 204 173)(138 205 174)(139 206 175)(140 207 176)(141 208 177)(142 209 178)(143 210 179)(144 211 180)(145 212 181)(146 213 182)(147 214 183)(148 215 184)(149 216 185)(150 217 186)(151 218 187)(152 219 188)(153 220 189)(154 221 190)(155 222 191)(156 223 192)
(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)
(1 39)(2 38)(3 37)(4 36)(5 35)(6 34)(7 33)(8 32)(9 31)(10 30)(11 29)(12 28)(13 27)(14 26)(15 25)(16 24)(17 23)(18 22)(19 21)(40 92)(41 91)(42 90)(43 89)(44 88)(45 87)(46 86)(47 85)(48 84)(49 83)(50 82)(51 81)(52 80)(53 79)(54 117)(55 116)(56 115)(57 114)(58 113)(59 112)(60 111)(61 110)(62 109)(63 108)(64 107)(65 106)(66 105)(67 104)(68 103)(69 102)(70 101)(71 100)(72 99)(73 98)(74 97)(75 96)(76 95)(77 94)(78 93)(118 133)(119 132)(120 131)(121 130)(122 129)(123 128)(124 127)(125 126)(134 156)(135 155)(136 154)(137 153)(138 152)(139 151)(140 150)(141 149)(142 148)(143 147)(144 146)(157 197)(158 196)(159 234)(160 233)(161 232)(162 231)(163 230)(164 229)(165 228)(166 227)(167 226)(168 225)(169 224)(170 223)(171 222)(172 221)(173 220)(174 219)(175 218)(176 217)(177 216)(178 215)(179 214)(180 213)(181 212)(182 211)(183 210)(184 209)(185 208)(186 207)(187 206)(188 205)(189 204)(190 203)(191 202)(192 201)(193 200)(194 199)(195 198)
G:=sub<Sym(234)| (1,126)(2,127)(3,128)(4,129)(5,130)(6,131)(7,132)(8,133)(9,134)(10,135)(11,136)(12,137)(13,138)(14,139)(15,140)(16,141)(17,142)(18,143)(19,144)(20,145)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,154)(30,155)(31,156)(32,118)(33,119)(34,120)(35,121)(36,122)(37,123)(38,124)(39,125)(40,172)(41,173)(42,174)(43,175)(44,176)(45,177)(46,178)(47,179)(48,180)(49,181)(50,182)(51,183)(52,184)(53,185)(54,186)(55,187)(56,188)(57,189)(58,190)(59,191)(60,192)(61,193)(62,194)(63,195)(64,157)(65,158)(66,159)(67,160)(68,161)(69,162)(70,163)(71,164)(72,165)(73,166)(74,167)(75,168)(76,169)(77,170)(78,171)(79,208)(80,209)(81,210)(82,211)(83,212)(84,213)(85,214)(86,215)(87,216)(88,217)(89,218)(90,219)(91,220)(92,221)(93,222)(94,223)(95,224)(96,225)(97,226)(98,227)(99,228)(100,229)(101,230)(102,231)(103,232)(104,233)(105,234)(106,196)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,203)(114,204)(115,205)(116,206)(117,207), (1,103,69)(2,104,70)(3,105,71)(4,106,72)(5,107,73)(6,108,74)(7,109,75)(8,110,76)(9,111,77)(10,112,78)(11,113,40)(12,114,41)(13,115,42)(14,116,43)(15,117,44)(16,79,45)(17,80,46)(18,81,47)(19,82,48)(20,83,49)(21,84,50)(22,85,51)(23,86,52)(24,87,53)(25,88,54)(26,89,55)(27,90,56)(28,91,57)(29,92,58)(30,93,59)(31,94,60)(32,95,61)(33,96,62)(34,97,63)(35,98,64)(36,99,65)(37,100,66)(38,101,67)(39,102,68)(118,224,193)(119,225,194)(120,226,195)(121,227,157)(122,228,158)(123,229,159)(124,230,160)(125,231,161)(126,232,162)(127,233,163)(128,234,164)(129,196,165)(130,197,166)(131,198,167)(132,199,168)(133,200,169)(134,201,170)(135,202,171)(136,203,172)(137,204,173)(138,205,174)(139,206,175)(140,207,176)(141,208,177)(142,209,178)(143,210,179)(144,211,180)(145,212,181)(146,213,182)(147,214,183)(148,215,184)(149,216,185)(150,217,186)(151,218,187)(152,219,188)(153,220,189)(154,221,190)(155,222,191)(156,223,192), (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), (1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)(40,92)(41,91)(42,90)(43,89)(44,88)(45,87)(46,86)(47,85)(48,84)(49,83)(50,82)(51,81)(52,80)(53,79)(54,117)(55,116)(56,115)(57,114)(58,113)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,106)(66,105)(67,104)(68,103)(69,102)(70,101)(71,100)(72,99)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(118,133)(119,132)(120,131)(121,130)(122,129)(123,128)(124,127)(125,126)(134,156)(135,155)(136,154)(137,153)(138,152)(139,151)(140,150)(141,149)(142,148)(143,147)(144,146)(157,197)(158,196)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)(180,213)(181,212)(182,211)(183,210)(184,209)(185,208)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)>;
G:=Group( (1,126)(2,127)(3,128)(4,129)(5,130)(6,131)(7,132)(8,133)(9,134)(10,135)(11,136)(12,137)(13,138)(14,139)(15,140)(16,141)(17,142)(18,143)(19,144)(20,145)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,154)(30,155)(31,156)(32,118)(33,119)(34,120)(35,121)(36,122)(37,123)(38,124)(39,125)(40,172)(41,173)(42,174)(43,175)(44,176)(45,177)(46,178)(47,179)(48,180)(49,181)(50,182)(51,183)(52,184)(53,185)(54,186)(55,187)(56,188)(57,189)(58,190)(59,191)(60,192)(61,193)(62,194)(63,195)(64,157)(65,158)(66,159)(67,160)(68,161)(69,162)(70,163)(71,164)(72,165)(73,166)(74,167)(75,168)(76,169)(77,170)(78,171)(79,208)(80,209)(81,210)(82,211)(83,212)(84,213)(85,214)(86,215)(87,216)(88,217)(89,218)(90,219)(91,220)(92,221)(93,222)(94,223)(95,224)(96,225)(97,226)(98,227)(99,228)(100,229)(101,230)(102,231)(103,232)(104,233)(105,234)(106,196)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,203)(114,204)(115,205)(116,206)(117,207), (1,103,69)(2,104,70)(3,105,71)(4,106,72)(5,107,73)(6,108,74)(7,109,75)(8,110,76)(9,111,77)(10,112,78)(11,113,40)(12,114,41)(13,115,42)(14,116,43)(15,117,44)(16,79,45)(17,80,46)(18,81,47)(19,82,48)(20,83,49)(21,84,50)(22,85,51)(23,86,52)(24,87,53)(25,88,54)(26,89,55)(27,90,56)(28,91,57)(29,92,58)(30,93,59)(31,94,60)(32,95,61)(33,96,62)(34,97,63)(35,98,64)(36,99,65)(37,100,66)(38,101,67)(39,102,68)(118,224,193)(119,225,194)(120,226,195)(121,227,157)(122,228,158)(123,229,159)(124,230,160)(125,231,161)(126,232,162)(127,233,163)(128,234,164)(129,196,165)(130,197,166)(131,198,167)(132,199,168)(133,200,169)(134,201,170)(135,202,171)(136,203,172)(137,204,173)(138,205,174)(139,206,175)(140,207,176)(141,208,177)(142,209,178)(143,210,179)(144,211,180)(145,212,181)(146,213,182)(147,214,183)(148,215,184)(149,216,185)(150,217,186)(151,218,187)(152,219,188)(153,220,189)(154,221,190)(155,222,191)(156,223,192), (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), (1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)(40,92)(41,91)(42,90)(43,89)(44,88)(45,87)(46,86)(47,85)(48,84)(49,83)(50,82)(51,81)(52,80)(53,79)(54,117)(55,116)(56,115)(57,114)(58,113)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,106)(66,105)(67,104)(68,103)(69,102)(70,101)(71,100)(72,99)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(118,133)(119,132)(120,131)(121,130)(122,129)(123,128)(124,127)(125,126)(134,156)(135,155)(136,154)(137,153)(138,152)(139,151)(140,150)(141,149)(142,148)(143,147)(144,146)(157,197)(158,196)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)(180,213)(181,212)(182,211)(183,210)(184,209)(185,208)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198) );
G=PermutationGroup([[(1,126),(2,127),(3,128),(4,129),(5,130),(6,131),(7,132),(8,133),(9,134),(10,135),(11,136),(12,137),(13,138),(14,139),(15,140),(16,141),(17,142),(18,143),(19,144),(20,145),(21,146),(22,147),(23,148),(24,149),(25,150),(26,151),(27,152),(28,153),(29,154),(30,155),(31,156),(32,118),(33,119),(34,120),(35,121),(36,122),(37,123),(38,124),(39,125),(40,172),(41,173),(42,174),(43,175),(44,176),(45,177),(46,178),(47,179),(48,180),(49,181),(50,182),(51,183),(52,184),(53,185),(54,186),(55,187),(56,188),(57,189),(58,190),(59,191),(60,192),(61,193),(62,194),(63,195),(64,157),(65,158),(66,159),(67,160),(68,161),(69,162),(70,163),(71,164),(72,165),(73,166),(74,167),(75,168),(76,169),(77,170),(78,171),(79,208),(80,209),(81,210),(82,211),(83,212),(84,213),(85,214),(86,215),(87,216),(88,217),(89,218),(90,219),(91,220),(92,221),(93,222),(94,223),(95,224),(96,225),(97,226),(98,227),(99,228),(100,229),(101,230),(102,231),(103,232),(104,233),(105,234),(106,196),(107,197),(108,198),(109,199),(110,200),(111,201),(112,202),(113,203),(114,204),(115,205),(116,206),(117,207)], [(1,103,69),(2,104,70),(3,105,71),(4,106,72),(5,107,73),(6,108,74),(7,109,75),(8,110,76),(9,111,77),(10,112,78),(11,113,40),(12,114,41),(13,115,42),(14,116,43),(15,117,44),(16,79,45),(17,80,46),(18,81,47),(19,82,48),(20,83,49),(21,84,50),(22,85,51),(23,86,52),(24,87,53),(25,88,54),(26,89,55),(27,90,56),(28,91,57),(29,92,58),(30,93,59),(31,94,60),(32,95,61),(33,96,62),(34,97,63),(35,98,64),(36,99,65),(37,100,66),(38,101,67),(39,102,68),(118,224,193),(119,225,194),(120,226,195),(121,227,157),(122,228,158),(123,229,159),(124,230,160),(125,231,161),(126,232,162),(127,233,163),(128,234,164),(129,196,165),(130,197,166),(131,198,167),(132,199,168),(133,200,169),(134,201,170),(135,202,171),(136,203,172),(137,204,173),(138,205,174),(139,206,175),(140,207,176),(141,208,177),(142,209,178),(143,210,179),(144,211,180),(145,212,181),(146,213,182),(147,214,183),(148,215,184),(149,216,185),(150,217,186),(151,218,187),(152,219,188),(153,220,189),(154,221,190),(155,222,191),(156,223,192)], [(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)], [(1,39),(2,38),(3,37),(4,36),(5,35),(6,34),(7,33),(8,32),(9,31),(10,30),(11,29),(12,28),(13,27),(14,26),(15,25),(16,24),(17,23),(18,22),(19,21),(40,92),(41,91),(42,90),(43,89),(44,88),(45,87),(46,86),(47,85),(48,84),(49,83),(50,82),(51,81),(52,80),(53,79),(54,117),(55,116),(56,115),(57,114),(58,113),(59,112),(60,111),(61,110),(62,109),(63,108),(64,107),(65,106),(66,105),(67,104),(68,103),(69,102),(70,101),(71,100),(72,99),(73,98),(74,97),(75,96),(76,95),(77,94),(78,93),(118,133),(119,132),(120,131),(121,130),(122,129),(123,128),(124,127),(125,126),(134,156),(135,155),(136,154),(137,153),(138,152),(139,151),(140,150),(141,149),(142,148),(143,147),(144,146),(157,197),(158,196),(159,234),(160,233),(161,232),(162,231),(163,230),(164,229),(165,228),(166,227),(167,226),(168,225),(169,224),(170,223),(171,222),(172,221),(173,220),(174,219),(175,218),(176,217),(177,216),(178,215),(179,214),(180,213),(181,212),(182,211),(183,210),(184,209),(185,208),(186,207),(187,206),(188,205),(189,204),(190,203),(191,202),(192,201),(193,200),(194,199),(195,198)]])
120 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 3C | 3D | 6A | 6B | 6C | 6D | 13A | ··· | 13F | 26A | ··· | 26F | 39A | ··· | 39AV | 78A | ··· | 78AV |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 6 | 6 | 6 | 6 | 13 | ··· | 13 | 26 | ··· | 26 | 39 | ··· | 39 | 78 | ··· | 78 |
| size | 1 | 1 | 117 | 117 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
120 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + |
| image | C1 | C2 | C2 | S3 | D6 | D13 | D26 | D39 | D78 |
| kernel | C2×C3⋊D39 | C3⋊D39 | C3×C78 | C78 | C39 | C3×C6 | C32 | C6 | C3 |
| # reps | 1 | 2 | 1 | 4 | 4 | 6 | 6 | 48 | 48 |
Matrix representation of C2×C3⋊D39 ►in GL4(𝔽79) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 78 | 0 |
| 0 | 0 | 0 | 78 |
| 44 | 6 | 0 | 0 |
| 78 | 34 | 0 | 0 |
| 0 | 0 | 62 | 73 |
| 0 | 0 | 6 | 16 |
| 69 | 7 | 0 | 0 |
| 12 | 31 | 0 | 0 |
| 0 | 0 | 10 | 7 |
| 0 | 0 | 72 | 11 |
| 4 | 48 | 0 | 0 |
| 54 | 75 | 0 | 0 |
| 0 | 0 | 49 | 27 |
| 0 | 0 | 34 | 30 |
G:=sub<GL(4,GF(79))| [1,0,0,0,0,1,0,0,0,0,78,0,0,0,0,78],[44,78,0,0,6,34,0,0,0,0,62,6,0,0,73,16],[69,12,0,0,7,31,0,0,0,0,10,72,0,0,7,11],[4,54,0,0,48,75,0,0,0,0,49,34,0,0,27,30] >;
C2×C3⋊D39 in GAP, Magma, Sage, TeX
C_2\times C_3\rtimes D_{39} % in TeX
G:=Group("C2xC3:D39"); // GroupNames label
G:=SmallGroup(468,54);
// by ID
G=gap.SmallGroup(468,54);
# by ID
G:=PCGroup([5,-2,-2,-3,-3,-13,122,483,10804]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^3=c^39=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations