direct product, metabelian, supersoluble, monomial, A-group
Aliases: C3⋊S3×C26, C78⋊3S3, C39⋊8D6, C6⋊(S3×C13), C3⋊2(S3×C26), (C3×C78)⋊5C2, (C3×C6)⋊2C26, C32⋊3(C2×C26), (C3×C39)⋊10C22, SmallGroup(468,53)
Series: Derived ►Chief ►Lower central ►Upper central
| C32 — C3⋊S3×C26 |
Generators and relations for C3⋊S3×C26
G = < a,b,c,d | a26=b3=c3=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >
Subgroups: 156 in 60 conjugacy classes, 30 normal (10 characteristic)
C1, C2, C2, C3, C22, S3, C6, C32, D6, C13, C3⋊S3, C3×C6, C26, C26, C2×C3⋊S3, C39, C2×C26, S3×C13, C78, C3×C39, S3×C26, C13×C3⋊S3, C3×C78, C3⋊S3×C26
Quotients: C1, C2, C22, S3, D6, C13, C3⋊S3, C26, C2×C3⋊S3, C2×C26, S3×C13, S3×C26, C13×C3⋊S3, C3⋊S3×C26
►On 234 points
Generators in S234
(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)
(1 136 172)(2 137 173)(3 138 174)(4 139 175)(5 140 176)(6 141 177)(7 142 178)(8 143 179)(9 144 180)(10 145 181)(11 146 182)(12 147 157)(13 148 158)(14 149 159)(15 150 160)(16 151 161)(17 152 162)(18 153 163)(19 154 164)(20 155 165)(21 156 166)(22 131 167)(23 132 168)(24 133 169)(25 134 170)(26 135 171)(27 122 191)(28 123 192)(29 124 193)(30 125 194)(31 126 195)(32 127 196)(33 128 197)(34 129 198)(35 130 199)(36 105 200)(37 106 201)(38 107 202)(39 108 203)(40 109 204)(41 110 205)(42 111 206)(43 112 207)(44 113 208)(45 114 183)(46 115 184)(47 116 185)(48 117 186)(49 118 187)(50 119 188)(51 120 189)(52 121 190)(53 83 222)(54 84 223)(55 85 224)(56 86 225)(57 87 226)(58 88 227)(59 89 228)(60 90 229)(61 91 230)(62 92 231)(63 93 232)(64 94 233)(65 95 234)(66 96 209)(67 97 210)(68 98 211)(69 99 212)(70 100 213)(71 101 214)(72 102 215)(73 103 216)(74 104 217)(75 79 218)(76 80 219)(77 81 220)(78 82 221)
(1 78 106)(2 53 107)(3 54 108)(4 55 109)(5 56 110)(6 57 111)(7 58 112)(8 59 113)(9 60 114)(10 61 115)(11 62 116)(12 63 117)(13 64 118)(14 65 119)(15 66 120)(16 67 121)(17 68 122)(18 69 123)(19 70 124)(20 71 125)(21 72 126)(22 73 127)(23 74 128)(24 75 129)(25 76 130)(26 77 105)(27 162 211)(28 163 212)(29 164 213)(30 165 214)(31 166 215)(32 167 216)(33 168 217)(34 169 218)(35 170 219)(36 171 220)(37 172 221)(38 173 222)(39 174 223)(40 175 224)(41 176 225)(42 177 226)(43 178 227)(44 179 228)(45 180 229)(46 181 230)(47 182 231)(48 157 232)(49 158 233)(50 159 234)(51 160 209)(52 161 210)(79 198 133)(80 199 134)(81 200 135)(82 201 136)(83 202 137)(84 203 138)(85 204 139)(86 205 140)(87 206 141)(88 207 142)(89 208 143)(90 183 144)(91 184 145)(92 185 146)(93 186 147)(94 187 148)(95 188 149)(96 189 150)(97 190 151)(98 191 152)(99 192 153)(100 193 154)(101 194 155)(102 195 156)(103 196 131)(104 197 132)
(1 14)(2 15)(3 16)(4 17)(5 18)(6 19)(7 20)(8 21)(9 22)(10 23)(11 24)(12 25)(13 26)(27 85)(28 86)(29 87)(30 88)(31 89)(32 90)(33 91)(34 92)(35 93)(36 94)(37 95)(38 96)(39 97)(40 98)(41 99)(42 100)(43 101)(44 102)(45 103)(46 104)(47 79)(48 80)(49 81)(50 82)(51 83)(52 84)(53 120)(54 121)(55 122)(56 123)(57 124)(58 125)(59 126)(60 127)(61 128)(62 129)(63 130)(64 105)(65 106)(66 107)(67 108)(68 109)(69 110)(70 111)(71 112)(72 113)(73 114)(74 115)(75 116)(76 117)(77 118)(78 119)(131 180)(132 181)(133 182)(134 157)(135 158)(136 159)(137 160)(138 161)(139 162)(140 163)(141 164)(142 165)(143 166)(144 167)(145 168)(146 169)(147 170)(148 171)(149 172)(150 173)(151 174)(152 175)(153 176)(154 177)(155 178)(156 179)(183 216)(184 217)(185 218)(186 219)(187 220)(188 221)(189 222)(190 223)(191 224)(192 225)(193 226)(194 227)(195 228)(196 229)(197 230)(198 231)(199 232)(200 233)(201 234)(202 209)(203 210)(204 211)(205 212)(206 213)(207 214)(208 215)
G:=sub<Sym(234)| (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), (1,136,172)(2,137,173)(3,138,174)(4,139,175)(5,140,176)(6,141,177)(7,142,178)(8,143,179)(9,144,180)(10,145,181)(11,146,182)(12,147,157)(13,148,158)(14,149,159)(15,150,160)(16,151,161)(17,152,162)(18,153,163)(19,154,164)(20,155,165)(21,156,166)(22,131,167)(23,132,168)(24,133,169)(25,134,170)(26,135,171)(27,122,191)(28,123,192)(29,124,193)(30,125,194)(31,126,195)(32,127,196)(33,128,197)(34,129,198)(35,130,199)(36,105,200)(37,106,201)(38,107,202)(39,108,203)(40,109,204)(41,110,205)(42,111,206)(43,112,207)(44,113,208)(45,114,183)(46,115,184)(47,116,185)(48,117,186)(49,118,187)(50,119,188)(51,120,189)(52,121,190)(53,83,222)(54,84,223)(55,85,224)(56,86,225)(57,87,226)(58,88,227)(59,89,228)(60,90,229)(61,91,230)(62,92,231)(63,93,232)(64,94,233)(65,95,234)(66,96,209)(67,97,210)(68,98,211)(69,99,212)(70,100,213)(71,101,214)(72,102,215)(73,103,216)(74,104,217)(75,79,218)(76,80,219)(77,81,220)(78,82,221), (1,78,106)(2,53,107)(3,54,108)(4,55,109)(5,56,110)(6,57,111)(7,58,112)(8,59,113)(9,60,114)(10,61,115)(11,62,116)(12,63,117)(13,64,118)(14,65,119)(15,66,120)(16,67,121)(17,68,122)(18,69,123)(19,70,124)(20,71,125)(21,72,126)(22,73,127)(23,74,128)(24,75,129)(25,76,130)(26,77,105)(27,162,211)(28,163,212)(29,164,213)(30,165,214)(31,166,215)(32,167,216)(33,168,217)(34,169,218)(35,170,219)(36,171,220)(37,172,221)(38,173,222)(39,174,223)(40,175,224)(41,176,225)(42,177,226)(43,178,227)(44,179,228)(45,180,229)(46,181,230)(47,182,231)(48,157,232)(49,158,233)(50,159,234)(51,160,209)(52,161,210)(79,198,133)(80,199,134)(81,200,135)(82,201,136)(83,202,137)(84,203,138)(85,204,139)(86,205,140)(87,206,141)(88,207,142)(89,208,143)(90,183,144)(91,184,145)(92,185,146)(93,186,147)(94,187,148)(95,188,149)(96,189,150)(97,190,151)(98,191,152)(99,192,153)(100,193,154)(101,194,155)(102,195,156)(103,196,131)(104,197,132), (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)(27,85)(28,86)(29,87)(30,88)(31,89)(32,90)(33,91)(34,92)(35,93)(36,94)(37,95)(38,96)(39,97)(40,98)(41,99)(42,100)(43,101)(44,102)(45,103)(46,104)(47,79)(48,80)(49,81)(50,82)(51,83)(52,84)(53,120)(54,121)(55,122)(56,123)(57,124)(58,125)(59,126)(60,127)(61,128)(62,129)(63,130)(64,105)(65,106)(66,107)(67,108)(68,109)(69,110)(70,111)(71,112)(72,113)(73,114)(74,115)(75,116)(76,117)(77,118)(78,119)(131,180)(132,181)(133,182)(134,157)(135,158)(136,159)(137,160)(138,161)(139,162)(140,163)(141,164)(142,165)(143,166)(144,167)(145,168)(146,169)(147,170)(148,171)(149,172)(150,173)(151,174)(152,175)(153,176)(154,177)(155,178)(156,179)(183,216)(184,217)(185,218)(186,219)(187,220)(188,221)(189,222)(190,223)(191,224)(192,225)(193,226)(194,227)(195,228)(196,229)(197,230)(198,231)(199,232)(200,233)(201,234)(202,209)(203,210)(204,211)(205,212)(206,213)(207,214)(208,215)>;
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), (1,136,172)(2,137,173)(3,138,174)(4,139,175)(5,140,176)(6,141,177)(7,142,178)(8,143,179)(9,144,180)(10,145,181)(11,146,182)(12,147,157)(13,148,158)(14,149,159)(15,150,160)(16,151,161)(17,152,162)(18,153,163)(19,154,164)(20,155,165)(21,156,166)(22,131,167)(23,132,168)(24,133,169)(25,134,170)(26,135,171)(27,122,191)(28,123,192)(29,124,193)(30,125,194)(31,126,195)(32,127,196)(33,128,197)(34,129,198)(35,130,199)(36,105,200)(37,106,201)(38,107,202)(39,108,203)(40,109,204)(41,110,205)(42,111,206)(43,112,207)(44,113,208)(45,114,183)(46,115,184)(47,116,185)(48,117,186)(49,118,187)(50,119,188)(51,120,189)(52,121,190)(53,83,222)(54,84,223)(55,85,224)(56,86,225)(57,87,226)(58,88,227)(59,89,228)(60,90,229)(61,91,230)(62,92,231)(63,93,232)(64,94,233)(65,95,234)(66,96,209)(67,97,210)(68,98,211)(69,99,212)(70,100,213)(71,101,214)(72,102,215)(73,103,216)(74,104,217)(75,79,218)(76,80,219)(77,81,220)(78,82,221), (1,78,106)(2,53,107)(3,54,108)(4,55,109)(5,56,110)(6,57,111)(7,58,112)(8,59,113)(9,60,114)(10,61,115)(11,62,116)(12,63,117)(13,64,118)(14,65,119)(15,66,120)(16,67,121)(17,68,122)(18,69,123)(19,70,124)(20,71,125)(21,72,126)(22,73,127)(23,74,128)(24,75,129)(25,76,130)(26,77,105)(27,162,211)(28,163,212)(29,164,213)(30,165,214)(31,166,215)(32,167,216)(33,168,217)(34,169,218)(35,170,219)(36,171,220)(37,172,221)(38,173,222)(39,174,223)(40,175,224)(41,176,225)(42,177,226)(43,178,227)(44,179,228)(45,180,229)(46,181,230)(47,182,231)(48,157,232)(49,158,233)(50,159,234)(51,160,209)(52,161,210)(79,198,133)(80,199,134)(81,200,135)(82,201,136)(83,202,137)(84,203,138)(85,204,139)(86,205,140)(87,206,141)(88,207,142)(89,208,143)(90,183,144)(91,184,145)(92,185,146)(93,186,147)(94,187,148)(95,188,149)(96,189,150)(97,190,151)(98,191,152)(99,192,153)(100,193,154)(101,194,155)(102,195,156)(103,196,131)(104,197,132), (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)(27,85)(28,86)(29,87)(30,88)(31,89)(32,90)(33,91)(34,92)(35,93)(36,94)(37,95)(38,96)(39,97)(40,98)(41,99)(42,100)(43,101)(44,102)(45,103)(46,104)(47,79)(48,80)(49,81)(50,82)(51,83)(52,84)(53,120)(54,121)(55,122)(56,123)(57,124)(58,125)(59,126)(60,127)(61,128)(62,129)(63,130)(64,105)(65,106)(66,107)(67,108)(68,109)(69,110)(70,111)(71,112)(72,113)(73,114)(74,115)(75,116)(76,117)(77,118)(78,119)(131,180)(132,181)(133,182)(134,157)(135,158)(136,159)(137,160)(138,161)(139,162)(140,163)(141,164)(142,165)(143,166)(144,167)(145,168)(146,169)(147,170)(148,171)(149,172)(150,173)(151,174)(152,175)(153,176)(154,177)(155,178)(156,179)(183,216)(184,217)(185,218)(186,219)(187,220)(188,221)(189,222)(190,223)(191,224)(192,225)(193,226)(194,227)(195,228)(196,229)(197,230)(198,231)(199,232)(200,233)(201,234)(202,209)(203,210)(204,211)(205,212)(206,213)(207,214)(208,215) );
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)], [(1,136,172),(2,137,173),(3,138,174),(4,139,175),(5,140,176),(6,141,177),(7,142,178),(8,143,179),(9,144,180),(10,145,181),(11,146,182),(12,147,157),(13,148,158),(14,149,159),(15,150,160),(16,151,161),(17,152,162),(18,153,163),(19,154,164),(20,155,165),(21,156,166),(22,131,167),(23,132,168),(24,133,169),(25,134,170),(26,135,171),(27,122,191),(28,123,192),(29,124,193),(30,125,194),(31,126,195),(32,127,196),(33,128,197),(34,129,198),(35,130,199),(36,105,200),(37,106,201),(38,107,202),(39,108,203),(40,109,204),(41,110,205),(42,111,206),(43,112,207),(44,113,208),(45,114,183),(46,115,184),(47,116,185),(48,117,186),(49,118,187),(50,119,188),(51,120,189),(52,121,190),(53,83,222),(54,84,223),(55,85,224),(56,86,225),(57,87,226),(58,88,227),(59,89,228),(60,90,229),(61,91,230),(62,92,231),(63,93,232),(64,94,233),(65,95,234),(66,96,209),(67,97,210),(68,98,211),(69,99,212),(70,100,213),(71,101,214),(72,102,215),(73,103,216),(74,104,217),(75,79,218),(76,80,219),(77,81,220),(78,82,221)], [(1,78,106),(2,53,107),(3,54,108),(4,55,109),(5,56,110),(6,57,111),(7,58,112),(8,59,113),(9,60,114),(10,61,115),(11,62,116),(12,63,117),(13,64,118),(14,65,119),(15,66,120),(16,67,121),(17,68,122),(18,69,123),(19,70,124),(20,71,125),(21,72,126),(22,73,127),(23,74,128),(24,75,129),(25,76,130),(26,77,105),(27,162,211),(28,163,212),(29,164,213),(30,165,214),(31,166,215),(32,167,216),(33,168,217),(34,169,218),(35,170,219),(36,171,220),(37,172,221),(38,173,222),(39,174,223),(40,175,224),(41,176,225),(42,177,226),(43,178,227),(44,179,228),(45,180,229),(46,181,230),(47,182,231),(48,157,232),(49,158,233),(50,159,234),(51,160,209),(52,161,210),(79,198,133),(80,199,134),(81,200,135),(82,201,136),(83,202,137),(84,203,138),(85,204,139),(86,205,140),(87,206,141),(88,207,142),(89,208,143),(90,183,144),(91,184,145),(92,185,146),(93,186,147),(94,187,148),(95,188,149),(96,189,150),(97,190,151),(98,191,152),(99,192,153),(100,193,154),(101,194,155),(102,195,156),(103,196,131),(104,197,132)], [(1,14),(2,15),(3,16),(4,17),(5,18),(6,19),(7,20),(8,21),(9,22),(10,23),(11,24),(12,25),(13,26),(27,85),(28,86),(29,87),(30,88),(31,89),(32,90),(33,91),(34,92),(35,93),(36,94),(37,95),(38,96),(39,97),(40,98),(41,99),(42,100),(43,101),(44,102),(45,103),(46,104),(47,79),(48,80),(49,81),(50,82),(51,83),(52,84),(53,120),(54,121),(55,122),(56,123),(57,124),(58,125),(59,126),(60,127),(61,128),(62,129),(63,130),(64,105),(65,106),(66,107),(67,108),(68,109),(69,110),(70,111),(71,112),(72,113),(73,114),(74,115),(75,116),(76,117),(77,118),(78,119),(131,180),(132,181),(133,182),(134,157),(135,158),(136,159),(137,160),(138,161),(139,162),(140,163),(141,164),(142,165),(143,166),(144,167),(145,168),(146,169),(147,170),(148,171),(149,172),(150,173),(151,174),(152,175),(153,176),(154,177),(155,178),(156,179),(183,216),(184,217),(185,218),(186,219),(187,220),(188,221),(189,222),(190,223),(191,224),(192,225),(193,226),(194,227),(195,228),(196,229),(197,230),(198,231),(199,232),(200,233),(201,234),(202,209),(203,210),(204,211),(205,212),(206,213),(207,214),(208,215)]])
156 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 3C | 3D | 6A | 6B | 6C | 6D | 13A | ··· | 13L | 26A | ··· | 26L | 26M | ··· | 26AJ | 39A | ··· | 39AV | 78A | ··· | 78AV |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 6 | 6 | 6 | 6 | 13 | ··· | 13 | 26 | ··· | 26 | 26 | ··· | 26 | 39 | ··· | 39 | 78 | ··· | 78 |
| size | 1 | 1 | 9 | 9 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 9 | ··· | 9 | 2 | ··· | 2 | 2 | ··· | 2 |
156 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C13 | C26 | C26 | S3 | D6 | S3×C13 | S3×C26 |
| kernel | C3⋊S3×C26 | C13×C3⋊S3 | C3×C78 | C2×C3⋊S3 | C3⋊S3 | C3×C6 | C78 | C39 | C6 | C3 |
| # reps | 1 | 2 | 1 | 12 | 24 | 12 | 4 | 4 | 48 | 48 |
Matrix representation of C3⋊S3×C26 ►in GL4(𝔽79) generated by
| 33 | 0 | 0 | 0 |
| 0 | 33 | 0 | 0 |
| 0 | 0 | 18 | 0 |
| 0 | 0 | 0 | 18 |
| 78 | 1 | 0 | 0 |
| 78 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 78 | 1 | 0 | 0 |
| 78 | 0 | 0 | 0 |
| 0 | 0 | 78 | 78 |
| 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 78 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 78 | 78 |
G:=sub<GL(4,GF(79))| [33,0,0,0,0,33,0,0,0,0,18,0,0,0,0,18],[78,78,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[78,78,0,0,1,0,0,0,0,0,78,1,0,0,78,0],[1,1,0,0,0,78,0,0,0,0,1,78,0,0,0,78] >;
C3⋊S3×C26 in GAP, Magma, Sage, TeX
C_3\rtimes S_3\times C_{26} % in TeX
G:=Group("C3:S3xC26"); // GroupNames label
G:=SmallGroup(468,53);
// by ID
G=gap.SmallGroup(468,53);
# by ID
G:=PCGroup([5,-2,-2,-13,-3,-3,2083,7804]);
// Polycyclic
G:=Group<a,b,c,d|a^26=b^3=c^3=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