direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: Dic3×C2×C10, C30.56C23, (C2×C6)⋊3C20, C6⋊2(C2×C20), C30⋊12(C2×C4), (C2×C30)⋊11C4, C3⋊2(C22×C20), C15⋊13(C22×C4), (C2×C10).39D6, C23.3(C5×S3), (C22×C10).6S3, (C22×C6).3C10, C6.9(C22×C10), (C22×C30).7C2, C10.46(C22×S3), (C2×C30).51C22, C22.11(S3×C10), C2.2(S3×C2×C10), (C2×C6).12(C2×C10), SmallGroup(240,173)
Series: Derived ►Chief ►Lower central ►Upper central
| C3 — Dic3×C2×C10 |
Generators and relations for Dic3×C2×C10
G = < a,b,c,d | a2=b10=c6=1, d2=c3, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 152 in 108 conjugacy classes, 86 normal (14 characteristic)
C1, C2, C2, C3, C4, C22, C5, C6, C6, C2×C4, C23, C10, C10, Dic3, C2×C6, C15, C22×C4, C20, C2×C10, C2×Dic3, C22×C6, C30, C30, C2×C20, C22×C10, C22×Dic3, C5×Dic3, C2×C30, C22×C20, C10×Dic3, C22×C30, Dic3×C2×C10
Quotients: C1, C2, C4, C22, C5, S3, C2×C4, C23, C10, Dic3, D6, C22×C4, C20, C2×C10, C2×Dic3, C22×S3, C5×S3, C2×C20, C22×C10, C22×Dic3, C5×Dic3, S3×C10, C22×C20, C10×Dic3, S3×C2×C10, Dic3×C2×C10
►Regular action on 240 points
Generators in S240
(1 112)(2 113)(3 114)(4 115)(5 116)(6 117)(7 118)(8 119)(9 120)(10 111)(11 192)(12 193)(13 194)(14 195)(15 196)(16 197)(17 198)(18 199)(19 200)(20 191)(21 171)(22 172)(23 173)(24 174)(25 175)(26 176)(27 177)(28 178)(29 179)(30 180)(31 181)(32 182)(33 183)(34 184)(35 185)(36 186)(37 187)(38 188)(39 189)(40 190)(41 216)(42 217)(43 218)(44 219)(45 220)(46 211)(47 212)(48 213)(49 214)(50 215)(51 226)(52 227)(53 228)(54 229)(55 230)(56 221)(57 222)(58 223)(59 224)(60 225)(61 153)(62 154)(63 155)(64 156)(65 157)(66 158)(67 159)(68 160)(69 151)(70 152)(71 169)(72 170)(73 161)(74 162)(75 163)(76 164)(77 165)(78 166)(79 167)(80 168)(81 145)(82 146)(83 147)(84 148)(85 149)(86 150)(87 141)(88 142)(89 143)(90 144)(91 129)(92 130)(93 121)(94 122)(95 123)(96 124)(97 125)(98 126)(99 127)(100 128)(101 133)(102 134)(103 135)(104 136)(105 137)(106 138)(107 139)(108 140)(109 131)(110 132)(201 239)(202 240)(203 231)(204 232)(205 233)(206 234)(207 235)(208 236)(209 237)(210 238)
(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)
(1 94 71 90 62 109)(2 95 72 81 63 110)(3 96 73 82 64 101)(4 97 74 83 65 102)(5 98 75 84 66 103)(6 99 76 85 67 104)(7 100 77 86 68 105)(8 91 78 87 69 106)(9 92 79 88 70 107)(10 93 80 89 61 108)(11 50 233 55 33 23)(12 41 234 56 34 24)(13 42 235 57 35 25)(14 43 236 58 36 26)(15 44 237 59 37 27)(16 45 238 60 38 28)(17 46 239 51 39 29)(18 47 240 52 40 30)(19 48 231 53 31 21)(20 49 232 54 32 22)(111 121 168 143 153 140)(112 122 169 144 154 131)(113 123 170 145 155 132)(114 124 161 146 156 133)(115 125 162 147 157 134)(116 126 163 148 158 135)(117 127 164 149 159 136)(118 128 165 150 160 137)(119 129 166 141 151 138)(120 130 167 142 152 139)(171 200 213 203 228 181)(172 191 214 204 229 182)(173 192 215 205 230 183)(174 193 216 206 221 184)(175 194 217 207 222 185)(176 195 218 208 223 186)(177 196 219 209 224 187)(178 197 220 210 225 188)(179 198 211 201 226 189)(180 199 212 202 227 190)
(1 209 90 177)(2 210 81 178)(3 201 82 179)(4 202 83 180)(5 203 84 171)(6 204 85 172)(7 205 86 173)(8 206 87 174)(9 207 88 175)(10 208 89 176)(11 137 55 165)(12 138 56 166)(13 139 57 167)(14 140 58 168)(15 131 59 169)(16 132 60 170)(17 133 51 161)(18 134 52 162)(19 135 53 163)(20 136 54 164)(21 116 231 148)(22 117 232 149)(23 118 233 150)(24 119 234 141)(25 120 235 142)(26 111 236 143)(27 112 237 144)(28 113 238 145)(29 114 239 146)(30 115 240 147)(31 126 48 158)(32 127 49 159)(33 128 50 160)(34 129 41 151)(35 130 42 152)(36 121 43 153)(37 122 44 154)(38 123 45 155)(39 124 46 156)(40 125 47 157)(61 186 93 218)(62 187 94 219)(63 188 95 220)(64 189 96 211)(65 190 97 212)(66 181 98 213)(67 182 99 214)(68 183 100 215)(69 184 91 216)(70 185 92 217)(71 196 109 224)(72 197 110 225)(73 198 101 226)(74 199 102 227)(75 200 103 228)(76 191 104 229)(77 192 105 230)(78 193 106 221)(79 194 107 222)(80 195 108 223)
G:=sub<Sym(240)| (1,112)(2,113)(3,114)(4,115)(5,116)(6,117)(7,118)(8,119)(9,120)(10,111)(11,192)(12,193)(13,194)(14,195)(15,196)(16,197)(17,198)(18,199)(19,200)(20,191)(21,171)(22,172)(23,173)(24,174)(25,175)(26,176)(27,177)(28,178)(29,179)(30,180)(31,181)(32,182)(33,183)(34,184)(35,185)(36,186)(37,187)(38,188)(39,189)(40,190)(41,216)(42,217)(43,218)(44,219)(45,220)(46,211)(47,212)(48,213)(49,214)(50,215)(51,226)(52,227)(53,228)(54,229)(55,230)(56,221)(57,222)(58,223)(59,224)(60,225)(61,153)(62,154)(63,155)(64,156)(65,157)(66,158)(67,159)(68,160)(69,151)(70,152)(71,169)(72,170)(73,161)(74,162)(75,163)(76,164)(77,165)(78,166)(79,167)(80,168)(81,145)(82,146)(83,147)(84,148)(85,149)(86,150)(87,141)(88,142)(89,143)(90,144)(91,129)(92,130)(93,121)(94,122)(95,123)(96,124)(97,125)(98,126)(99,127)(100,128)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,139)(108,140)(109,131)(110,132)(201,239)(202,240)(203,231)(204,232)(205,233)(206,234)(207,235)(208,236)(209,237)(210,238), (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), (1,94,71,90,62,109)(2,95,72,81,63,110)(3,96,73,82,64,101)(4,97,74,83,65,102)(5,98,75,84,66,103)(6,99,76,85,67,104)(7,100,77,86,68,105)(8,91,78,87,69,106)(9,92,79,88,70,107)(10,93,80,89,61,108)(11,50,233,55,33,23)(12,41,234,56,34,24)(13,42,235,57,35,25)(14,43,236,58,36,26)(15,44,237,59,37,27)(16,45,238,60,38,28)(17,46,239,51,39,29)(18,47,240,52,40,30)(19,48,231,53,31,21)(20,49,232,54,32,22)(111,121,168,143,153,140)(112,122,169,144,154,131)(113,123,170,145,155,132)(114,124,161,146,156,133)(115,125,162,147,157,134)(116,126,163,148,158,135)(117,127,164,149,159,136)(118,128,165,150,160,137)(119,129,166,141,151,138)(120,130,167,142,152,139)(171,200,213,203,228,181)(172,191,214,204,229,182)(173,192,215,205,230,183)(174,193,216,206,221,184)(175,194,217,207,222,185)(176,195,218,208,223,186)(177,196,219,209,224,187)(178,197,220,210,225,188)(179,198,211,201,226,189)(180,199,212,202,227,190), (1,209,90,177)(2,210,81,178)(3,201,82,179)(4,202,83,180)(5,203,84,171)(6,204,85,172)(7,205,86,173)(8,206,87,174)(9,207,88,175)(10,208,89,176)(11,137,55,165)(12,138,56,166)(13,139,57,167)(14,140,58,168)(15,131,59,169)(16,132,60,170)(17,133,51,161)(18,134,52,162)(19,135,53,163)(20,136,54,164)(21,116,231,148)(22,117,232,149)(23,118,233,150)(24,119,234,141)(25,120,235,142)(26,111,236,143)(27,112,237,144)(28,113,238,145)(29,114,239,146)(30,115,240,147)(31,126,48,158)(32,127,49,159)(33,128,50,160)(34,129,41,151)(35,130,42,152)(36,121,43,153)(37,122,44,154)(38,123,45,155)(39,124,46,156)(40,125,47,157)(61,186,93,218)(62,187,94,219)(63,188,95,220)(64,189,96,211)(65,190,97,212)(66,181,98,213)(67,182,99,214)(68,183,100,215)(69,184,91,216)(70,185,92,217)(71,196,109,224)(72,197,110,225)(73,198,101,226)(74,199,102,227)(75,200,103,228)(76,191,104,229)(77,192,105,230)(78,193,106,221)(79,194,107,222)(80,195,108,223)>;
G:=Group( (1,112)(2,113)(3,114)(4,115)(5,116)(6,117)(7,118)(8,119)(9,120)(10,111)(11,192)(12,193)(13,194)(14,195)(15,196)(16,197)(17,198)(18,199)(19,200)(20,191)(21,171)(22,172)(23,173)(24,174)(25,175)(26,176)(27,177)(28,178)(29,179)(30,180)(31,181)(32,182)(33,183)(34,184)(35,185)(36,186)(37,187)(38,188)(39,189)(40,190)(41,216)(42,217)(43,218)(44,219)(45,220)(46,211)(47,212)(48,213)(49,214)(50,215)(51,226)(52,227)(53,228)(54,229)(55,230)(56,221)(57,222)(58,223)(59,224)(60,225)(61,153)(62,154)(63,155)(64,156)(65,157)(66,158)(67,159)(68,160)(69,151)(70,152)(71,169)(72,170)(73,161)(74,162)(75,163)(76,164)(77,165)(78,166)(79,167)(80,168)(81,145)(82,146)(83,147)(84,148)(85,149)(86,150)(87,141)(88,142)(89,143)(90,144)(91,129)(92,130)(93,121)(94,122)(95,123)(96,124)(97,125)(98,126)(99,127)(100,128)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,139)(108,140)(109,131)(110,132)(201,239)(202,240)(203,231)(204,232)(205,233)(206,234)(207,235)(208,236)(209,237)(210,238), (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), (1,94,71,90,62,109)(2,95,72,81,63,110)(3,96,73,82,64,101)(4,97,74,83,65,102)(5,98,75,84,66,103)(6,99,76,85,67,104)(7,100,77,86,68,105)(8,91,78,87,69,106)(9,92,79,88,70,107)(10,93,80,89,61,108)(11,50,233,55,33,23)(12,41,234,56,34,24)(13,42,235,57,35,25)(14,43,236,58,36,26)(15,44,237,59,37,27)(16,45,238,60,38,28)(17,46,239,51,39,29)(18,47,240,52,40,30)(19,48,231,53,31,21)(20,49,232,54,32,22)(111,121,168,143,153,140)(112,122,169,144,154,131)(113,123,170,145,155,132)(114,124,161,146,156,133)(115,125,162,147,157,134)(116,126,163,148,158,135)(117,127,164,149,159,136)(118,128,165,150,160,137)(119,129,166,141,151,138)(120,130,167,142,152,139)(171,200,213,203,228,181)(172,191,214,204,229,182)(173,192,215,205,230,183)(174,193,216,206,221,184)(175,194,217,207,222,185)(176,195,218,208,223,186)(177,196,219,209,224,187)(178,197,220,210,225,188)(179,198,211,201,226,189)(180,199,212,202,227,190), (1,209,90,177)(2,210,81,178)(3,201,82,179)(4,202,83,180)(5,203,84,171)(6,204,85,172)(7,205,86,173)(8,206,87,174)(9,207,88,175)(10,208,89,176)(11,137,55,165)(12,138,56,166)(13,139,57,167)(14,140,58,168)(15,131,59,169)(16,132,60,170)(17,133,51,161)(18,134,52,162)(19,135,53,163)(20,136,54,164)(21,116,231,148)(22,117,232,149)(23,118,233,150)(24,119,234,141)(25,120,235,142)(26,111,236,143)(27,112,237,144)(28,113,238,145)(29,114,239,146)(30,115,240,147)(31,126,48,158)(32,127,49,159)(33,128,50,160)(34,129,41,151)(35,130,42,152)(36,121,43,153)(37,122,44,154)(38,123,45,155)(39,124,46,156)(40,125,47,157)(61,186,93,218)(62,187,94,219)(63,188,95,220)(64,189,96,211)(65,190,97,212)(66,181,98,213)(67,182,99,214)(68,183,100,215)(69,184,91,216)(70,185,92,217)(71,196,109,224)(72,197,110,225)(73,198,101,226)(74,199,102,227)(75,200,103,228)(76,191,104,229)(77,192,105,230)(78,193,106,221)(79,194,107,222)(80,195,108,223) );
G=PermutationGroup([[(1,112),(2,113),(3,114),(4,115),(5,116),(6,117),(7,118),(8,119),(9,120),(10,111),(11,192),(12,193),(13,194),(14,195),(15,196),(16,197),(17,198),(18,199),(19,200),(20,191),(21,171),(22,172),(23,173),(24,174),(25,175),(26,176),(27,177),(28,178),(29,179),(30,180),(31,181),(32,182),(33,183),(34,184),(35,185),(36,186),(37,187),(38,188),(39,189),(40,190),(41,216),(42,217),(43,218),(44,219),(45,220),(46,211),(47,212),(48,213),(49,214),(50,215),(51,226),(52,227),(53,228),(54,229),(55,230),(56,221),(57,222),(58,223),(59,224),(60,225),(61,153),(62,154),(63,155),(64,156),(65,157),(66,158),(67,159),(68,160),(69,151),(70,152),(71,169),(72,170),(73,161),(74,162),(75,163),(76,164),(77,165),(78,166),(79,167),(80,168),(81,145),(82,146),(83,147),(84,148),(85,149),(86,150),(87,141),(88,142),(89,143),(90,144),(91,129),(92,130),(93,121),(94,122),(95,123),(96,124),(97,125),(98,126),(99,127),(100,128),(101,133),(102,134),(103,135),(104,136),(105,137),(106,138),(107,139),(108,140),(109,131),(110,132),(201,239),(202,240),(203,231),(204,232),(205,233),(206,234),(207,235),(208,236),(209,237),(210,238)], [(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)], [(1,94,71,90,62,109),(2,95,72,81,63,110),(3,96,73,82,64,101),(4,97,74,83,65,102),(5,98,75,84,66,103),(6,99,76,85,67,104),(7,100,77,86,68,105),(8,91,78,87,69,106),(9,92,79,88,70,107),(10,93,80,89,61,108),(11,50,233,55,33,23),(12,41,234,56,34,24),(13,42,235,57,35,25),(14,43,236,58,36,26),(15,44,237,59,37,27),(16,45,238,60,38,28),(17,46,239,51,39,29),(18,47,240,52,40,30),(19,48,231,53,31,21),(20,49,232,54,32,22),(111,121,168,143,153,140),(112,122,169,144,154,131),(113,123,170,145,155,132),(114,124,161,146,156,133),(115,125,162,147,157,134),(116,126,163,148,158,135),(117,127,164,149,159,136),(118,128,165,150,160,137),(119,129,166,141,151,138),(120,130,167,142,152,139),(171,200,213,203,228,181),(172,191,214,204,229,182),(173,192,215,205,230,183),(174,193,216,206,221,184),(175,194,217,207,222,185),(176,195,218,208,223,186),(177,196,219,209,224,187),(178,197,220,210,225,188),(179,198,211,201,226,189),(180,199,212,202,227,190)], [(1,209,90,177),(2,210,81,178),(3,201,82,179),(4,202,83,180),(5,203,84,171),(6,204,85,172),(7,205,86,173),(8,206,87,174),(9,207,88,175),(10,208,89,176),(11,137,55,165),(12,138,56,166),(13,139,57,167),(14,140,58,168),(15,131,59,169),(16,132,60,170),(17,133,51,161),(18,134,52,162),(19,135,53,163),(20,136,54,164),(21,116,231,148),(22,117,232,149),(23,118,233,150),(24,119,234,141),(25,120,235,142),(26,111,236,143),(27,112,237,144),(28,113,238,145),(29,114,239,146),(30,115,240,147),(31,126,48,158),(32,127,49,159),(33,128,50,160),(34,129,41,151),(35,130,42,152),(36,121,43,153),(37,122,44,154),(38,123,45,155),(39,124,46,156),(40,125,47,157),(61,186,93,218),(62,187,94,219),(63,188,95,220),(64,189,96,211),(65,190,97,212),(66,181,98,213),(67,182,99,214),(68,183,100,215),(69,184,91,216),(70,185,92,217),(71,196,109,224),(72,197,110,225),(73,198,101,226),(74,199,102,227),(75,200,103,228),(76,191,104,229),(77,192,105,230),(78,193,106,221),(79,194,107,222),(80,195,108,223)]])
Dic3×C2×C10 is a maximal subgroup of
C30.24C42 C23.26(S3×D5) (C2×C30).D4 C10.(C2×D12) C15⋊28(C4×D4) (C2×C6)⋊D20 (C2×C10)⋊8Dic6 S3×C22×C20
120 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | ··· | 4H | 5A | 5B | 5C | 5D | 6A | ··· | 6G | 10A | ··· | 10AB | 15A | 15B | 15C | 15D | 20A | ··· | 20AF | 30A | ··· | 30AB |
| order | 1 | 2 | ··· | 2 | 3 | 4 | ··· | 4 | 5 | 5 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 |
| size | 1 | 1 | ··· | 1 | 2 | 3 | ··· | 3 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 3 | ··· | 3 | 2 | ··· | 2 |
120 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | ||||||||
| image | C1 | C2 | C2 | C4 | C5 | C10 | C10 | C20 | S3 | Dic3 | D6 | C5×S3 | C5×Dic3 | S3×C10 |
| kernel | Dic3×C2×C10 | C10×Dic3 | C22×C30 | C2×C30 | C22×Dic3 | C2×Dic3 | C22×C6 | C2×C6 | C22×C10 | C2×C10 | C2×C10 | C23 | C22 | C22 |
| # reps | 1 | 6 | 1 | 8 | 4 | 24 | 4 | 32 | 1 | 4 | 3 | 4 | 16 | 12 |
Matrix representation of Dic3×C2×C10 ►in GL4(𝔽61) generated by
| 1 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 60 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 9 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 60 |
| 0 | 0 | 1 | 0 |
| 60 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 57 | 31 |
| 0 | 0 | 27 | 4 |
G:=sub<GL(4,GF(61))| [1,0,0,0,0,60,0,0,0,0,1,0,0,0,0,1],[60,0,0,0,0,60,0,0,0,0,9,0,0,0,0,9],[1,0,0,0,0,1,0,0,0,0,1,1,0,0,60,0],[60,0,0,0,0,1,0,0,0,0,57,27,0,0,31,4] >;
Dic3×C2×C10 in GAP, Magma, Sage, TeX
{\rm Dic}_3\times C_2\times C_{10} % in TeX
G:=Group("Dic3xC2xC10"); // GroupNames label
G:=SmallGroup(240,173);
// by ID
G=gap.SmallGroup(240,173);
# by ID
G:=PCGroup([6,-2,-2,-2,-5,-2,-3,240,5765]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^10=c^6=1,d^2=c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations