direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C6×Dic5, C30.46C23, (C2×C30)⋊9C4, (C2×C10)⋊8C12, C30⋊11(C2×C4), C10⋊3(C2×C12), C5⋊3(C22×C12), C15⋊12(C22×C4), (C2×C6).39D10, C23.3(C3×D5), (C22×C6).4D5, (C22×C10).5C6, C10.9(C22×C6), (C22×C30).5C2, C22.11(C6×D5), C6.46(C22×D5), (C2×C30).41C22, C2.2(D5×C2×C6), (C2×C10).12(C2×C6), SmallGroup(240,163)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — C2×C6×Dic5 |
Generators and relations for C2×C6×Dic5
G = < a,b,c,d | a2=b6=c10=1, d2=c5, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 196 in 108 conjugacy classes, 86 normal (14 characteristic)
C1, C2, C2, C3, C4, C22, C5, C6, C6, C2×C4, C23, C10, C10, C12, C2×C6, C15, C22×C4, Dic5, C2×C10, C2×C12, C22×C6, C30, C30, C2×Dic5, C22×C10, C22×C12, C3×Dic5, C2×C30, C22×Dic5, C6×Dic5, C22×C30, C2×C6×Dic5
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, C23, D5, C12, C2×C6, C22×C4, Dic5, D10, C2×C12, C22×C6, C3×D5, C2×Dic5, C22×D5, C22×C12, C3×Dic5, C6×D5, C22×Dic5, C6×Dic5, D5×C2×C6, C2×C6×Dic5
►Regular action on 240 points
Generators in S240
(1 64)(2 65)(3 66)(4 67)(5 68)(6 69)(7 70)(8 61)(9 62)(10 63)(11 76)(12 77)(13 78)(14 79)(15 80)(16 71)(17 72)(18 73)(19 74)(20 75)(21 86)(22 87)(23 88)(24 89)(25 90)(26 81)(27 82)(28 83)(29 84)(30 85)(31 96)(32 97)(33 98)(34 99)(35 100)(36 91)(37 92)(38 93)(39 94)(40 95)(41 106)(42 107)(43 108)(44 109)(45 110)(46 101)(47 102)(48 103)(49 104)(50 105)(51 116)(52 117)(53 118)(54 119)(55 120)(56 111)(57 112)(58 113)(59 114)(60 115)(121 186)(122 187)(123 188)(124 189)(125 190)(126 181)(127 182)(128 183)(129 184)(130 185)(131 196)(132 197)(133 198)(134 199)(135 200)(136 191)(137 192)(138 193)(139 194)(140 195)(141 206)(142 207)(143 208)(144 209)(145 210)(146 201)(147 202)(148 203)(149 204)(150 205)(151 216)(152 217)(153 218)(154 219)(155 220)(156 211)(157 212)(158 213)(159 214)(160 215)(161 226)(162 227)(163 228)(164 229)(165 230)(166 221)(167 222)(168 223)(169 224)(170 225)(171 236)(172 237)(173 238)(174 239)(175 240)(176 231)(177 232)(178 233)(179 234)(180 235)
(1 44 29 34 19 54)(2 45 30 35 20 55)(3 46 21 36 11 56)(4 47 22 37 12 57)(5 48 23 38 13 58)(6 49 24 39 14 59)(7 50 25 40 15 60)(8 41 26 31 16 51)(9 42 27 32 17 52)(10 43 28 33 18 53)(61 106 81 96 71 116)(62 107 82 97 72 117)(63 108 83 98 73 118)(64 109 84 99 74 119)(65 110 85 100 75 120)(66 101 86 91 76 111)(67 102 87 92 77 112)(68 103 88 93 78 113)(69 104 89 94 79 114)(70 105 90 95 80 115)(121 166 141 156 131 176)(122 167 142 157 132 177)(123 168 143 158 133 178)(124 169 144 159 134 179)(125 170 145 160 135 180)(126 161 146 151 136 171)(127 162 147 152 137 172)(128 163 148 153 138 173)(129 164 149 154 139 174)(130 165 150 155 140 175)(181 226 201 216 191 236)(182 227 202 217 192 237)(183 228 203 218 193 238)(184 229 204 219 194 239)(185 230 205 220 195 240)(186 221 206 211 196 231)(187 222 207 212 197 232)(188 223 208 213 198 233)(189 224 209 214 199 234)(190 225 210 215 200 235)
(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)
(1 156 6 151)(2 155 7 160)(3 154 8 159)(4 153 9 158)(5 152 10 157)(11 164 16 169)(12 163 17 168)(13 162 18 167)(14 161 19 166)(15 170 20 165)(21 174 26 179)(22 173 27 178)(23 172 28 177)(24 171 29 176)(25 180 30 175)(31 124 36 129)(32 123 37 128)(33 122 38 127)(34 121 39 126)(35 130 40 125)(41 134 46 139)(42 133 47 138)(43 132 48 137)(44 131 49 136)(45 140 50 135)(51 144 56 149)(52 143 57 148)(53 142 58 147)(54 141 59 146)(55 150 60 145)(61 214 66 219)(62 213 67 218)(63 212 68 217)(64 211 69 216)(65 220 70 215)(71 224 76 229)(72 223 77 228)(73 222 78 227)(74 221 79 226)(75 230 80 225)(81 234 86 239)(82 233 87 238)(83 232 88 237)(84 231 89 236)(85 240 90 235)(91 184 96 189)(92 183 97 188)(93 182 98 187)(94 181 99 186)(95 190 100 185)(101 194 106 199)(102 193 107 198)(103 192 108 197)(104 191 109 196)(105 200 110 195)(111 204 116 209)(112 203 117 208)(113 202 118 207)(114 201 119 206)(115 210 120 205)
G:=sub<Sym(240)| (1,64)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,61)(9,62)(10,63)(11,76)(12,77)(13,78)(14,79)(15,80)(16,71)(17,72)(18,73)(19,74)(20,75)(21,86)(22,87)(23,88)(24,89)(25,90)(26,81)(27,82)(28,83)(29,84)(30,85)(31,96)(32,97)(33,98)(34,99)(35,100)(36,91)(37,92)(38,93)(39,94)(40,95)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(51,116)(52,117)(53,118)(54,119)(55,120)(56,111)(57,112)(58,113)(59,114)(60,115)(121,186)(122,187)(123,188)(124,189)(125,190)(126,181)(127,182)(128,183)(129,184)(130,185)(131,196)(132,197)(133,198)(134,199)(135,200)(136,191)(137,192)(138,193)(139,194)(140,195)(141,206)(142,207)(143,208)(144,209)(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,216)(152,217)(153,218)(154,219)(155,220)(156,211)(157,212)(158,213)(159,214)(160,215)(161,226)(162,227)(163,228)(164,229)(165,230)(166,221)(167,222)(168,223)(169,224)(170,225)(171,236)(172,237)(173,238)(174,239)(175,240)(176,231)(177,232)(178,233)(179,234)(180,235), (1,44,29,34,19,54)(2,45,30,35,20,55)(3,46,21,36,11,56)(4,47,22,37,12,57)(5,48,23,38,13,58)(6,49,24,39,14,59)(7,50,25,40,15,60)(8,41,26,31,16,51)(9,42,27,32,17,52)(10,43,28,33,18,53)(61,106,81,96,71,116)(62,107,82,97,72,117)(63,108,83,98,73,118)(64,109,84,99,74,119)(65,110,85,100,75,120)(66,101,86,91,76,111)(67,102,87,92,77,112)(68,103,88,93,78,113)(69,104,89,94,79,114)(70,105,90,95,80,115)(121,166,141,156,131,176)(122,167,142,157,132,177)(123,168,143,158,133,178)(124,169,144,159,134,179)(125,170,145,160,135,180)(126,161,146,151,136,171)(127,162,147,152,137,172)(128,163,148,153,138,173)(129,164,149,154,139,174)(130,165,150,155,140,175)(181,226,201,216,191,236)(182,227,202,217,192,237)(183,228,203,218,193,238)(184,229,204,219,194,239)(185,230,205,220,195,240)(186,221,206,211,196,231)(187,222,207,212,197,232)(188,223,208,213,198,233)(189,224,209,214,199,234)(190,225,210,215,200,235), (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), (1,156,6,151)(2,155,7,160)(3,154,8,159)(4,153,9,158)(5,152,10,157)(11,164,16,169)(12,163,17,168)(13,162,18,167)(14,161,19,166)(15,170,20,165)(21,174,26,179)(22,173,27,178)(23,172,28,177)(24,171,29,176)(25,180,30,175)(31,124,36,129)(32,123,37,128)(33,122,38,127)(34,121,39,126)(35,130,40,125)(41,134,46,139)(42,133,47,138)(43,132,48,137)(44,131,49,136)(45,140,50,135)(51,144,56,149)(52,143,57,148)(53,142,58,147)(54,141,59,146)(55,150,60,145)(61,214,66,219)(62,213,67,218)(63,212,68,217)(64,211,69,216)(65,220,70,215)(71,224,76,229)(72,223,77,228)(73,222,78,227)(74,221,79,226)(75,230,80,225)(81,234,86,239)(82,233,87,238)(83,232,88,237)(84,231,89,236)(85,240,90,235)(91,184,96,189)(92,183,97,188)(93,182,98,187)(94,181,99,186)(95,190,100,185)(101,194,106,199)(102,193,107,198)(103,192,108,197)(104,191,109,196)(105,200,110,195)(111,204,116,209)(112,203,117,208)(113,202,118,207)(114,201,119,206)(115,210,120,205)>;
G:=Group( (1,64)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,61)(9,62)(10,63)(11,76)(12,77)(13,78)(14,79)(15,80)(16,71)(17,72)(18,73)(19,74)(20,75)(21,86)(22,87)(23,88)(24,89)(25,90)(26,81)(27,82)(28,83)(29,84)(30,85)(31,96)(32,97)(33,98)(34,99)(35,100)(36,91)(37,92)(38,93)(39,94)(40,95)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(51,116)(52,117)(53,118)(54,119)(55,120)(56,111)(57,112)(58,113)(59,114)(60,115)(121,186)(122,187)(123,188)(124,189)(125,190)(126,181)(127,182)(128,183)(129,184)(130,185)(131,196)(132,197)(133,198)(134,199)(135,200)(136,191)(137,192)(138,193)(139,194)(140,195)(141,206)(142,207)(143,208)(144,209)(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,216)(152,217)(153,218)(154,219)(155,220)(156,211)(157,212)(158,213)(159,214)(160,215)(161,226)(162,227)(163,228)(164,229)(165,230)(166,221)(167,222)(168,223)(169,224)(170,225)(171,236)(172,237)(173,238)(174,239)(175,240)(176,231)(177,232)(178,233)(179,234)(180,235), (1,44,29,34,19,54)(2,45,30,35,20,55)(3,46,21,36,11,56)(4,47,22,37,12,57)(5,48,23,38,13,58)(6,49,24,39,14,59)(7,50,25,40,15,60)(8,41,26,31,16,51)(9,42,27,32,17,52)(10,43,28,33,18,53)(61,106,81,96,71,116)(62,107,82,97,72,117)(63,108,83,98,73,118)(64,109,84,99,74,119)(65,110,85,100,75,120)(66,101,86,91,76,111)(67,102,87,92,77,112)(68,103,88,93,78,113)(69,104,89,94,79,114)(70,105,90,95,80,115)(121,166,141,156,131,176)(122,167,142,157,132,177)(123,168,143,158,133,178)(124,169,144,159,134,179)(125,170,145,160,135,180)(126,161,146,151,136,171)(127,162,147,152,137,172)(128,163,148,153,138,173)(129,164,149,154,139,174)(130,165,150,155,140,175)(181,226,201,216,191,236)(182,227,202,217,192,237)(183,228,203,218,193,238)(184,229,204,219,194,239)(185,230,205,220,195,240)(186,221,206,211,196,231)(187,222,207,212,197,232)(188,223,208,213,198,233)(189,224,209,214,199,234)(190,225,210,215,200,235), (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), (1,156,6,151)(2,155,7,160)(3,154,8,159)(4,153,9,158)(5,152,10,157)(11,164,16,169)(12,163,17,168)(13,162,18,167)(14,161,19,166)(15,170,20,165)(21,174,26,179)(22,173,27,178)(23,172,28,177)(24,171,29,176)(25,180,30,175)(31,124,36,129)(32,123,37,128)(33,122,38,127)(34,121,39,126)(35,130,40,125)(41,134,46,139)(42,133,47,138)(43,132,48,137)(44,131,49,136)(45,140,50,135)(51,144,56,149)(52,143,57,148)(53,142,58,147)(54,141,59,146)(55,150,60,145)(61,214,66,219)(62,213,67,218)(63,212,68,217)(64,211,69,216)(65,220,70,215)(71,224,76,229)(72,223,77,228)(73,222,78,227)(74,221,79,226)(75,230,80,225)(81,234,86,239)(82,233,87,238)(83,232,88,237)(84,231,89,236)(85,240,90,235)(91,184,96,189)(92,183,97,188)(93,182,98,187)(94,181,99,186)(95,190,100,185)(101,194,106,199)(102,193,107,198)(103,192,108,197)(104,191,109,196)(105,200,110,195)(111,204,116,209)(112,203,117,208)(113,202,118,207)(114,201,119,206)(115,210,120,205) );
G=PermutationGroup([[(1,64),(2,65),(3,66),(4,67),(5,68),(6,69),(7,70),(8,61),(9,62),(10,63),(11,76),(12,77),(13,78),(14,79),(15,80),(16,71),(17,72),(18,73),(19,74),(20,75),(21,86),(22,87),(23,88),(24,89),(25,90),(26,81),(27,82),(28,83),(29,84),(30,85),(31,96),(32,97),(33,98),(34,99),(35,100),(36,91),(37,92),(38,93),(39,94),(40,95),(41,106),(42,107),(43,108),(44,109),(45,110),(46,101),(47,102),(48,103),(49,104),(50,105),(51,116),(52,117),(53,118),(54,119),(55,120),(56,111),(57,112),(58,113),(59,114),(60,115),(121,186),(122,187),(123,188),(124,189),(125,190),(126,181),(127,182),(128,183),(129,184),(130,185),(131,196),(132,197),(133,198),(134,199),(135,200),(136,191),(137,192),(138,193),(139,194),(140,195),(141,206),(142,207),(143,208),(144,209),(145,210),(146,201),(147,202),(148,203),(149,204),(150,205),(151,216),(152,217),(153,218),(154,219),(155,220),(156,211),(157,212),(158,213),(159,214),(160,215),(161,226),(162,227),(163,228),(164,229),(165,230),(166,221),(167,222),(168,223),(169,224),(170,225),(171,236),(172,237),(173,238),(174,239),(175,240),(176,231),(177,232),(178,233),(179,234),(180,235)], [(1,44,29,34,19,54),(2,45,30,35,20,55),(3,46,21,36,11,56),(4,47,22,37,12,57),(5,48,23,38,13,58),(6,49,24,39,14,59),(7,50,25,40,15,60),(8,41,26,31,16,51),(9,42,27,32,17,52),(10,43,28,33,18,53),(61,106,81,96,71,116),(62,107,82,97,72,117),(63,108,83,98,73,118),(64,109,84,99,74,119),(65,110,85,100,75,120),(66,101,86,91,76,111),(67,102,87,92,77,112),(68,103,88,93,78,113),(69,104,89,94,79,114),(70,105,90,95,80,115),(121,166,141,156,131,176),(122,167,142,157,132,177),(123,168,143,158,133,178),(124,169,144,159,134,179),(125,170,145,160,135,180),(126,161,146,151,136,171),(127,162,147,152,137,172),(128,163,148,153,138,173),(129,164,149,154,139,174),(130,165,150,155,140,175),(181,226,201,216,191,236),(182,227,202,217,192,237),(183,228,203,218,193,238),(184,229,204,219,194,239),(185,230,205,220,195,240),(186,221,206,211,196,231),(187,222,207,212,197,232),(188,223,208,213,198,233),(189,224,209,214,199,234),(190,225,210,215,200,235)], [(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)], [(1,156,6,151),(2,155,7,160),(3,154,8,159),(4,153,9,158),(5,152,10,157),(11,164,16,169),(12,163,17,168),(13,162,18,167),(14,161,19,166),(15,170,20,165),(21,174,26,179),(22,173,27,178),(23,172,28,177),(24,171,29,176),(25,180,30,175),(31,124,36,129),(32,123,37,128),(33,122,38,127),(34,121,39,126),(35,130,40,125),(41,134,46,139),(42,133,47,138),(43,132,48,137),(44,131,49,136),(45,140,50,135),(51,144,56,149),(52,143,57,148),(53,142,58,147),(54,141,59,146),(55,150,60,145),(61,214,66,219),(62,213,67,218),(63,212,68,217),(64,211,69,216),(65,220,70,215),(71,224,76,229),(72,223,77,228),(73,222,78,227),(74,221,79,226),(75,230,80,225),(81,234,86,239),(82,233,87,238),(83,232,88,237),(84,231,89,236),(85,240,90,235),(91,184,96,189),(92,183,97,188),(93,182,98,187),(94,181,99,186),(95,190,100,185),(101,194,106,199),(102,193,107,198),(103,192,108,197),(104,191,109,196),(105,200,110,195),(111,204,116,209),(112,203,117,208),(113,202,118,207),(114,201,119,206),(115,210,120,205)]])
C2×C6×Dic5 is a maximal subgroup of
C30.24C42 C30.22M4(2) (C6×Dic5)⋊7C4 C30.(C2×D4) C6.D4⋊D5 C15⋊26(C4×D4) (C2×C10)⋊4D12 (C2×C30)⋊Q8 D5×C22×C12
96 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3A | 3B | 4A | ··· | 4H | 5A | 5B | 6A | ··· | 6N | 10A | ··· | 10N | 12A | ··· | 12P | 15A | 15B | 15C | 15D | 30A | ··· | 30AB |
| order | 1 | 2 | ··· | 2 | 3 | 3 | 4 | ··· | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 30 | ··· | 30 |
| size | 1 | 1 | ··· | 1 | 1 | 1 | 5 | ··· | 5 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 5 | ··· | 5 | 2 | 2 | 2 | 2 | 2 | ··· | 2 |
96 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | ||||||||
| image | C1 | C2 | C2 | C3 | C4 | C6 | C6 | C12 | D5 | Dic5 | D10 | C3×D5 | C3×Dic5 | C6×D5 |
| kernel | C2×C6×Dic5 | C6×Dic5 | C22×C30 | C22×Dic5 | C2×C30 | C2×Dic5 | C22×C10 | C2×C10 | C22×C6 | C2×C6 | C2×C6 | C23 | C22 | C22 |
| # reps | 1 | 6 | 1 | 2 | 8 | 12 | 2 | 16 | 2 | 8 | 6 | 4 | 16 | 12 |
Matrix representation of C2×C6×Dic5 ►in GL4(𝔽61) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 60 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 13 | 0 |
| 0 | 0 | 0 | 13 |
| 60 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 60 | 43 |
| 50 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 18 | 18 |
| 0 | 0 | 60 | 43 |
G:=sub<GL(4,GF(61))| [1,0,0,0,0,1,0,0,0,0,60,0,0,0,0,60],[60,0,0,0,0,60,0,0,0,0,13,0,0,0,0,13],[60,0,0,0,0,1,0,0,0,0,0,60,0,0,1,43],[50,0,0,0,0,1,0,0,0,0,18,60,0,0,18,43] >;
C2×C6×Dic5 in GAP, Magma, Sage, TeX
C_2\times C_6\times {\rm Dic}_5 % in TeX
G:=Group("C2xC6xDic5"); // GroupNames label
G:=SmallGroup(240,163);
// by ID
G=gap.SmallGroup(240,163);
# by ID
G:=PCGroup([6,-2,-2,-2,-3,-2,-5,144,6917]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^6=c^10=1,d^2=c^5,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