metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊1D60, C12⋊4D20, C60⋊22D4, C20⋊4D12, C42⋊6D15, (C4×C20)⋊6S3, (C4×C60)⋊6C2, (C4×C12)⋊4D5, (C2×D60)⋊4C2, C2.5(C2×D60), C15⋊5(C4⋊1D4), C3⋊1(C20⋊4D4), C5⋊1(C4⋊D12), C6.31(C2×D20), (C2×C4).78D30, C30.260(C2×D4), C10.32(C2×D12), (C2×C20).389D6, (C2×C12).394D10, (C2×C30).271C23, (C2×C60).476C22, (C22×D15).1C22, C22.36(C22×D15), (C2×C6).267(C22×D5), (C2×C10).266(C22×S3), SmallGroup(480,839)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42⋊6D15
G = < a,b,c,d | a4=b4=c15=d2=1, ab=ba, ac=ca, dad=a-1, bc=cb, dbd=b-1, dcd=c-1 >
Subgroups: 1860 in 216 conjugacy classes, 71 normal (13 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, S3, C6, C2×C4, D4, C23, D5, C10, C12, D6, C2×C6, C15, C42, C2×D4, C20, D10, C2×C10, D12, C2×C12, C22×S3, D15, C30, C4⋊1D4, D20, C2×C20, C22×D5, C4×C12, C2×D12, C60, D30, C2×C30, C4×C20, C2×D20, C4⋊D12, D60, C2×C60, C22×D15, C20⋊4D4, C4×C60, C2×D60, C42⋊6D15
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, C2×D4, D10, D12, C22×S3, D15, C4⋊1D4, D20, C22×D5, C2×D12, D30, C2×D20, C4⋊D12, D60, C22×D15, C20⋊4D4, C2×D60, C42⋊6D15
►On 240 points
Generators in S240
(1 140 16 125)(2 141 17 126)(3 142 18 127)(4 143 19 128)(5 144 20 129)(6 145 21 130)(7 146 22 131)(8 147 23 132)(9 148 24 133)(10 149 25 134)(11 150 26 135)(12 136 27 121)(13 137 28 122)(14 138 29 123)(15 139 30 124)(31 177 57 155)(32 178 58 156)(33 179 59 157)(34 180 60 158)(35 166 46 159)(36 167 47 160)(37 168 48 161)(38 169 49 162)(39 170 50 163)(40 171 51 164)(41 172 52 165)(42 173 53 151)(43 174 54 152)(44 175 55 153)(45 176 56 154)(61 200 88 192)(62 201 89 193)(63 202 90 194)(64 203 76 195)(65 204 77 181)(66 205 78 182)(67 206 79 183)(68 207 80 184)(69 208 81 185)(70 209 82 186)(71 210 83 187)(72 196 84 188)(73 197 85 189)(74 198 86 190)(75 199 87 191)(91 226 120 211)(92 227 106 212)(93 228 107 213)(94 229 108 214)(95 230 109 215)(96 231 110 216)(97 232 111 217)(98 233 112 218)(99 234 113 219)(100 235 114 220)(101 236 115 221)(102 237 116 222)(103 238 117 223)(104 239 118 224)(105 240 119 225)
(1 92 35 65)(2 93 36 66)(3 94 37 67)(4 95 38 68)(5 96 39 69)(6 97 40 70)(7 98 41 71)(8 99 42 72)(9 100 43 73)(10 101 44 74)(11 102 45 75)(12 103 31 61)(13 104 32 62)(14 105 33 63)(15 91 34 64)(16 106 46 77)(17 107 47 78)(18 108 48 79)(19 109 49 80)(20 110 50 81)(21 111 51 82)(22 112 52 83)(23 113 53 84)(24 114 54 85)(25 115 55 86)(26 116 56 87)(27 117 57 88)(28 118 58 89)(29 119 59 90)(30 120 60 76)(121 223 155 192)(122 224 156 193)(123 225 157 194)(124 211 158 195)(125 212 159 181)(126 213 160 182)(127 214 161 183)(128 215 162 184)(129 216 163 185)(130 217 164 186)(131 218 165 187)(132 219 151 188)(133 220 152 189)(134 221 153 190)(135 222 154 191)(136 238 177 200)(137 239 178 201)(138 240 179 202)(139 226 180 203)(140 227 166 204)(141 228 167 205)(142 229 168 206)(143 230 169 207)(144 231 170 208)(145 232 171 209)(146 233 172 210)(147 234 173 196)(148 235 174 197)(149 236 175 198)(150 237 176 199)
(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)
(1 195)(2 194)(3 193)(4 192)(5 191)(6 190)(7 189)(8 188)(9 187)(10 186)(11 185)(12 184)(13 183)(14 182)(15 181)(16 203)(17 202)(18 201)(19 200)(20 199)(21 198)(22 197)(23 196)(24 210)(25 209)(26 208)(27 207)(28 206)(29 205)(30 204)(31 215)(32 214)(33 213)(34 212)(35 211)(36 225)(37 224)(38 223)(39 222)(40 221)(41 220)(42 219)(43 218)(44 217)(45 216)(46 226)(47 240)(48 239)(49 238)(50 237)(51 236)(52 235)(53 234)(54 233)(55 232)(56 231)(57 230)(58 229)(59 228)(60 227)(61 128)(62 127)(63 126)(64 125)(65 124)(66 123)(67 122)(68 121)(69 135)(70 134)(71 133)(72 132)(73 131)(74 130)(75 129)(76 140)(77 139)(78 138)(79 137)(80 136)(81 150)(82 149)(83 148)(84 147)(85 146)(86 145)(87 144)(88 143)(89 142)(90 141)(91 159)(92 158)(93 157)(94 156)(95 155)(96 154)(97 153)(98 152)(99 151)(100 165)(101 164)(102 163)(103 162)(104 161)(105 160)(106 180)(107 179)(108 178)(109 177)(110 176)(111 175)(112 174)(113 173)(114 172)(115 171)(116 170)(117 169)(118 168)(119 167)(120 166)
G:=sub<Sym(240)| (1,140,16,125)(2,141,17,126)(3,142,18,127)(4,143,19,128)(5,144,20,129)(6,145,21,130)(7,146,22,131)(8,147,23,132)(9,148,24,133)(10,149,25,134)(11,150,26,135)(12,136,27,121)(13,137,28,122)(14,138,29,123)(15,139,30,124)(31,177,57,155)(32,178,58,156)(33,179,59,157)(34,180,60,158)(35,166,46,159)(36,167,47,160)(37,168,48,161)(38,169,49,162)(39,170,50,163)(40,171,51,164)(41,172,52,165)(42,173,53,151)(43,174,54,152)(44,175,55,153)(45,176,56,154)(61,200,88,192)(62,201,89,193)(63,202,90,194)(64,203,76,195)(65,204,77,181)(66,205,78,182)(67,206,79,183)(68,207,80,184)(69,208,81,185)(70,209,82,186)(71,210,83,187)(72,196,84,188)(73,197,85,189)(74,198,86,190)(75,199,87,191)(91,226,120,211)(92,227,106,212)(93,228,107,213)(94,229,108,214)(95,230,109,215)(96,231,110,216)(97,232,111,217)(98,233,112,218)(99,234,113,219)(100,235,114,220)(101,236,115,221)(102,237,116,222)(103,238,117,223)(104,239,118,224)(105,240,119,225), (1,92,35,65)(2,93,36,66)(3,94,37,67)(4,95,38,68)(5,96,39,69)(6,97,40,70)(7,98,41,71)(8,99,42,72)(9,100,43,73)(10,101,44,74)(11,102,45,75)(12,103,31,61)(13,104,32,62)(14,105,33,63)(15,91,34,64)(16,106,46,77)(17,107,47,78)(18,108,48,79)(19,109,49,80)(20,110,50,81)(21,111,51,82)(22,112,52,83)(23,113,53,84)(24,114,54,85)(25,115,55,86)(26,116,56,87)(27,117,57,88)(28,118,58,89)(29,119,59,90)(30,120,60,76)(121,223,155,192)(122,224,156,193)(123,225,157,194)(124,211,158,195)(125,212,159,181)(126,213,160,182)(127,214,161,183)(128,215,162,184)(129,216,163,185)(130,217,164,186)(131,218,165,187)(132,219,151,188)(133,220,152,189)(134,221,153,190)(135,222,154,191)(136,238,177,200)(137,239,178,201)(138,240,179,202)(139,226,180,203)(140,227,166,204)(141,228,167,205)(142,229,168,206)(143,230,169,207)(144,231,170,208)(145,232,171,209)(146,233,172,210)(147,234,173,196)(148,235,174,197)(149,236,175,198)(150,237,176,199), (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), (1,195)(2,194)(3,193)(4,192)(5,191)(6,190)(7,189)(8,188)(9,187)(10,186)(11,185)(12,184)(13,183)(14,182)(15,181)(16,203)(17,202)(18,201)(19,200)(20,199)(21,198)(22,197)(23,196)(24,210)(25,209)(26,208)(27,207)(28,206)(29,205)(30,204)(31,215)(32,214)(33,213)(34,212)(35,211)(36,225)(37,224)(38,223)(39,222)(40,221)(41,220)(42,219)(43,218)(44,217)(45,216)(46,226)(47,240)(48,239)(49,238)(50,237)(51,236)(52,235)(53,234)(54,233)(55,232)(56,231)(57,230)(58,229)(59,228)(60,227)(61,128)(62,127)(63,126)(64,125)(65,124)(66,123)(67,122)(68,121)(69,135)(70,134)(71,133)(72,132)(73,131)(74,130)(75,129)(76,140)(77,139)(78,138)(79,137)(80,136)(81,150)(82,149)(83,148)(84,147)(85,146)(86,145)(87,144)(88,143)(89,142)(90,141)(91,159)(92,158)(93,157)(94,156)(95,155)(96,154)(97,153)(98,152)(99,151)(100,165)(101,164)(102,163)(103,162)(104,161)(105,160)(106,180)(107,179)(108,178)(109,177)(110,176)(111,175)(112,174)(113,173)(114,172)(115,171)(116,170)(117,169)(118,168)(119,167)(120,166)>;
G:=Group( (1,140,16,125)(2,141,17,126)(3,142,18,127)(4,143,19,128)(5,144,20,129)(6,145,21,130)(7,146,22,131)(8,147,23,132)(9,148,24,133)(10,149,25,134)(11,150,26,135)(12,136,27,121)(13,137,28,122)(14,138,29,123)(15,139,30,124)(31,177,57,155)(32,178,58,156)(33,179,59,157)(34,180,60,158)(35,166,46,159)(36,167,47,160)(37,168,48,161)(38,169,49,162)(39,170,50,163)(40,171,51,164)(41,172,52,165)(42,173,53,151)(43,174,54,152)(44,175,55,153)(45,176,56,154)(61,200,88,192)(62,201,89,193)(63,202,90,194)(64,203,76,195)(65,204,77,181)(66,205,78,182)(67,206,79,183)(68,207,80,184)(69,208,81,185)(70,209,82,186)(71,210,83,187)(72,196,84,188)(73,197,85,189)(74,198,86,190)(75,199,87,191)(91,226,120,211)(92,227,106,212)(93,228,107,213)(94,229,108,214)(95,230,109,215)(96,231,110,216)(97,232,111,217)(98,233,112,218)(99,234,113,219)(100,235,114,220)(101,236,115,221)(102,237,116,222)(103,238,117,223)(104,239,118,224)(105,240,119,225), (1,92,35,65)(2,93,36,66)(3,94,37,67)(4,95,38,68)(5,96,39,69)(6,97,40,70)(7,98,41,71)(8,99,42,72)(9,100,43,73)(10,101,44,74)(11,102,45,75)(12,103,31,61)(13,104,32,62)(14,105,33,63)(15,91,34,64)(16,106,46,77)(17,107,47,78)(18,108,48,79)(19,109,49,80)(20,110,50,81)(21,111,51,82)(22,112,52,83)(23,113,53,84)(24,114,54,85)(25,115,55,86)(26,116,56,87)(27,117,57,88)(28,118,58,89)(29,119,59,90)(30,120,60,76)(121,223,155,192)(122,224,156,193)(123,225,157,194)(124,211,158,195)(125,212,159,181)(126,213,160,182)(127,214,161,183)(128,215,162,184)(129,216,163,185)(130,217,164,186)(131,218,165,187)(132,219,151,188)(133,220,152,189)(134,221,153,190)(135,222,154,191)(136,238,177,200)(137,239,178,201)(138,240,179,202)(139,226,180,203)(140,227,166,204)(141,228,167,205)(142,229,168,206)(143,230,169,207)(144,231,170,208)(145,232,171,209)(146,233,172,210)(147,234,173,196)(148,235,174,197)(149,236,175,198)(150,237,176,199), (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), (1,195)(2,194)(3,193)(4,192)(5,191)(6,190)(7,189)(8,188)(9,187)(10,186)(11,185)(12,184)(13,183)(14,182)(15,181)(16,203)(17,202)(18,201)(19,200)(20,199)(21,198)(22,197)(23,196)(24,210)(25,209)(26,208)(27,207)(28,206)(29,205)(30,204)(31,215)(32,214)(33,213)(34,212)(35,211)(36,225)(37,224)(38,223)(39,222)(40,221)(41,220)(42,219)(43,218)(44,217)(45,216)(46,226)(47,240)(48,239)(49,238)(50,237)(51,236)(52,235)(53,234)(54,233)(55,232)(56,231)(57,230)(58,229)(59,228)(60,227)(61,128)(62,127)(63,126)(64,125)(65,124)(66,123)(67,122)(68,121)(69,135)(70,134)(71,133)(72,132)(73,131)(74,130)(75,129)(76,140)(77,139)(78,138)(79,137)(80,136)(81,150)(82,149)(83,148)(84,147)(85,146)(86,145)(87,144)(88,143)(89,142)(90,141)(91,159)(92,158)(93,157)(94,156)(95,155)(96,154)(97,153)(98,152)(99,151)(100,165)(101,164)(102,163)(103,162)(104,161)(105,160)(106,180)(107,179)(108,178)(109,177)(110,176)(111,175)(112,174)(113,173)(114,172)(115,171)(116,170)(117,169)(118,168)(119,167)(120,166) );
G=PermutationGroup([[(1,140,16,125),(2,141,17,126),(3,142,18,127),(4,143,19,128),(5,144,20,129),(6,145,21,130),(7,146,22,131),(8,147,23,132),(9,148,24,133),(10,149,25,134),(11,150,26,135),(12,136,27,121),(13,137,28,122),(14,138,29,123),(15,139,30,124),(31,177,57,155),(32,178,58,156),(33,179,59,157),(34,180,60,158),(35,166,46,159),(36,167,47,160),(37,168,48,161),(38,169,49,162),(39,170,50,163),(40,171,51,164),(41,172,52,165),(42,173,53,151),(43,174,54,152),(44,175,55,153),(45,176,56,154),(61,200,88,192),(62,201,89,193),(63,202,90,194),(64,203,76,195),(65,204,77,181),(66,205,78,182),(67,206,79,183),(68,207,80,184),(69,208,81,185),(70,209,82,186),(71,210,83,187),(72,196,84,188),(73,197,85,189),(74,198,86,190),(75,199,87,191),(91,226,120,211),(92,227,106,212),(93,228,107,213),(94,229,108,214),(95,230,109,215),(96,231,110,216),(97,232,111,217),(98,233,112,218),(99,234,113,219),(100,235,114,220),(101,236,115,221),(102,237,116,222),(103,238,117,223),(104,239,118,224),(105,240,119,225)], [(1,92,35,65),(2,93,36,66),(3,94,37,67),(4,95,38,68),(5,96,39,69),(6,97,40,70),(7,98,41,71),(8,99,42,72),(9,100,43,73),(10,101,44,74),(11,102,45,75),(12,103,31,61),(13,104,32,62),(14,105,33,63),(15,91,34,64),(16,106,46,77),(17,107,47,78),(18,108,48,79),(19,109,49,80),(20,110,50,81),(21,111,51,82),(22,112,52,83),(23,113,53,84),(24,114,54,85),(25,115,55,86),(26,116,56,87),(27,117,57,88),(28,118,58,89),(29,119,59,90),(30,120,60,76),(121,223,155,192),(122,224,156,193),(123,225,157,194),(124,211,158,195),(125,212,159,181),(126,213,160,182),(127,214,161,183),(128,215,162,184),(129,216,163,185),(130,217,164,186),(131,218,165,187),(132,219,151,188),(133,220,152,189),(134,221,153,190),(135,222,154,191),(136,238,177,200),(137,239,178,201),(138,240,179,202),(139,226,180,203),(140,227,166,204),(141,228,167,205),(142,229,168,206),(143,230,169,207),(144,231,170,208),(145,232,171,209),(146,233,172,210),(147,234,173,196),(148,235,174,197),(149,236,175,198),(150,237,176,199)], [(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)], [(1,195),(2,194),(3,193),(4,192),(5,191),(6,190),(7,189),(8,188),(9,187),(10,186),(11,185),(12,184),(13,183),(14,182),(15,181),(16,203),(17,202),(18,201),(19,200),(20,199),(21,198),(22,197),(23,196),(24,210),(25,209),(26,208),(27,207),(28,206),(29,205),(30,204),(31,215),(32,214),(33,213),(34,212),(35,211),(36,225),(37,224),(38,223),(39,222),(40,221),(41,220),(42,219),(43,218),(44,217),(45,216),(46,226),(47,240),(48,239),(49,238),(50,237),(51,236),(52,235),(53,234),(54,233),(55,232),(56,231),(57,230),(58,229),(59,228),(60,227),(61,128),(62,127),(63,126),(64,125),(65,124),(66,123),(67,122),(68,121),(69,135),(70,134),(71,133),(72,132),(73,131),(74,130),(75,129),(76,140),(77,139),(78,138),(79,137),(80,136),(81,150),(82,149),(83,148),(84,147),(85,146),(86,145),(87,144),(88,143),(89,142),(90,141),(91,159),(92,158),(93,157),(94,156),(95,155),(96,154),(97,153),(98,152),(99,151),(100,165),(101,164),(102,163),(103,162),(104,161),(105,160),(106,180),(107,179),(108,178),(109,177),(110,176),(111,175),(112,174),(113,173),(114,172),(115,171),(116,170),(117,169),(118,168),(119,167),(120,166)]])
126 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | ··· | 4F | 5A | 5B | 6A | 6B | 6C | 10A | ··· | 10F | 12A | ··· | 12L | 15A | 15B | 15C | 15D | 20A | ··· | 20X | 30A | ··· | 30L | 60A | ··· | 60AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | ··· | 4 | 5 | 5 | 6 | 6 | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 60 | 60 | 60 | 60 | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
126 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + |
| image | C1 | C2 | C2 | S3 | D4 | D5 | D6 | D10 | D12 | D15 | D20 | D30 | D60 |
| kernel | C42⋊6D15 | C4×C60 | C2×D60 | C4×C20 | C60 | C4×C12 | C2×C20 | C2×C12 | C20 | C42 | C12 | C2×C4 | C4 |
| # reps | 1 | 1 | 6 | 1 | 6 | 2 | 3 | 6 | 12 | 4 | 24 | 12 | 48 |
Matrix representation of C42⋊6D15 ►in GL6(𝔽61)
| 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 7 |
| 0 | 0 | 0 | 0 | 54 | 29 |
| 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 57 | 0 | 0 |
| 0 | 0 | 4 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 29 | 54 |
| 0 | 0 | 0 | 0 | 7 | 32 |
| 14 | 56 | 0 | 0 | 0 | 0 |
| 42 | 33 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 43 | 0 | 0 |
| 0 | 0 | 18 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 17 |
| 0 | 0 | 0 | 0 | 44 | 44 |
| 60 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 27 | 0 | 0 |
| 0 | 0 | 4 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 17 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(61))| [60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,32,54,0,0,0,0,7,29],[60,0,0,0,0,0,0,60,0,0,0,0,0,0,25,4,0,0,0,0,57,36,0,0,0,0,0,0,29,7,0,0,0,0,54,32],[14,42,0,0,0,0,56,33,0,0,0,0,0,0,60,18,0,0,0,0,43,18,0,0,0,0,0,0,60,44,0,0,0,0,17,44],[60,0,0,0,0,0,1,1,0,0,0,0,0,0,25,4,0,0,0,0,27,36,0,0,0,0,0,0,60,0,0,0,0,0,17,1] >;
C42⋊6D15 in GAP, Magma, Sage, TeX
C_4^2\rtimes_6D_{15} % in TeX
G:=Group("C4^2:6D15"); // GroupNames label
G:=SmallGroup(480,839);
// by ID
G=gap.SmallGroup(480,839);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,120,254,58,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^15=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