direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C5×C8.6D6, C30.55D8, C40.58D6, C15⋊15SD32, D24.2C10, C60.138D4, C120.65C22, C3⋊C16⋊3C10, C3⋊3(C5×SD32), C8.6(S3×C10), Q16⋊1(C5×S3), (C5×Q16)⋊5S3, C12.5(C5×D4), C6.10(C5×D8), C24.4(C2×C10), (C3×Q16)⋊1C10, (C15×Q16)⋊8C2, (C5×D24).4C2, C10.26(D4⋊S3), C20.68(C3⋊D4), (C5×C3⋊C16)⋊10C2, C2.6(C5×D4⋊S3), C4.3(C5×C3⋊D4), SmallGroup(480,147)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×C8.6D6
G = < a,b,c,d | a5=b8=1, c6=b4, d2=b3, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd-1=b-1c5 >
Smallest permutation representation of C5×C8.6D6
►On 240 points
Generators in S240
(1 68 231 31 150)(2 69 232 32 151)(3 70 233 17 152)(4 71 234 18 153)(5 72 235 19 154)(6 73 236 20 155)(7 74 237 21 156)(8 75 238 22 157)(9 76 239 23 158)(10 77 240 24 159)(11 78 225 25 160)(12 79 226 26 145)(13 80 227 27 146)(14 65 228 28 147)(15 66 229 29 148)(16 67 230 30 149)(33 116 220 139 49)(34 117 221 140 50)(35 118 222 141 51)(36 119 223 142 52)(37 120 224 143 53)(38 121 209 144 54)(39 122 210 129 55)(40 123 211 130 56)(41 124 212 131 57)(42 125 213 132 58)(43 126 214 133 59)(44 127 215 134 60)(45 128 216 135 61)(46 113 217 136 62)(47 114 218 137 63)(48 115 219 138 64)(81 110 198 170 189)(82 111 199 171 190)(83 112 200 172 191)(84 97 201 173 192)(85 98 202 174 177)(86 99 203 175 178)(87 100 204 176 179)(88 101 205 161 180)(89 102 206 162 181)(90 103 207 163 182)(91 104 208 164 183)(92 105 193 165 184)(93 106 194 166 185)(94 107 195 167 186)(95 108 196 168 187)(96 109 197 169 188)
(1 7 13 3 9 15 5 11)(2 8 14 4 10 16 6 12)(17 23 29 19 25 31 21 27)(18 24 30 20 26 32 22 28)(33 39 45 35 41 47 37 43)(34 40 46 36 42 48 38 44)(49 55 61 51 57 63 53 59)(50 56 62 52 58 64 54 60)(65 71 77 67 73 79 69 75)(66 72 78 68 74 80 70 76)(81 87 93 83 89 95 85 91)(82 88 94 84 90 96 86 92)(97 103 109 99 105 111 101 107)(98 104 110 100 106 112 102 108)(113 119 125 115 121 127 117 123)(114 120 126 116 122 128 118 124)(129 135 141 131 137 143 133 139)(130 136 142 132 138 144 134 140)(145 151 157 147 153 159 149 155)(146 152 158 148 154 160 150 156)(161 167 173 163 169 175 165 171)(162 168 174 164 170 176 166 172)(177 183 189 179 185 191 181 187)(178 184 190 180 186 192 182 188)(193 199 205 195 201 207 197 203)(194 200 206 196 202 208 198 204)(209 215 221 211 217 223 213 219)(210 216 222 212 218 224 214 220)(225 231 237 227 233 239 229 235)(226 232 238 228 234 240 230 236)
(1 48 182 183 47 2 9 40 190 191 39 10)(3 46 184 181 33 16 11 38 192 189 41 8)(4 7 42 188 177 37 12 15 34 180 185 45)(5 44 186 179 35 14 13 36 178 187 43 6)(17 136 193 206 139 30 25 144 201 198 131 22)(18 21 132 197 202 143 26 29 140 205 194 135)(19 134 195 204 141 28 27 142 203 196 133 20)(23 130 199 200 129 24 31 138 207 208 137 32)(49 149 160 54 173 170 57 157 152 62 165 162)(50 161 166 61 153 156 58 169 174 53 145 148)(51 147 146 52 175 168 59 155 154 60 167 176)(55 159 150 64 163 164 63 151 158 56 171 172)(65 80 119 86 95 126 73 72 127 94 87 118)(66 117 88 93 128 71 74 125 96 85 120 79)(67 78 121 84 81 124 75 70 113 92 89 116)(68 115 90 91 114 69 76 123 82 83 122 77)(97 110 212 238 233 217 105 102 220 230 225 209)(98 224 226 229 221 101 106 216 234 237 213 109)(99 108 214 236 235 215 107 100 222 228 227 223)(103 104 218 232 239 211 111 112 210 240 231 219)
(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)
G:=sub<Sym(240)| (1,68,231,31,150)(2,69,232,32,151)(3,70,233,17,152)(4,71,234,18,153)(5,72,235,19,154)(6,73,236,20,155)(7,74,237,21,156)(8,75,238,22,157)(9,76,239,23,158)(10,77,240,24,159)(11,78,225,25,160)(12,79,226,26,145)(13,80,227,27,146)(14,65,228,28,147)(15,66,229,29,148)(16,67,230,30,149)(33,116,220,139,49)(34,117,221,140,50)(35,118,222,141,51)(36,119,223,142,52)(37,120,224,143,53)(38,121,209,144,54)(39,122,210,129,55)(40,123,211,130,56)(41,124,212,131,57)(42,125,213,132,58)(43,126,214,133,59)(44,127,215,134,60)(45,128,216,135,61)(46,113,217,136,62)(47,114,218,137,63)(48,115,219,138,64)(81,110,198,170,189)(82,111,199,171,190)(83,112,200,172,191)(84,97,201,173,192)(85,98,202,174,177)(86,99,203,175,178)(87,100,204,176,179)(88,101,205,161,180)(89,102,206,162,181)(90,103,207,163,182)(91,104,208,164,183)(92,105,193,165,184)(93,106,194,166,185)(94,107,195,167,186)(95,108,196,168,187)(96,109,197,169,188), (1,7,13,3,9,15,5,11)(2,8,14,4,10,16,6,12)(17,23,29,19,25,31,21,27)(18,24,30,20,26,32,22,28)(33,39,45,35,41,47,37,43)(34,40,46,36,42,48,38,44)(49,55,61,51,57,63,53,59)(50,56,62,52,58,64,54,60)(65,71,77,67,73,79,69,75)(66,72,78,68,74,80,70,76)(81,87,93,83,89,95,85,91)(82,88,94,84,90,96,86,92)(97,103,109,99,105,111,101,107)(98,104,110,100,106,112,102,108)(113,119,125,115,121,127,117,123)(114,120,126,116,122,128,118,124)(129,135,141,131,137,143,133,139)(130,136,142,132,138,144,134,140)(145,151,157,147,153,159,149,155)(146,152,158,148,154,160,150,156)(161,167,173,163,169,175,165,171)(162,168,174,164,170,176,166,172)(177,183,189,179,185,191,181,187)(178,184,190,180,186,192,182,188)(193,199,205,195,201,207,197,203)(194,200,206,196,202,208,198,204)(209,215,221,211,217,223,213,219)(210,216,222,212,218,224,214,220)(225,231,237,227,233,239,229,235)(226,232,238,228,234,240,230,236), (1,48,182,183,47,2,9,40,190,191,39,10)(3,46,184,181,33,16,11,38,192,189,41,8)(4,7,42,188,177,37,12,15,34,180,185,45)(5,44,186,179,35,14,13,36,178,187,43,6)(17,136,193,206,139,30,25,144,201,198,131,22)(18,21,132,197,202,143,26,29,140,205,194,135)(19,134,195,204,141,28,27,142,203,196,133,20)(23,130,199,200,129,24,31,138,207,208,137,32)(49,149,160,54,173,170,57,157,152,62,165,162)(50,161,166,61,153,156,58,169,174,53,145,148)(51,147,146,52,175,168,59,155,154,60,167,176)(55,159,150,64,163,164,63,151,158,56,171,172)(65,80,119,86,95,126,73,72,127,94,87,118)(66,117,88,93,128,71,74,125,96,85,120,79)(67,78,121,84,81,124,75,70,113,92,89,116)(68,115,90,91,114,69,76,123,82,83,122,77)(97,110,212,238,233,217,105,102,220,230,225,209)(98,224,226,229,221,101,106,216,234,237,213,109)(99,108,214,236,235,215,107,100,222,228,227,223)(103,104,218,232,239,211,111,112,210,240,231,219), (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)>;
G:=Group( (1,68,231,31,150)(2,69,232,32,151)(3,70,233,17,152)(4,71,234,18,153)(5,72,235,19,154)(6,73,236,20,155)(7,74,237,21,156)(8,75,238,22,157)(9,76,239,23,158)(10,77,240,24,159)(11,78,225,25,160)(12,79,226,26,145)(13,80,227,27,146)(14,65,228,28,147)(15,66,229,29,148)(16,67,230,30,149)(33,116,220,139,49)(34,117,221,140,50)(35,118,222,141,51)(36,119,223,142,52)(37,120,224,143,53)(38,121,209,144,54)(39,122,210,129,55)(40,123,211,130,56)(41,124,212,131,57)(42,125,213,132,58)(43,126,214,133,59)(44,127,215,134,60)(45,128,216,135,61)(46,113,217,136,62)(47,114,218,137,63)(48,115,219,138,64)(81,110,198,170,189)(82,111,199,171,190)(83,112,200,172,191)(84,97,201,173,192)(85,98,202,174,177)(86,99,203,175,178)(87,100,204,176,179)(88,101,205,161,180)(89,102,206,162,181)(90,103,207,163,182)(91,104,208,164,183)(92,105,193,165,184)(93,106,194,166,185)(94,107,195,167,186)(95,108,196,168,187)(96,109,197,169,188), (1,7,13,3,9,15,5,11)(2,8,14,4,10,16,6,12)(17,23,29,19,25,31,21,27)(18,24,30,20,26,32,22,28)(33,39,45,35,41,47,37,43)(34,40,46,36,42,48,38,44)(49,55,61,51,57,63,53,59)(50,56,62,52,58,64,54,60)(65,71,77,67,73,79,69,75)(66,72,78,68,74,80,70,76)(81,87,93,83,89,95,85,91)(82,88,94,84,90,96,86,92)(97,103,109,99,105,111,101,107)(98,104,110,100,106,112,102,108)(113,119,125,115,121,127,117,123)(114,120,126,116,122,128,118,124)(129,135,141,131,137,143,133,139)(130,136,142,132,138,144,134,140)(145,151,157,147,153,159,149,155)(146,152,158,148,154,160,150,156)(161,167,173,163,169,175,165,171)(162,168,174,164,170,176,166,172)(177,183,189,179,185,191,181,187)(178,184,190,180,186,192,182,188)(193,199,205,195,201,207,197,203)(194,200,206,196,202,208,198,204)(209,215,221,211,217,223,213,219)(210,216,222,212,218,224,214,220)(225,231,237,227,233,239,229,235)(226,232,238,228,234,240,230,236), (1,48,182,183,47,2,9,40,190,191,39,10)(3,46,184,181,33,16,11,38,192,189,41,8)(4,7,42,188,177,37,12,15,34,180,185,45)(5,44,186,179,35,14,13,36,178,187,43,6)(17,136,193,206,139,30,25,144,201,198,131,22)(18,21,132,197,202,143,26,29,140,205,194,135)(19,134,195,204,141,28,27,142,203,196,133,20)(23,130,199,200,129,24,31,138,207,208,137,32)(49,149,160,54,173,170,57,157,152,62,165,162)(50,161,166,61,153,156,58,169,174,53,145,148)(51,147,146,52,175,168,59,155,154,60,167,176)(55,159,150,64,163,164,63,151,158,56,171,172)(65,80,119,86,95,126,73,72,127,94,87,118)(66,117,88,93,128,71,74,125,96,85,120,79)(67,78,121,84,81,124,75,70,113,92,89,116)(68,115,90,91,114,69,76,123,82,83,122,77)(97,110,212,238,233,217,105,102,220,230,225,209)(98,224,226,229,221,101,106,216,234,237,213,109)(99,108,214,236,235,215,107,100,222,228,227,223)(103,104,218,232,239,211,111,112,210,240,231,219), (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) );
G=PermutationGroup([[(1,68,231,31,150),(2,69,232,32,151),(3,70,233,17,152),(4,71,234,18,153),(5,72,235,19,154),(6,73,236,20,155),(7,74,237,21,156),(8,75,238,22,157),(9,76,239,23,158),(10,77,240,24,159),(11,78,225,25,160),(12,79,226,26,145),(13,80,227,27,146),(14,65,228,28,147),(15,66,229,29,148),(16,67,230,30,149),(33,116,220,139,49),(34,117,221,140,50),(35,118,222,141,51),(36,119,223,142,52),(37,120,224,143,53),(38,121,209,144,54),(39,122,210,129,55),(40,123,211,130,56),(41,124,212,131,57),(42,125,213,132,58),(43,126,214,133,59),(44,127,215,134,60),(45,128,216,135,61),(46,113,217,136,62),(47,114,218,137,63),(48,115,219,138,64),(81,110,198,170,189),(82,111,199,171,190),(83,112,200,172,191),(84,97,201,173,192),(85,98,202,174,177),(86,99,203,175,178),(87,100,204,176,179),(88,101,205,161,180),(89,102,206,162,181),(90,103,207,163,182),(91,104,208,164,183),(92,105,193,165,184),(93,106,194,166,185),(94,107,195,167,186),(95,108,196,168,187),(96,109,197,169,188)], [(1,7,13,3,9,15,5,11),(2,8,14,4,10,16,6,12),(17,23,29,19,25,31,21,27),(18,24,30,20,26,32,22,28),(33,39,45,35,41,47,37,43),(34,40,46,36,42,48,38,44),(49,55,61,51,57,63,53,59),(50,56,62,52,58,64,54,60),(65,71,77,67,73,79,69,75),(66,72,78,68,74,80,70,76),(81,87,93,83,89,95,85,91),(82,88,94,84,90,96,86,92),(97,103,109,99,105,111,101,107),(98,104,110,100,106,112,102,108),(113,119,125,115,121,127,117,123),(114,120,126,116,122,128,118,124),(129,135,141,131,137,143,133,139),(130,136,142,132,138,144,134,140),(145,151,157,147,153,159,149,155),(146,152,158,148,154,160,150,156),(161,167,173,163,169,175,165,171),(162,168,174,164,170,176,166,172),(177,183,189,179,185,191,181,187),(178,184,190,180,186,192,182,188),(193,199,205,195,201,207,197,203),(194,200,206,196,202,208,198,204),(209,215,221,211,217,223,213,219),(210,216,222,212,218,224,214,220),(225,231,237,227,233,239,229,235),(226,232,238,228,234,240,230,236)], [(1,48,182,183,47,2,9,40,190,191,39,10),(3,46,184,181,33,16,11,38,192,189,41,8),(4,7,42,188,177,37,12,15,34,180,185,45),(5,44,186,179,35,14,13,36,178,187,43,6),(17,136,193,206,139,30,25,144,201,198,131,22),(18,21,132,197,202,143,26,29,140,205,194,135),(19,134,195,204,141,28,27,142,203,196,133,20),(23,130,199,200,129,24,31,138,207,208,137,32),(49,149,160,54,173,170,57,157,152,62,165,162),(50,161,166,61,153,156,58,169,174,53,145,148),(51,147,146,52,175,168,59,155,154,60,167,176),(55,159,150,64,163,164,63,151,158,56,171,172),(65,80,119,86,95,126,73,72,127,94,87,118),(66,117,88,93,128,71,74,125,96,85,120,79),(67,78,121,84,81,124,75,70,113,92,89,116),(68,115,90,91,114,69,76,123,82,83,122,77),(97,110,212,238,233,217,105,102,220,230,225,209),(98,224,226,229,221,101,106,216,234,237,213,109),(99,108,214,236,235,215,107,100,222,228,227,223),(103,104,218,232,239,211,111,112,210,240,231,219)], [(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)]])
90 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 5A | 5B | 5C | 5D | 6 | 8A | 8B | 10A | 10B | 10C | 10D | 10E | 10F | 10G | 10H | 12A | 12B | 12C | 15A | 15B | 15C | 15D | 16A | 16B | 16C | 16D | 20A | 20B | 20C | 20D | 20E | 20F | 20G | 20H | 24A | 24B | 30A | 30B | 30C | 30D | 40A | ··· | 40H | 60A | 60B | 60C | 60D | 60E | ··· | 60L | 80A | ··· | 80P | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 30 | 30 | 30 | 30 | 40 | ··· | 40 | 60 | 60 | 60 | 60 | 60 | ··· | 60 | 80 | ··· | 80 | 120 | ··· | 120 |
| size | 1 | 1 | 24 | 2 | 2 | 8 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 24 | 24 | 24 | 24 | 4 | 8 | 8 | 2 | 2 | 2 | 2 | 6 | 6 | 6 | 6 | 2 | 2 | 2 | 2 | 8 | 8 | 8 | 8 | 4 | 4 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 6 | ··· | 6 | 4 | ··· | 4 |
90 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | ||||||||||||||
| image | C1 | C2 | C2 | C2 | C5 | C10 | C10 | C10 | S3 | D4 | D6 | D8 | C3⋊D4 | C5×S3 | SD32 | C5×D4 | S3×C10 | C5×D8 | C5×C3⋊D4 | C5×SD32 | D4⋊S3 | C8.6D6 | C5×D4⋊S3 | C5×C8.6D6 |
| kernel | C5×C8.6D6 | C5×C3⋊C16 | C5×D24 | C15×Q16 | C8.6D6 | C3⋊C16 | D24 | C3×Q16 | C5×Q16 | C60 | C40 | C30 | C20 | Q16 | C15 | C12 | C8 | C6 | C4 | C3 | C10 | C5 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 16 | 1 | 2 | 4 | 8 |
Matrix representation of C5×C8.6D6 ►in GL4(𝔽241) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 91 | 0 |
| 0 | 0 | 0 | 91 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 219 | 22 |
| 0 | 0 | 230 | 0 |
| 0 | 1 | 0 | 0 |
| 240 | 240 | 0 | 0 |
| 0 | 0 | 62 | 82 |
| 0 | 0 | 103 | 179 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 62 | 82 |
| 0 | 0 | 200 | 144 |
G:=sub<GL(4,GF(241))| [1,0,0,0,0,1,0,0,0,0,91,0,0,0,0,91],[1,0,0,0,0,1,0,0,0,0,219,230,0,0,22,0],[0,240,0,0,1,240,0,0,0,0,62,103,0,0,82,179],[0,1,0,0,1,0,0,0,0,0,62,200,0,0,82,144] >;
C5×C8.6D6 in GAP, Magma, Sage, TeX
C_5\times C_8._6D_6
% in TeX
G:=Group("C5xC8.6D6"); // GroupNames label
G:=SmallGroup(480,147);
// by ID
G=gap.SmallGroup(480,147);
# by ID
G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,309,568,1683,850,192,4204,2111,102,15686]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^8=1,c^6=b^4,d^2=b^3,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^5>;
// generators/relations
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