direct product, metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C5×D6.C8, C80⋊7S3, D6.C40, C48⋊6C10, C240⋊14C2, C40.81D6, Dic3.C40, C15⋊12M5(2), C120.108C22, C3⋊C16⋊4C10, C16⋊3(C5×S3), C3⋊C8.2C20, C2.3(S3×C40), C6.2(C2×C40), C3⋊1(C5×M5(2)), (S3×C40).5C2, (C4×S3).2C20, (S3×C10).5C8, (S3×C8).2C10, C8.19(S3×C10), C4.17(S3×C20), C10.26(S3×C8), C30.54(C2×C8), (S3×C20).13C4, C20.119(C4×S3), C12.22(C2×C20), C24.24(C2×C10), C60.217(C2×C4), (C5×Dic3).5C8, (C5×C3⋊C8).9C4, (C5×C3⋊C16)⋊11C2, SmallGroup(480,117)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×D6.C8
G = < a,b,c,d | a5=b6=c2=1, d8=b3, ab=ba, ac=ca, ad=da, cbc=b-1, bd=db, dcd-1=b3c >
Smallest permutation representation of C5×D6.C8
►On 240 points
Generators in S240
(1 166 234 207 40)(2 167 235 208 41)(3 168 236 193 42)(4 169 237 194 43)(5 170 238 195 44)(6 171 239 196 45)(7 172 240 197 46)(8 173 225 198 47)(9 174 226 199 48)(10 175 227 200 33)(11 176 228 201 34)(12 161 229 202 35)(13 162 230 203 36)(14 163 231 204 37)(15 164 232 205 38)(16 165 233 206 39)(17 134 188 217 63)(18 135 189 218 64)(19 136 190 219 49)(20 137 191 220 50)(21 138 192 221 51)(22 139 177 222 52)(23 140 178 223 53)(24 141 179 224 54)(25 142 180 209 55)(26 143 181 210 56)(27 144 182 211 57)(28 129 183 212 58)(29 130 184 213 59)(30 131 185 214 60)(31 132 186 215 61)(32 133 187 216 62)(65 98 125 147 92)(66 99 126 148 93)(67 100 127 149 94)(68 101 128 150 95)(69 102 113 151 96)(70 103 114 152 81)(71 104 115 153 82)(72 105 116 154 83)(73 106 117 155 84)(74 107 118 156 85)(75 108 119 157 86)(76 109 120 158 87)(77 110 121 159 88)(78 111 122 160 89)(79 112 123 145 90)(80 97 124 146 91)
(1 76 28 9 68 20)(2 77 29 10 69 21)(3 78 30 11 70 22)(4 79 31 12 71 23)(5 80 32 13 72 24)(6 65 17 14 73 25)(7 66 18 15 74 26)(8 67 19 16 75 27)(33 96 51 41 88 59)(34 81 52 42 89 60)(35 82 53 43 90 61)(36 83 54 44 91 62)(37 84 55 45 92 63)(38 85 56 46 93 64)(39 86 57 47 94 49)(40 87 58 48 95 50)(97 133 162 105 141 170)(98 134 163 106 142 171)(99 135 164 107 143 172)(100 136 165 108 144 173)(101 137 166 109 129 174)(102 138 167 110 130 175)(103 139 168 111 131 176)(104 140 169 112 132 161)(113 192 235 121 184 227)(114 177 236 122 185 228)(115 178 237 123 186 229)(116 179 238 124 187 230)(117 180 239 125 188 231)(118 181 240 126 189 232)(119 182 225 127 190 233)(120 183 226 128 191 234)(145 215 202 153 223 194)(146 216 203 154 224 195)(147 217 204 155 209 196)(148 218 205 156 210 197)(149 219 206 157 211 198)(150 220 207 158 212 199)(151 221 208 159 213 200)(152 222 193 160 214 201)
(1 20)(2 29)(3 22)(4 31)(5 24)(6 17)(7 26)(8 19)(9 28)(10 21)(11 30)(12 23)(13 32)(14 25)(15 18)(16 27)(33 51)(34 60)(35 53)(36 62)(37 55)(38 64)(39 57)(40 50)(41 59)(42 52)(43 61)(44 54)(45 63)(46 56)(47 49)(48 58)(66 74)(68 76)(70 78)(72 80)(81 89)(83 91)(85 93)(87 95)(97 105)(99 107)(101 109)(103 111)(114 122)(116 124)(118 126)(120 128)(129 174)(130 167)(131 176)(132 169)(133 162)(134 171)(135 164)(136 173)(137 166)(138 175)(139 168)(140 161)(141 170)(142 163)(143 172)(144 165)(146 154)(148 156)(150 158)(152 160)(177 236)(178 229)(179 238)(180 231)(181 240)(182 233)(183 226)(184 235)(185 228)(186 237)(187 230)(188 239)(189 232)(190 225)(191 234)(192 227)(193 222)(194 215)(195 224)(196 217)(197 210)(198 219)(199 212)(200 221)(201 214)(202 223)(203 216)(204 209)(205 218)(206 211)(207 220)(208 213)
(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)| (1,166,234,207,40)(2,167,235,208,41)(3,168,236,193,42)(4,169,237,194,43)(5,170,238,195,44)(6,171,239,196,45)(7,172,240,197,46)(8,173,225,198,47)(9,174,226,199,48)(10,175,227,200,33)(11,176,228,201,34)(12,161,229,202,35)(13,162,230,203,36)(14,163,231,204,37)(15,164,232,205,38)(16,165,233,206,39)(17,134,188,217,63)(18,135,189,218,64)(19,136,190,219,49)(20,137,191,220,50)(21,138,192,221,51)(22,139,177,222,52)(23,140,178,223,53)(24,141,179,224,54)(25,142,180,209,55)(26,143,181,210,56)(27,144,182,211,57)(28,129,183,212,58)(29,130,184,213,59)(30,131,185,214,60)(31,132,186,215,61)(32,133,187,216,62)(65,98,125,147,92)(66,99,126,148,93)(67,100,127,149,94)(68,101,128,150,95)(69,102,113,151,96)(70,103,114,152,81)(71,104,115,153,82)(72,105,116,154,83)(73,106,117,155,84)(74,107,118,156,85)(75,108,119,157,86)(76,109,120,158,87)(77,110,121,159,88)(78,111,122,160,89)(79,112,123,145,90)(80,97,124,146,91), (1,76,28,9,68,20)(2,77,29,10,69,21)(3,78,30,11,70,22)(4,79,31,12,71,23)(5,80,32,13,72,24)(6,65,17,14,73,25)(7,66,18,15,74,26)(8,67,19,16,75,27)(33,96,51,41,88,59)(34,81,52,42,89,60)(35,82,53,43,90,61)(36,83,54,44,91,62)(37,84,55,45,92,63)(38,85,56,46,93,64)(39,86,57,47,94,49)(40,87,58,48,95,50)(97,133,162,105,141,170)(98,134,163,106,142,171)(99,135,164,107,143,172)(100,136,165,108,144,173)(101,137,166,109,129,174)(102,138,167,110,130,175)(103,139,168,111,131,176)(104,140,169,112,132,161)(113,192,235,121,184,227)(114,177,236,122,185,228)(115,178,237,123,186,229)(116,179,238,124,187,230)(117,180,239,125,188,231)(118,181,240,126,189,232)(119,182,225,127,190,233)(120,183,226,128,191,234)(145,215,202,153,223,194)(146,216,203,154,224,195)(147,217,204,155,209,196)(148,218,205,156,210,197)(149,219,206,157,211,198)(150,220,207,158,212,199)(151,221,208,159,213,200)(152,222,193,160,214,201), (1,20)(2,29)(3,22)(4,31)(5,24)(6,17)(7,26)(8,19)(9,28)(10,21)(11,30)(12,23)(13,32)(14,25)(15,18)(16,27)(33,51)(34,60)(35,53)(36,62)(37,55)(38,64)(39,57)(40,50)(41,59)(42,52)(43,61)(44,54)(45,63)(46,56)(47,49)(48,58)(66,74)(68,76)(70,78)(72,80)(81,89)(83,91)(85,93)(87,95)(97,105)(99,107)(101,109)(103,111)(114,122)(116,124)(118,126)(120,128)(129,174)(130,167)(131,176)(132,169)(133,162)(134,171)(135,164)(136,173)(137,166)(138,175)(139,168)(140,161)(141,170)(142,163)(143,172)(144,165)(146,154)(148,156)(150,158)(152,160)(177,236)(178,229)(179,238)(180,231)(181,240)(182,233)(183,226)(184,235)(185,228)(186,237)(187,230)(188,239)(189,232)(190,225)(191,234)(192,227)(193,222)(194,215)(195,224)(196,217)(197,210)(198,219)(199,212)(200,221)(201,214)(202,223)(203,216)(204,209)(205,218)(206,211)(207,220)(208,213), (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( (1,166,234,207,40)(2,167,235,208,41)(3,168,236,193,42)(4,169,237,194,43)(5,170,238,195,44)(6,171,239,196,45)(7,172,240,197,46)(8,173,225,198,47)(9,174,226,199,48)(10,175,227,200,33)(11,176,228,201,34)(12,161,229,202,35)(13,162,230,203,36)(14,163,231,204,37)(15,164,232,205,38)(16,165,233,206,39)(17,134,188,217,63)(18,135,189,218,64)(19,136,190,219,49)(20,137,191,220,50)(21,138,192,221,51)(22,139,177,222,52)(23,140,178,223,53)(24,141,179,224,54)(25,142,180,209,55)(26,143,181,210,56)(27,144,182,211,57)(28,129,183,212,58)(29,130,184,213,59)(30,131,185,214,60)(31,132,186,215,61)(32,133,187,216,62)(65,98,125,147,92)(66,99,126,148,93)(67,100,127,149,94)(68,101,128,150,95)(69,102,113,151,96)(70,103,114,152,81)(71,104,115,153,82)(72,105,116,154,83)(73,106,117,155,84)(74,107,118,156,85)(75,108,119,157,86)(76,109,120,158,87)(77,110,121,159,88)(78,111,122,160,89)(79,112,123,145,90)(80,97,124,146,91), (1,76,28,9,68,20)(2,77,29,10,69,21)(3,78,30,11,70,22)(4,79,31,12,71,23)(5,80,32,13,72,24)(6,65,17,14,73,25)(7,66,18,15,74,26)(8,67,19,16,75,27)(33,96,51,41,88,59)(34,81,52,42,89,60)(35,82,53,43,90,61)(36,83,54,44,91,62)(37,84,55,45,92,63)(38,85,56,46,93,64)(39,86,57,47,94,49)(40,87,58,48,95,50)(97,133,162,105,141,170)(98,134,163,106,142,171)(99,135,164,107,143,172)(100,136,165,108,144,173)(101,137,166,109,129,174)(102,138,167,110,130,175)(103,139,168,111,131,176)(104,140,169,112,132,161)(113,192,235,121,184,227)(114,177,236,122,185,228)(115,178,237,123,186,229)(116,179,238,124,187,230)(117,180,239,125,188,231)(118,181,240,126,189,232)(119,182,225,127,190,233)(120,183,226,128,191,234)(145,215,202,153,223,194)(146,216,203,154,224,195)(147,217,204,155,209,196)(148,218,205,156,210,197)(149,219,206,157,211,198)(150,220,207,158,212,199)(151,221,208,159,213,200)(152,222,193,160,214,201), (1,20)(2,29)(3,22)(4,31)(5,24)(6,17)(7,26)(8,19)(9,28)(10,21)(11,30)(12,23)(13,32)(14,25)(15,18)(16,27)(33,51)(34,60)(35,53)(36,62)(37,55)(38,64)(39,57)(40,50)(41,59)(42,52)(43,61)(44,54)(45,63)(46,56)(47,49)(48,58)(66,74)(68,76)(70,78)(72,80)(81,89)(83,91)(85,93)(87,95)(97,105)(99,107)(101,109)(103,111)(114,122)(116,124)(118,126)(120,128)(129,174)(130,167)(131,176)(132,169)(133,162)(134,171)(135,164)(136,173)(137,166)(138,175)(139,168)(140,161)(141,170)(142,163)(143,172)(144,165)(146,154)(148,156)(150,158)(152,160)(177,236)(178,229)(179,238)(180,231)(181,240)(182,233)(183,226)(184,235)(185,228)(186,237)(187,230)(188,239)(189,232)(190,225)(191,234)(192,227)(193,222)(194,215)(195,224)(196,217)(197,210)(198,219)(199,212)(200,221)(201,214)(202,223)(203,216)(204,209)(205,218)(206,211)(207,220)(208,213), (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([[(1,166,234,207,40),(2,167,235,208,41),(3,168,236,193,42),(4,169,237,194,43),(5,170,238,195,44),(6,171,239,196,45),(7,172,240,197,46),(8,173,225,198,47),(9,174,226,199,48),(10,175,227,200,33),(11,176,228,201,34),(12,161,229,202,35),(13,162,230,203,36),(14,163,231,204,37),(15,164,232,205,38),(16,165,233,206,39),(17,134,188,217,63),(18,135,189,218,64),(19,136,190,219,49),(20,137,191,220,50),(21,138,192,221,51),(22,139,177,222,52),(23,140,178,223,53),(24,141,179,224,54),(25,142,180,209,55),(26,143,181,210,56),(27,144,182,211,57),(28,129,183,212,58),(29,130,184,213,59),(30,131,185,214,60),(31,132,186,215,61),(32,133,187,216,62),(65,98,125,147,92),(66,99,126,148,93),(67,100,127,149,94),(68,101,128,150,95),(69,102,113,151,96),(70,103,114,152,81),(71,104,115,153,82),(72,105,116,154,83),(73,106,117,155,84),(74,107,118,156,85),(75,108,119,157,86),(76,109,120,158,87),(77,110,121,159,88),(78,111,122,160,89),(79,112,123,145,90),(80,97,124,146,91)], [(1,76,28,9,68,20),(2,77,29,10,69,21),(3,78,30,11,70,22),(4,79,31,12,71,23),(5,80,32,13,72,24),(6,65,17,14,73,25),(7,66,18,15,74,26),(8,67,19,16,75,27),(33,96,51,41,88,59),(34,81,52,42,89,60),(35,82,53,43,90,61),(36,83,54,44,91,62),(37,84,55,45,92,63),(38,85,56,46,93,64),(39,86,57,47,94,49),(40,87,58,48,95,50),(97,133,162,105,141,170),(98,134,163,106,142,171),(99,135,164,107,143,172),(100,136,165,108,144,173),(101,137,166,109,129,174),(102,138,167,110,130,175),(103,139,168,111,131,176),(104,140,169,112,132,161),(113,192,235,121,184,227),(114,177,236,122,185,228),(115,178,237,123,186,229),(116,179,238,124,187,230),(117,180,239,125,188,231),(118,181,240,126,189,232),(119,182,225,127,190,233),(120,183,226,128,191,234),(145,215,202,153,223,194),(146,216,203,154,224,195),(147,217,204,155,209,196),(148,218,205,156,210,197),(149,219,206,157,211,198),(150,220,207,158,212,199),(151,221,208,159,213,200),(152,222,193,160,214,201)], [(1,20),(2,29),(3,22),(4,31),(5,24),(6,17),(7,26),(8,19),(9,28),(10,21),(11,30),(12,23),(13,32),(14,25),(15,18),(16,27),(33,51),(34,60),(35,53),(36,62),(37,55),(38,64),(39,57),(40,50),(41,59),(42,52),(43,61),(44,54),(45,63),(46,56),(47,49),(48,58),(66,74),(68,76),(70,78),(72,80),(81,89),(83,91),(85,93),(87,95),(97,105),(99,107),(101,109),(103,111),(114,122),(116,124),(118,126),(120,128),(129,174),(130,167),(131,176),(132,169),(133,162),(134,171),(135,164),(136,173),(137,166),(138,175),(139,168),(140,161),(141,170),(142,163),(143,172),(144,165),(146,154),(148,156),(150,158),(152,160),(177,236),(178,229),(179,238),(180,231),(181,240),(182,233),(183,226),(184,235),(185,228),(186,237),(187,230),(188,239),(189,232),(190,225),(191,234),(192,227),(193,222),(194,215),(195,224),(196,217),(197,210),(198,219),(199,212),(200,221),(201,214),(202,223),(203,216),(204,209),(205,218),(206,211),(207,220),(208,213)], [(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)]])
180 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 4C | 5A | 5B | 5C | 5D | 6 | 8A | 8B | 8C | 8D | 8E | 8F | 10A | 10B | 10C | 10D | 10E | 10F | 10G | 10H | 12A | 12B | 15A | 15B | 15C | 15D | 16A | 16B | 16C | 16D | 16E | 16F | 16G | 16H | 20A | ··· | 20H | 20I | 20J | 20K | 20L | 24A | 24B | 24C | 24D | 30A | 30B | 30C | 30D | 40A | ··· | 40P | 40Q | ··· | 40X | 48A | ··· | 48H | 60A | ··· | 60H | 80A | ··· | 80P | 80Q | ··· | 80AF | 120A | ··· | 120P | 240A | ··· | 240AF |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 15 | 15 | 15 | 15 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 20 | ··· | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 30 | 30 | 30 | 30 | 40 | ··· | 40 | 40 | ··· | 40 | 48 | ··· | 48 | 60 | ··· | 60 | 80 | ··· | 80 | 80 | ··· | 80 | 120 | ··· | 120 | 240 | ··· | 240 |
| size | 1 | 1 | 6 | 2 | 1 | 1 | 6 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 6 | 6 | 1 | 1 | 1 | 1 | 6 | 6 | 6 | 6 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 6 | 6 | 6 | 6 | 1 | ··· | 1 | 6 | 6 | 6 | 6 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 6 | ··· | 6 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 6 | ··· | 6 | 2 | ··· | 2 | 2 | ··· | 2 |
180 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | ||||||||||||||||||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C5 | C8 | C8 | C10 | C10 | C10 | C20 | C20 | C40 | C40 | S3 | D6 | C4×S3 | C5×S3 | M5(2) | S3×C8 | S3×C10 | D6.C8 | S3×C20 | C5×M5(2) | S3×C40 | C5×D6.C8 |
| kernel | C5×D6.C8 | C5×C3⋊C16 | C240 | S3×C40 | C5×C3⋊C8 | S3×C20 | D6.C8 | C5×Dic3 | S3×C10 | C3⋊C16 | C48 | S3×C8 | C3⋊C8 | C4×S3 | Dic3 | D6 | C80 | C40 | C20 | C16 | C15 | C10 | C8 | C5 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 16 | 16 | 1 | 1 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 16 | 16 | 32 |
Matrix representation of C5×D6.C8 ►in GL2(𝔽41) generated by
| 16 | 0 |
| 0 | 16 |
| 1 | 33 |
| 36 | 0 |
| 0 | 33 |
| 5 | 0 |
| 32 | 21 |
| 8 | 9 |
G:=sub<GL(2,GF(41))| [16,0,0,16],[1,36,33,0],[0,5,33,0],[32,8,21,9] >;
C5×D6.C8 in GAP, Magma, Sage, TeX
C_5\times D_6.C_8
% in TeX
G:=Group("C5xD6.C8"); // GroupNames label
G:=SmallGroup(480,117);
// by ID
G=gap.SmallGroup(480,117);
# by ID
G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,1149,148,80,102,15686]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^6=c^2=1,d^8=b^3,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,b*d=d*b,d*c*d^-1=b^3*c>;
// generators/relations
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