direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×C5⋊D16, C15⋊8D16, D40⋊3C6, C30.46D8, C24.48D10, C60.113D4, C120.41C22, C5⋊2(C3×D16), (C5×D8)⋊1C6, D8⋊1(C3×D5), (C3×D8)⋊5D5, C5⋊2C16⋊1C6, C8.4(C6×D5), (C15×D8)⋊5C2, C40.2(C2×C6), C10.8(C3×D8), C20.3(C3×D4), (C3×D40)⋊11C2, C6.24(D4⋊D5), C12.69(C5⋊D4), C2.4(C3×D4⋊D5), (C3×C5⋊2C16)⋊4C2, C4.1(C3×C5⋊D4), SmallGroup(480,104)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C5⋊D16
G = < a,b,c,d | a3=b5=c16=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
Smallest permutation representation of C3×C5⋊D16
►On 240 points
Generators in S240
(1 184 78)(2 185 79)(3 186 80)(4 187 65)(5 188 66)(6 189 67)(7 190 68)(8 191 69)(9 192 70)(10 177 71)(11 178 72)(12 179 73)(13 180 74)(14 181 75)(15 182 76)(16 183 77)(17 97 61)(18 98 62)(19 99 63)(20 100 64)(21 101 49)(22 102 50)(23 103 51)(24 104 52)(25 105 53)(26 106 54)(27 107 55)(28 108 56)(29 109 57)(30 110 58)(31 111 59)(32 112 60)(33 120 221)(34 121 222)(35 122 223)(36 123 224)(37 124 209)(38 125 210)(39 126 211)(40 127 212)(41 128 213)(42 113 214)(43 114 215)(44 115 216)(45 116 217)(46 117 218)(47 118 219)(48 119 220)(81 153 236)(82 154 237)(83 155 238)(84 156 239)(85 157 240)(86 158 225)(87 159 226)(88 160 227)(89 145 228)(90 146 229)(91 147 230)(92 148 231)(93 149 232)(94 150 233)(95 151 234)(96 152 235)(129 175 198)(130 176 199)(131 161 200)(132 162 201)(133 163 202)(134 164 203)(135 165 204)(136 166 205)(137 167 206)(138 168 207)(139 169 208)(140 170 193)(141 171 194)(142 172 195)(143 173 196)(144 174 197)
(1 51 197 43 81)(2 82 44 198 52)(3 53 199 45 83)(4 84 46 200 54)(5 55 201 47 85)(6 86 48 202 56)(7 57 203 33 87)(8 88 34 204 58)(9 59 205 35 89)(10 90 36 206 60)(11 61 207 37 91)(12 92 38 208 62)(13 63 193 39 93)(14 94 40 194 64)(15 49 195 41 95)(16 96 42 196 50)(17 138 124 147 178)(18 179 148 125 139)(19 140 126 149 180)(20 181 150 127 141)(21 142 128 151 182)(22 183 152 113 143)(23 144 114 153 184)(24 185 154 115 129)(25 130 116 155 186)(26 187 156 117 131)(27 132 118 157 188)(28 189 158 119 133)(29 134 120 159 190)(30 191 160 121 135)(31 136 122 145 192)(32 177 146 123 137)(65 239 218 161 106)(66 107 162 219 240)(67 225 220 163 108)(68 109 164 221 226)(69 227 222 165 110)(70 111 166 223 228)(71 229 224 167 112)(72 97 168 209 230)(73 231 210 169 98)(74 99 170 211 232)(75 233 212 171 100)(76 101 172 213 234)(77 235 214 173 102)(78 103 174 215 236)(79 237 216 175 104)(80 105 176 217 238)
(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)
(2 16)(3 15)(4 14)(5 13)(6 12)(7 11)(8 10)(17 159)(18 158)(19 157)(20 156)(21 155)(22 154)(23 153)(24 152)(25 151)(26 150)(27 149)(28 148)(29 147)(30 146)(31 145)(32 160)(33 207)(34 206)(35 205)(36 204)(37 203)(38 202)(39 201)(40 200)(41 199)(42 198)(43 197)(44 196)(45 195)(46 194)(47 193)(48 208)(49 83)(50 82)(51 81)(52 96)(53 95)(54 94)(55 93)(56 92)(57 91)(58 90)(59 89)(60 88)(61 87)(62 86)(63 85)(64 84)(65 75)(66 74)(67 73)(68 72)(69 71)(76 80)(77 79)(97 226)(98 225)(99 240)(100 239)(101 238)(102 237)(103 236)(104 235)(105 234)(106 233)(107 232)(108 231)(109 230)(110 229)(111 228)(112 227)(113 129)(114 144)(115 143)(116 142)(117 141)(118 140)(119 139)(120 138)(121 137)(122 136)(123 135)(124 134)(125 133)(126 132)(127 131)(128 130)(161 212)(162 211)(163 210)(164 209)(165 224)(166 223)(167 222)(168 221)(169 220)(170 219)(171 218)(172 217)(173 216)(174 215)(175 214)(176 213)(177 191)(178 190)(179 189)(180 188)(181 187)(182 186)(183 185)
G:=sub<Sym(240)| (1,184,78)(2,185,79)(3,186,80)(4,187,65)(5,188,66)(6,189,67)(7,190,68)(8,191,69)(9,192,70)(10,177,71)(11,178,72)(12,179,73)(13,180,74)(14,181,75)(15,182,76)(16,183,77)(17,97,61)(18,98,62)(19,99,63)(20,100,64)(21,101,49)(22,102,50)(23,103,51)(24,104,52)(25,105,53)(26,106,54)(27,107,55)(28,108,56)(29,109,57)(30,110,58)(31,111,59)(32,112,60)(33,120,221)(34,121,222)(35,122,223)(36,123,224)(37,124,209)(38,125,210)(39,126,211)(40,127,212)(41,128,213)(42,113,214)(43,114,215)(44,115,216)(45,116,217)(46,117,218)(47,118,219)(48,119,220)(81,153,236)(82,154,237)(83,155,238)(84,156,239)(85,157,240)(86,158,225)(87,159,226)(88,160,227)(89,145,228)(90,146,229)(91,147,230)(92,148,231)(93,149,232)(94,150,233)(95,151,234)(96,152,235)(129,175,198)(130,176,199)(131,161,200)(132,162,201)(133,163,202)(134,164,203)(135,165,204)(136,166,205)(137,167,206)(138,168,207)(139,169,208)(140,170,193)(141,171,194)(142,172,195)(143,173,196)(144,174,197), (1,51,197,43,81)(2,82,44,198,52)(3,53,199,45,83)(4,84,46,200,54)(5,55,201,47,85)(6,86,48,202,56)(7,57,203,33,87)(8,88,34,204,58)(9,59,205,35,89)(10,90,36,206,60)(11,61,207,37,91)(12,92,38,208,62)(13,63,193,39,93)(14,94,40,194,64)(15,49,195,41,95)(16,96,42,196,50)(17,138,124,147,178)(18,179,148,125,139)(19,140,126,149,180)(20,181,150,127,141)(21,142,128,151,182)(22,183,152,113,143)(23,144,114,153,184)(24,185,154,115,129)(25,130,116,155,186)(26,187,156,117,131)(27,132,118,157,188)(28,189,158,119,133)(29,134,120,159,190)(30,191,160,121,135)(31,136,122,145,192)(32,177,146,123,137)(65,239,218,161,106)(66,107,162,219,240)(67,225,220,163,108)(68,109,164,221,226)(69,227,222,165,110)(70,111,166,223,228)(71,229,224,167,112)(72,97,168,209,230)(73,231,210,169,98)(74,99,170,211,232)(75,233,212,171,100)(76,101,172,213,234)(77,235,214,173,102)(78,103,174,215,236)(79,237,216,175,104)(80,105,176,217,238), (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), (2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(17,159)(18,158)(19,157)(20,156)(21,155)(22,154)(23,153)(24,152)(25,151)(26,150)(27,149)(28,148)(29,147)(30,146)(31,145)(32,160)(33,207)(34,206)(35,205)(36,204)(37,203)(38,202)(39,201)(40,200)(41,199)(42,198)(43,197)(44,196)(45,195)(46,194)(47,193)(48,208)(49,83)(50,82)(51,81)(52,96)(53,95)(54,94)(55,93)(56,92)(57,91)(58,90)(59,89)(60,88)(61,87)(62,86)(63,85)(64,84)(65,75)(66,74)(67,73)(68,72)(69,71)(76,80)(77,79)(97,226)(98,225)(99,240)(100,239)(101,238)(102,237)(103,236)(104,235)(105,234)(106,233)(107,232)(108,231)(109,230)(110,229)(111,228)(112,227)(113,129)(114,144)(115,143)(116,142)(117,141)(118,140)(119,139)(120,138)(121,137)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130)(161,212)(162,211)(163,210)(164,209)(165,224)(166,223)(167,222)(168,221)(169,220)(170,219)(171,218)(172,217)(173,216)(174,215)(175,214)(176,213)(177,191)(178,190)(179,189)(180,188)(181,187)(182,186)(183,185)>;
G:=Group( (1,184,78)(2,185,79)(3,186,80)(4,187,65)(5,188,66)(6,189,67)(7,190,68)(8,191,69)(9,192,70)(10,177,71)(11,178,72)(12,179,73)(13,180,74)(14,181,75)(15,182,76)(16,183,77)(17,97,61)(18,98,62)(19,99,63)(20,100,64)(21,101,49)(22,102,50)(23,103,51)(24,104,52)(25,105,53)(26,106,54)(27,107,55)(28,108,56)(29,109,57)(30,110,58)(31,111,59)(32,112,60)(33,120,221)(34,121,222)(35,122,223)(36,123,224)(37,124,209)(38,125,210)(39,126,211)(40,127,212)(41,128,213)(42,113,214)(43,114,215)(44,115,216)(45,116,217)(46,117,218)(47,118,219)(48,119,220)(81,153,236)(82,154,237)(83,155,238)(84,156,239)(85,157,240)(86,158,225)(87,159,226)(88,160,227)(89,145,228)(90,146,229)(91,147,230)(92,148,231)(93,149,232)(94,150,233)(95,151,234)(96,152,235)(129,175,198)(130,176,199)(131,161,200)(132,162,201)(133,163,202)(134,164,203)(135,165,204)(136,166,205)(137,167,206)(138,168,207)(139,169,208)(140,170,193)(141,171,194)(142,172,195)(143,173,196)(144,174,197), (1,51,197,43,81)(2,82,44,198,52)(3,53,199,45,83)(4,84,46,200,54)(5,55,201,47,85)(6,86,48,202,56)(7,57,203,33,87)(8,88,34,204,58)(9,59,205,35,89)(10,90,36,206,60)(11,61,207,37,91)(12,92,38,208,62)(13,63,193,39,93)(14,94,40,194,64)(15,49,195,41,95)(16,96,42,196,50)(17,138,124,147,178)(18,179,148,125,139)(19,140,126,149,180)(20,181,150,127,141)(21,142,128,151,182)(22,183,152,113,143)(23,144,114,153,184)(24,185,154,115,129)(25,130,116,155,186)(26,187,156,117,131)(27,132,118,157,188)(28,189,158,119,133)(29,134,120,159,190)(30,191,160,121,135)(31,136,122,145,192)(32,177,146,123,137)(65,239,218,161,106)(66,107,162,219,240)(67,225,220,163,108)(68,109,164,221,226)(69,227,222,165,110)(70,111,166,223,228)(71,229,224,167,112)(72,97,168,209,230)(73,231,210,169,98)(74,99,170,211,232)(75,233,212,171,100)(76,101,172,213,234)(77,235,214,173,102)(78,103,174,215,236)(79,237,216,175,104)(80,105,176,217,238), (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), (2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(17,159)(18,158)(19,157)(20,156)(21,155)(22,154)(23,153)(24,152)(25,151)(26,150)(27,149)(28,148)(29,147)(30,146)(31,145)(32,160)(33,207)(34,206)(35,205)(36,204)(37,203)(38,202)(39,201)(40,200)(41,199)(42,198)(43,197)(44,196)(45,195)(46,194)(47,193)(48,208)(49,83)(50,82)(51,81)(52,96)(53,95)(54,94)(55,93)(56,92)(57,91)(58,90)(59,89)(60,88)(61,87)(62,86)(63,85)(64,84)(65,75)(66,74)(67,73)(68,72)(69,71)(76,80)(77,79)(97,226)(98,225)(99,240)(100,239)(101,238)(102,237)(103,236)(104,235)(105,234)(106,233)(107,232)(108,231)(109,230)(110,229)(111,228)(112,227)(113,129)(114,144)(115,143)(116,142)(117,141)(118,140)(119,139)(120,138)(121,137)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130)(161,212)(162,211)(163,210)(164,209)(165,224)(166,223)(167,222)(168,221)(169,220)(170,219)(171,218)(172,217)(173,216)(174,215)(175,214)(176,213)(177,191)(178,190)(179,189)(180,188)(181,187)(182,186)(183,185) );
G=PermutationGroup([[(1,184,78),(2,185,79),(3,186,80),(4,187,65),(5,188,66),(6,189,67),(7,190,68),(8,191,69),(9,192,70),(10,177,71),(11,178,72),(12,179,73),(13,180,74),(14,181,75),(15,182,76),(16,183,77),(17,97,61),(18,98,62),(19,99,63),(20,100,64),(21,101,49),(22,102,50),(23,103,51),(24,104,52),(25,105,53),(26,106,54),(27,107,55),(28,108,56),(29,109,57),(30,110,58),(31,111,59),(32,112,60),(33,120,221),(34,121,222),(35,122,223),(36,123,224),(37,124,209),(38,125,210),(39,126,211),(40,127,212),(41,128,213),(42,113,214),(43,114,215),(44,115,216),(45,116,217),(46,117,218),(47,118,219),(48,119,220),(81,153,236),(82,154,237),(83,155,238),(84,156,239),(85,157,240),(86,158,225),(87,159,226),(88,160,227),(89,145,228),(90,146,229),(91,147,230),(92,148,231),(93,149,232),(94,150,233),(95,151,234),(96,152,235),(129,175,198),(130,176,199),(131,161,200),(132,162,201),(133,163,202),(134,164,203),(135,165,204),(136,166,205),(137,167,206),(138,168,207),(139,169,208),(140,170,193),(141,171,194),(142,172,195),(143,173,196),(144,174,197)], [(1,51,197,43,81),(2,82,44,198,52),(3,53,199,45,83),(4,84,46,200,54),(5,55,201,47,85),(6,86,48,202,56),(7,57,203,33,87),(8,88,34,204,58),(9,59,205,35,89),(10,90,36,206,60),(11,61,207,37,91),(12,92,38,208,62),(13,63,193,39,93),(14,94,40,194,64),(15,49,195,41,95),(16,96,42,196,50),(17,138,124,147,178),(18,179,148,125,139),(19,140,126,149,180),(20,181,150,127,141),(21,142,128,151,182),(22,183,152,113,143),(23,144,114,153,184),(24,185,154,115,129),(25,130,116,155,186),(26,187,156,117,131),(27,132,118,157,188),(28,189,158,119,133),(29,134,120,159,190),(30,191,160,121,135),(31,136,122,145,192),(32,177,146,123,137),(65,239,218,161,106),(66,107,162,219,240),(67,225,220,163,108),(68,109,164,221,226),(69,227,222,165,110),(70,111,166,223,228),(71,229,224,167,112),(72,97,168,209,230),(73,231,210,169,98),(74,99,170,211,232),(75,233,212,171,100),(76,101,172,213,234),(77,235,214,173,102),(78,103,174,215,236),(79,237,216,175,104),(80,105,176,217,238)], [(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)], [(2,16),(3,15),(4,14),(5,13),(6,12),(7,11),(8,10),(17,159),(18,158),(19,157),(20,156),(21,155),(22,154),(23,153),(24,152),(25,151),(26,150),(27,149),(28,148),(29,147),(30,146),(31,145),(32,160),(33,207),(34,206),(35,205),(36,204),(37,203),(38,202),(39,201),(40,200),(41,199),(42,198),(43,197),(44,196),(45,195),(46,194),(47,193),(48,208),(49,83),(50,82),(51,81),(52,96),(53,95),(54,94),(55,93),(56,92),(57,91),(58,90),(59,89),(60,88),(61,87),(62,86),(63,85),(64,84),(65,75),(66,74),(67,73),(68,72),(69,71),(76,80),(77,79),(97,226),(98,225),(99,240),(100,239),(101,238),(102,237),(103,236),(104,235),(105,234),(106,233),(107,232),(108,231),(109,230),(110,229),(111,228),(112,227),(113,129),(114,144),(115,143),(116,142),(117,141),(118,140),(119,139),(120,138),(121,137),(122,136),(123,135),(124,134),(125,133),(126,132),(127,131),(128,130),(161,212),(162,211),(163,210),(164,209),(165,224),(166,223),(167,222),(168,221),(169,220),(170,219),(171,218),(172,217),(173,216),(174,215),(175,214),(176,213),(177,191),(178,190),(179,189),(180,188),(181,187),(182,186),(183,185)]])
75 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4 | 5A | 5B | 6A | 6B | 6C | 6D | 6E | 6F | 8A | 8B | 10A | 10B | 10C | 10D | 10E | 10F | 12A | 12B | 15A | 15B | 15C | 15D | 16A | 16B | 16C | 16D | 20A | 20B | 24A | 24B | 24C | 24D | 30A | 30B | 30C | 30D | 30E | ··· | 30L | 40A | 40B | 40C | 40D | 48A | ··· | 48H | 60A | 60B | 60C | 60D | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 15 | 15 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 24 | 24 | 24 | 24 | 30 | 30 | 30 | 30 | 30 | ··· | 30 | 40 | 40 | 40 | 40 | 48 | ··· | 48 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 8 | 40 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 8 | 8 | 40 | 40 | 2 | 2 | 2 | 2 | 8 | 8 | 8 | 8 | 2 | 2 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 4 | 4 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 8 | ··· | 8 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
75 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 | C3 | C6 | C6 | C6 | D4 | D5 | D8 | D10 | C3×D4 | C3×D5 | D16 | C5⋊D4 | C3×D8 | C6×D5 | C3×D16 | C3×C5⋊D4 | D4⋊D5 | C5⋊D16 | C3×D4⋊D5 | C3×C5⋊D16 |
| kernel | C3×C5⋊D16 | C3×C5⋊2C16 | C3×D40 | C15×D8 | C5⋊D16 | C5⋊2C16 | D40 | C5×D8 | C60 | C3×D8 | C30 | C24 | C20 | D8 | C15 | C12 | C10 | C8 | C5 | C4 | C6 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 2 | 4 | 4 | 8 |
Matrix representation of C3×C5⋊D16 ►in GL4(𝔽241) generated by
| 225 | 0 | 0 | 0 |
| 0 | 225 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 189 | 240 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 96 | 27 | 0 | 0 |
| 96 | 145 | 0 | 0 |
| 0 | 0 | 156 | 27 |
| 0 | 0 | 214 | 156 |
| 189 | 240 | 0 | 0 |
| 52 | 52 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
G:=sub<GL(4,GF(241))| [225,0,0,0,0,225,0,0,0,0,1,0,0,0,0,1],[189,1,0,0,240,0,0,0,0,0,1,0,0,0,0,1],[96,96,0,0,27,145,0,0,0,0,156,214,0,0,27,156],[189,52,0,0,240,52,0,0,0,0,0,1,0,0,1,0] >;
C3×C5⋊D16 in GAP, Magma, Sage, TeX
C_3\times C_5\rtimes D_{16} % in TeX
G:=Group("C3xC5:D16"); // GroupNames label
G:=SmallGroup(480,104);
// by ID
G=gap.SmallGroup(480,104);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,197,1011,514,192,2524,1271,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^5=c^16=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations
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