direct product, metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C3×C16⋊D5, C80⋊2C6, C48⋊4D5, C240⋊5C2, C15⋊8SD32, D40.1C6, C6.14D40, C30.28D8, Dic20⋊1C6, C60.170D4, C24.71D10, C12.40D20, C120.84C22, C16⋊2(C3×D5), C5⋊1(C3×SD32), C8.14(C6×D5), C2.4(C3×D40), C4.2(C3×D20), C10.2(C3×D8), C40.15(C2×C6), (C3×D40).2C2, C20.25(C3×D4), (C3×Dic20)⋊5C2, SmallGroup(480,78)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C16⋊D5
G = < a,b,c,d | a3=b16=c5=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b7, dcd=c-1 >
Smallest permutation representation of C3×C16⋊D5
►On 240 points
Generators in S240
(1 150 103)(2 151 104)(3 152 105)(4 153 106)(5 154 107)(6 155 108)(7 156 109)(8 157 110)(9 158 111)(10 159 112)(11 160 97)(12 145 98)(13 146 99)(14 147 100)(15 148 101)(16 149 102)(17 209 130)(18 210 131)(19 211 132)(20 212 133)(21 213 134)(22 214 135)(23 215 136)(24 216 137)(25 217 138)(26 218 139)(27 219 140)(28 220 141)(29 221 142)(30 222 143)(31 223 144)(32 224 129)(33 205 87)(34 206 88)(35 207 89)(36 208 90)(37 193 91)(38 194 92)(39 195 93)(40 196 94)(41 197 95)(42 198 96)(43 199 81)(44 200 82)(45 201 83)(46 202 84)(47 203 85)(48 204 86)(49 65 185)(50 66 186)(51 67 187)(52 68 188)(53 69 189)(54 70 190)(55 71 191)(56 72 192)(57 73 177)(58 74 178)(59 75 179)(60 76 180)(61 77 181)(62 78 182)(63 79 183)(64 80 184)(113 232 162)(114 233 163)(115 234 164)(116 235 165)(117 236 166)(118 237 167)(119 238 168)(120 239 169)(121 240 170)(122 225 171)(123 226 172)(124 227 173)(125 228 174)(126 229 175)(127 230 176)(128 231 161)
(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)
(1 197 64 212 172)(2 198 49 213 173)(3 199 50 214 174)(4 200 51 215 175)(5 201 52 216 176)(6 202 53 217 161)(7 203 54 218 162)(8 204 55 219 163)(9 205 56 220 164)(10 206 57 221 165)(11 207 58 222 166)(12 208 59 223 167)(13 193 60 224 168)(14 194 61 209 169)(15 195 62 210 170)(16 196 63 211 171)(17 239 100 38 181)(18 240 101 39 182)(19 225 102 40 183)(20 226 103 41 184)(21 227 104 42 185)(22 228 105 43 186)(23 229 106 44 187)(24 230 107 45 188)(25 231 108 46 189)(26 232 109 47 190)(27 233 110 48 191)(28 234 111 33 192)(29 235 112 34 177)(30 236 97 35 178)(31 237 98 36 179)(32 238 99 37 180)(65 134 124 151 96)(66 135 125 152 81)(67 136 126 153 82)(68 137 127 154 83)(69 138 128 155 84)(70 139 113 156 85)(71 140 114 157 86)(72 141 115 158 87)(73 142 116 159 88)(74 143 117 160 89)(75 144 118 145 90)(76 129 119 146 91)(77 130 120 147 92)(78 131 121 148 93)(79 132 122 149 94)(80 133 123 150 95)
(1 172)(2 163)(3 170)(4 161)(5 168)(6 175)(7 166)(8 173)(9 164)(10 171)(11 162)(12 169)(13 176)(14 167)(15 174)(16 165)(17 36)(18 43)(19 34)(20 41)(21 48)(22 39)(23 46)(24 37)(25 44)(26 35)(27 42)(28 33)(29 40)(30 47)(31 38)(32 45)(49 55)(50 62)(51 53)(52 60)(54 58)(57 63)(59 61)(65 71)(66 78)(67 69)(68 76)(70 74)(73 79)(75 77)(81 131)(82 138)(83 129)(84 136)(85 143)(86 134)(87 141)(88 132)(89 139)(90 130)(91 137)(92 144)(93 135)(94 142)(95 133)(96 140)(97 232)(98 239)(99 230)(100 237)(101 228)(102 235)(103 226)(104 233)(105 240)(106 231)(107 238)(108 229)(109 236)(110 227)(111 234)(112 225)(113 160)(114 151)(115 158)(116 149)(117 156)(118 147)(119 154)(120 145)(121 152)(122 159)(123 150)(124 157)(125 148)(126 155)(127 146)(128 153)(177 183)(178 190)(179 181)(180 188)(182 186)(185 191)(187 189)(193 216)(194 223)(195 214)(196 221)(197 212)(198 219)(199 210)(200 217)(201 224)(202 215)(203 222)(204 213)(205 220)(206 211)(207 218)(208 209)
G:=sub<Sym(240)| (1,150,103)(2,151,104)(3,152,105)(4,153,106)(5,154,107)(6,155,108)(7,156,109)(8,157,110)(9,158,111)(10,159,112)(11,160,97)(12,145,98)(13,146,99)(14,147,100)(15,148,101)(16,149,102)(17,209,130)(18,210,131)(19,211,132)(20,212,133)(21,213,134)(22,214,135)(23,215,136)(24,216,137)(25,217,138)(26,218,139)(27,219,140)(28,220,141)(29,221,142)(30,222,143)(31,223,144)(32,224,129)(33,205,87)(34,206,88)(35,207,89)(36,208,90)(37,193,91)(38,194,92)(39,195,93)(40,196,94)(41,197,95)(42,198,96)(43,199,81)(44,200,82)(45,201,83)(46,202,84)(47,203,85)(48,204,86)(49,65,185)(50,66,186)(51,67,187)(52,68,188)(53,69,189)(54,70,190)(55,71,191)(56,72,192)(57,73,177)(58,74,178)(59,75,179)(60,76,180)(61,77,181)(62,78,182)(63,79,183)(64,80,184)(113,232,162)(114,233,163)(115,234,164)(116,235,165)(117,236,166)(118,237,167)(119,238,168)(120,239,169)(121,240,170)(122,225,171)(123,226,172)(124,227,173)(125,228,174)(126,229,175)(127,230,176)(128,231,161), (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), (1,197,64,212,172)(2,198,49,213,173)(3,199,50,214,174)(4,200,51,215,175)(5,201,52,216,176)(6,202,53,217,161)(7,203,54,218,162)(8,204,55,219,163)(9,205,56,220,164)(10,206,57,221,165)(11,207,58,222,166)(12,208,59,223,167)(13,193,60,224,168)(14,194,61,209,169)(15,195,62,210,170)(16,196,63,211,171)(17,239,100,38,181)(18,240,101,39,182)(19,225,102,40,183)(20,226,103,41,184)(21,227,104,42,185)(22,228,105,43,186)(23,229,106,44,187)(24,230,107,45,188)(25,231,108,46,189)(26,232,109,47,190)(27,233,110,48,191)(28,234,111,33,192)(29,235,112,34,177)(30,236,97,35,178)(31,237,98,36,179)(32,238,99,37,180)(65,134,124,151,96)(66,135,125,152,81)(67,136,126,153,82)(68,137,127,154,83)(69,138,128,155,84)(70,139,113,156,85)(71,140,114,157,86)(72,141,115,158,87)(73,142,116,159,88)(74,143,117,160,89)(75,144,118,145,90)(76,129,119,146,91)(77,130,120,147,92)(78,131,121,148,93)(79,132,122,149,94)(80,133,123,150,95), (1,172)(2,163)(3,170)(4,161)(5,168)(6,175)(7,166)(8,173)(9,164)(10,171)(11,162)(12,169)(13,176)(14,167)(15,174)(16,165)(17,36)(18,43)(19,34)(20,41)(21,48)(22,39)(23,46)(24,37)(25,44)(26,35)(27,42)(28,33)(29,40)(30,47)(31,38)(32,45)(49,55)(50,62)(51,53)(52,60)(54,58)(57,63)(59,61)(65,71)(66,78)(67,69)(68,76)(70,74)(73,79)(75,77)(81,131)(82,138)(83,129)(84,136)(85,143)(86,134)(87,141)(88,132)(89,139)(90,130)(91,137)(92,144)(93,135)(94,142)(95,133)(96,140)(97,232)(98,239)(99,230)(100,237)(101,228)(102,235)(103,226)(104,233)(105,240)(106,231)(107,238)(108,229)(109,236)(110,227)(111,234)(112,225)(113,160)(114,151)(115,158)(116,149)(117,156)(118,147)(119,154)(120,145)(121,152)(122,159)(123,150)(124,157)(125,148)(126,155)(127,146)(128,153)(177,183)(178,190)(179,181)(180,188)(182,186)(185,191)(187,189)(193,216)(194,223)(195,214)(196,221)(197,212)(198,219)(199,210)(200,217)(201,224)(202,215)(203,222)(204,213)(205,220)(206,211)(207,218)(208,209)>;
G:=Group( (1,150,103)(2,151,104)(3,152,105)(4,153,106)(5,154,107)(6,155,108)(7,156,109)(8,157,110)(9,158,111)(10,159,112)(11,160,97)(12,145,98)(13,146,99)(14,147,100)(15,148,101)(16,149,102)(17,209,130)(18,210,131)(19,211,132)(20,212,133)(21,213,134)(22,214,135)(23,215,136)(24,216,137)(25,217,138)(26,218,139)(27,219,140)(28,220,141)(29,221,142)(30,222,143)(31,223,144)(32,224,129)(33,205,87)(34,206,88)(35,207,89)(36,208,90)(37,193,91)(38,194,92)(39,195,93)(40,196,94)(41,197,95)(42,198,96)(43,199,81)(44,200,82)(45,201,83)(46,202,84)(47,203,85)(48,204,86)(49,65,185)(50,66,186)(51,67,187)(52,68,188)(53,69,189)(54,70,190)(55,71,191)(56,72,192)(57,73,177)(58,74,178)(59,75,179)(60,76,180)(61,77,181)(62,78,182)(63,79,183)(64,80,184)(113,232,162)(114,233,163)(115,234,164)(116,235,165)(117,236,166)(118,237,167)(119,238,168)(120,239,169)(121,240,170)(122,225,171)(123,226,172)(124,227,173)(125,228,174)(126,229,175)(127,230,176)(128,231,161), (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), (1,197,64,212,172)(2,198,49,213,173)(3,199,50,214,174)(4,200,51,215,175)(5,201,52,216,176)(6,202,53,217,161)(7,203,54,218,162)(8,204,55,219,163)(9,205,56,220,164)(10,206,57,221,165)(11,207,58,222,166)(12,208,59,223,167)(13,193,60,224,168)(14,194,61,209,169)(15,195,62,210,170)(16,196,63,211,171)(17,239,100,38,181)(18,240,101,39,182)(19,225,102,40,183)(20,226,103,41,184)(21,227,104,42,185)(22,228,105,43,186)(23,229,106,44,187)(24,230,107,45,188)(25,231,108,46,189)(26,232,109,47,190)(27,233,110,48,191)(28,234,111,33,192)(29,235,112,34,177)(30,236,97,35,178)(31,237,98,36,179)(32,238,99,37,180)(65,134,124,151,96)(66,135,125,152,81)(67,136,126,153,82)(68,137,127,154,83)(69,138,128,155,84)(70,139,113,156,85)(71,140,114,157,86)(72,141,115,158,87)(73,142,116,159,88)(74,143,117,160,89)(75,144,118,145,90)(76,129,119,146,91)(77,130,120,147,92)(78,131,121,148,93)(79,132,122,149,94)(80,133,123,150,95), (1,172)(2,163)(3,170)(4,161)(5,168)(6,175)(7,166)(8,173)(9,164)(10,171)(11,162)(12,169)(13,176)(14,167)(15,174)(16,165)(17,36)(18,43)(19,34)(20,41)(21,48)(22,39)(23,46)(24,37)(25,44)(26,35)(27,42)(28,33)(29,40)(30,47)(31,38)(32,45)(49,55)(50,62)(51,53)(52,60)(54,58)(57,63)(59,61)(65,71)(66,78)(67,69)(68,76)(70,74)(73,79)(75,77)(81,131)(82,138)(83,129)(84,136)(85,143)(86,134)(87,141)(88,132)(89,139)(90,130)(91,137)(92,144)(93,135)(94,142)(95,133)(96,140)(97,232)(98,239)(99,230)(100,237)(101,228)(102,235)(103,226)(104,233)(105,240)(106,231)(107,238)(108,229)(109,236)(110,227)(111,234)(112,225)(113,160)(114,151)(115,158)(116,149)(117,156)(118,147)(119,154)(120,145)(121,152)(122,159)(123,150)(124,157)(125,148)(126,155)(127,146)(128,153)(177,183)(178,190)(179,181)(180,188)(182,186)(185,191)(187,189)(193,216)(194,223)(195,214)(196,221)(197,212)(198,219)(199,210)(200,217)(201,224)(202,215)(203,222)(204,213)(205,220)(206,211)(207,218)(208,209) );
G=PermutationGroup([[(1,150,103),(2,151,104),(3,152,105),(4,153,106),(5,154,107),(6,155,108),(7,156,109),(8,157,110),(9,158,111),(10,159,112),(11,160,97),(12,145,98),(13,146,99),(14,147,100),(15,148,101),(16,149,102),(17,209,130),(18,210,131),(19,211,132),(20,212,133),(21,213,134),(22,214,135),(23,215,136),(24,216,137),(25,217,138),(26,218,139),(27,219,140),(28,220,141),(29,221,142),(30,222,143),(31,223,144),(32,224,129),(33,205,87),(34,206,88),(35,207,89),(36,208,90),(37,193,91),(38,194,92),(39,195,93),(40,196,94),(41,197,95),(42,198,96),(43,199,81),(44,200,82),(45,201,83),(46,202,84),(47,203,85),(48,204,86),(49,65,185),(50,66,186),(51,67,187),(52,68,188),(53,69,189),(54,70,190),(55,71,191),(56,72,192),(57,73,177),(58,74,178),(59,75,179),(60,76,180),(61,77,181),(62,78,182),(63,79,183),(64,80,184),(113,232,162),(114,233,163),(115,234,164),(116,235,165),(117,236,166),(118,237,167),(119,238,168),(120,239,169),(121,240,170),(122,225,171),(123,226,172),(124,227,173),(125,228,174),(126,229,175),(127,230,176),(128,231,161)], [(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)], [(1,197,64,212,172),(2,198,49,213,173),(3,199,50,214,174),(4,200,51,215,175),(5,201,52,216,176),(6,202,53,217,161),(7,203,54,218,162),(8,204,55,219,163),(9,205,56,220,164),(10,206,57,221,165),(11,207,58,222,166),(12,208,59,223,167),(13,193,60,224,168),(14,194,61,209,169),(15,195,62,210,170),(16,196,63,211,171),(17,239,100,38,181),(18,240,101,39,182),(19,225,102,40,183),(20,226,103,41,184),(21,227,104,42,185),(22,228,105,43,186),(23,229,106,44,187),(24,230,107,45,188),(25,231,108,46,189),(26,232,109,47,190),(27,233,110,48,191),(28,234,111,33,192),(29,235,112,34,177),(30,236,97,35,178),(31,237,98,36,179),(32,238,99,37,180),(65,134,124,151,96),(66,135,125,152,81),(67,136,126,153,82),(68,137,127,154,83),(69,138,128,155,84),(70,139,113,156,85),(71,140,114,157,86),(72,141,115,158,87),(73,142,116,159,88),(74,143,117,160,89),(75,144,118,145,90),(76,129,119,146,91),(77,130,120,147,92),(78,131,121,148,93),(79,132,122,149,94),(80,133,123,150,95)], [(1,172),(2,163),(3,170),(4,161),(5,168),(6,175),(7,166),(8,173),(9,164),(10,171),(11,162),(12,169),(13,176),(14,167),(15,174),(16,165),(17,36),(18,43),(19,34),(20,41),(21,48),(22,39),(23,46),(24,37),(25,44),(26,35),(27,42),(28,33),(29,40),(30,47),(31,38),(32,45),(49,55),(50,62),(51,53),(52,60),(54,58),(57,63),(59,61),(65,71),(66,78),(67,69),(68,76),(70,74),(73,79),(75,77),(81,131),(82,138),(83,129),(84,136),(85,143),(86,134),(87,141),(88,132),(89,139),(90,130),(91,137),(92,144),(93,135),(94,142),(95,133),(96,140),(97,232),(98,239),(99,230),(100,237),(101,228),(102,235),(103,226),(104,233),(105,240),(106,231),(107,238),(108,229),(109,236),(110,227),(111,234),(112,225),(113,160),(114,151),(115,158),(116,149),(117,156),(118,147),(119,154),(120,145),(121,152),(122,159),(123,150),(124,157),(125,148),(126,155),(127,146),(128,153),(177,183),(178,190),(179,181),(180,188),(182,186),(185,191),(187,189),(193,216),(194,223),(195,214),(196,221),(197,212),(198,219),(199,210),(200,217),(201,224),(202,215),(203,222),(204,213),(205,220),(206,211),(207,218),(208,209)]])
129 conjugacy classes
| class | 1 | 2A | 2B | 3A | 3B | 4A | 4B | 5A | 5B | 6A | 6B | 6C | 6D | 8A | 8B | 10A | 10B | 12A | 12B | 12C | 12D | 15A | 15B | 15C | 15D | 16A | 16B | 16C | 16D | 20A | 20B | 20C | 20D | 24A | 24B | 24C | 24D | 30A | 30B | 30C | 30D | 40A | ··· | 40H | 48A | ··· | 48H | 60A | ··· | 60H | 80A | ··· | 80P | 120A | ··· | 120P | 240A | ··· | 240AF |
| order | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 8 | 8 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 30 | 30 | 30 | 30 | 40 | ··· | 40 | 48 | ··· | 48 | 60 | ··· | 60 | 80 | ··· | 80 | 120 | ··· | 120 | 240 | ··· | 240 |
| size | 1 | 1 | 40 | 1 | 1 | 2 | 40 | 2 | 2 | 1 | 1 | 40 | 40 | 2 | 2 | 2 | 2 | 2 | 2 | 40 | 40 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
129 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | ||||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | D4 | D5 | D8 | D10 | C3×D4 | C3×D5 | SD32 | D20 | C3×D8 | C6×D5 | D40 | C3×SD32 | C3×D20 | C16⋊D5 | C3×D40 | C3×C16⋊D5 |
| kernel | C3×C16⋊D5 | C240 | C3×D40 | C3×Dic20 | C16⋊D5 | C80 | D40 | Dic20 | C60 | C48 | C30 | C24 | C20 | C16 | C15 | C12 | C10 | C8 | C6 | C5 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 16 | 16 | 32 |
Matrix representation of C3×C16⋊D5 ►in GL4(𝔽241) generated by
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 221 | 33 | 0 | 0 |
| 179 | 42 | 0 | 0 |
| 0 | 0 | 179 | 138 |
| 0 | 0 | 206 | 144 |
| 52 | 240 | 0 | 0 |
| 53 | 240 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 51 | 0 | 0 |
| 52 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 0 | 0 | 240 |
G:=sub<GL(4,GF(241))| [15,0,0,0,0,15,0,0,0,0,1,0,0,0,0,1],[221,179,0,0,33,42,0,0,0,0,179,206,0,0,138,144],[52,53,0,0,240,240,0,0,0,0,1,0,0,0,0,1],[0,52,0,0,51,0,0,0,0,0,1,0,0,0,1,240] >;
C3×C16⋊D5 in GAP, Magma, Sage, TeX
C_3\times C_{16}\rtimes D_5 % in TeX
G:=Group("C3xC16:D5"); // GroupNames label
G:=SmallGroup(480,78);
// by ID
G=gap.SmallGroup(480,78);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,197,260,2355,80,2524,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^16=c^5=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b^7,d*c*d=c^-1>;
// generators/relations
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