direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C5×C3⋊D16, C15⋊9D16, D24⋊3C10, C40.56D6, C30.53D8, C60.136D4, C120.63C22, C3⋊2(C5×D16), C3⋊C16⋊1C10, (C5×D8)⋊5S3, D8⋊1(C5×S3), C6.8(C5×D8), (C15×D8)⋊8C2, (C3×D8)⋊1C10, C8.4(S3×C10), C12.3(C5×D4), (C5×D24)⋊11C2, C24.2(C2×C10), C10.24(D4⋊S3), C20.66(C3⋊D4), (C5×C3⋊C16)⋊8C2, C2.4(C5×D4⋊S3), C4.1(C5×C3⋊D4), SmallGroup(480,145)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×C3⋊D16
G = < a,b,c,d | a5=b3=c16=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
Smallest permutation representation of C5×C3⋊D16
►On 240 points
Generators in S240
(1 164 146 43 30)(2 165 147 44 31)(3 166 148 45 32)(4 167 149 46 17)(5 168 150 47 18)(6 169 151 48 19)(7 170 152 33 20)(8 171 153 34 21)(9 172 154 35 22)(10 173 155 36 23)(11 174 156 37 24)(12 175 157 38 25)(13 176 158 39 26)(14 161 159 40 27)(15 162 160 41 28)(16 163 145 42 29)(49 78 104 178 217)(50 79 105 179 218)(51 80 106 180 219)(52 65 107 181 220)(53 66 108 182 221)(54 67 109 183 222)(55 68 110 184 223)(56 69 111 185 224)(57 70 112 186 209)(58 71 97 187 210)(59 72 98 188 211)(60 73 99 189 212)(61 74 100 190 213)(62 75 101 191 214)(63 76 102 192 215)(64 77 103 177 216)(81 208 115 237 139)(82 193 116 238 140)(83 194 117 239 141)(84 195 118 240 142)(85 196 119 225 143)(86 197 120 226 144)(87 198 121 227 129)(88 199 122 228 130)(89 200 123 229 131)(90 201 124 230 132)(91 202 125 231 133)(92 203 126 232 134)(93 204 127 233 135)(94 205 128 234 136)(95 206 113 235 137)(96 207 114 236 138)
(1 194 57)(2 58 195)(3 196 59)(4 60 197)(5 198 61)(6 62 199)(7 200 63)(8 64 201)(9 202 49)(10 50 203)(11 204 51)(12 52 205)(13 206 53)(14 54 207)(15 208 55)(16 56 193)(17 212 86)(18 87 213)(19 214 88)(20 89 215)(21 216 90)(22 91 217)(23 218 92)(24 93 219)(25 220 94)(26 95 221)(27 222 96)(28 81 223)(29 224 82)(30 83 209)(31 210 84)(32 85 211)(33 131 192)(34 177 132)(35 133 178)(36 179 134)(37 135 180)(38 181 136)(39 137 182)(40 183 138)(41 139 184)(42 185 140)(43 141 186)(44 187 142)(45 143 188)(46 189 144)(47 129 190)(48 191 130)(65 128 175)(66 176 113)(67 114 161)(68 162 115)(69 116 163)(70 164 117)(71 118 165)(72 166 119)(73 120 167)(74 168 121)(75 122 169)(76 170 123)(77 124 171)(78 172 125)(79 126 173)(80 174 127)(97 240 147)(98 148 225)(99 226 149)(100 150 227)(101 228 151)(102 152 229)(103 230 153)(104 154 231)(105 232 155)(106 156 233)(107 234 157)(108 158 235)(109 236 159)(110 160 237)(111 238 145)(112 146 239)
(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 27)(18 26)(19 25)(20 24)(21 23)(28 32)(29 31)(33 37)(34 36)(38 48)(39 47)(40 46)(41 45)(42 44)(49 202)(50 201)(51 200)(52 199)(53 198)(54 197)(55 196)(56 195)(57 194)(58 193)(59 208)(60 207)(61 206)(62 205)(63 204)(64 203)(65 122)(66 121)(67 120)(68 119)(69 118)(70 117)(71 116)(72 115)(73 114)(74 113)(75 128)(76 127)(77 126)(78 125)(79 124)(80 123)(81 211)(82 210)(83 209)(84 224)(85 223)(86 222)(87 221)(88 220)(89 219)(90 218)(91 217)(92 216)(93 215)(94 214)(95 213)(96 212)(97 238)(98 237)(99 236)(100 235)(101 234)(102 233)(103 232)(104 231)(105 230)(106 229)(107 228)(108 227)(109 226)(110 225)(111 240)(112 239)(129 182)(130 181)(131 180)(132 179)(133 178)(134 177)(135 192)(136 191)(137 190)(138 189)(139 188)(140 187)(141 186)(142 185)(143 184)(144 183)(145 147)(148 160)(149 159)(150 158)(151 157)(152 156)(153 155)(161 167)(162 166)(163 165)(168 176)(169 175)(170 174)(171 173)
G:=sub<Sym(240)| (1,164,146,43,30)(2,165,147,44,31)(3,166,148,45,32)(4,167,149,46,17)(5,168,150,47,18)(6,169,151,48,19)(7,170,152,33,20)(8,171,153,34,21)(9,172,154,35,22)(10,173,155,36,23)(11,174,156,37,24)(12,175,157,38,25)(13,176,158,39,26)(14,161,159,40,27)(15,162,160,41,28)(16,163,145,42,29)(49,78,104,178,217)(50,79,105,179,218)(51,80,106,180,219)(52,65,107,181,220)(53,66,108,182,221)(54,67,109,183,222)(55,68,110,184,223)(56,69,111,185,224)(57,70,112,186,209)(58,71,97,187,210)(59,72,98,188,211)(60,73,99,189,212)(61,74,100,190,213)(62,75,101,191,214)(63,76,102,192,215)(64,77,103,177,216)(81,208,115,237,139)(82,193,116,238,140)(83,194,117,239,141)(84,195,118,240,142)(85,196,119,225,143)(86,197,120,226,144)(87,198,121,227,129)(88,199,122,228,130)(89,200,123,229,131)(90,201,124,230,132)(91,202,125,231,133)(92,203,126,232,134)(93,204,127,233,135)(94,205,128,234,136)(95,206,113,235,137)(96,207,114,236,138), (1,194,57)(2,58,195)(3,196,59)(4,60,197)(5,198,61)(6,62,199)(7,200,63)(8,64,201)(9,202,49)(10,50,203)(11,204,51)(12,52,205)(13,206,53)(14,54,207)(15,208,55)(16,56,193)(17,212,86)(18,87,213)(19,214,88)(20,89,215)(21,216,90)(22,91,217)(23,218,92)(24,93,219)(25,220,94)(26,95,221)(27,222,96)(28,81,223)(29,224,82)(30,83,209)(31,210,84)(32,85,211)(33,131,192)(34,177,132)(35,133,178)(36,179,134)(37,135,180)(38,181,136)(39,137,182)(40,183,138)(41,139,184)(42,185,140)(43,141,186)(44,187,142)(45,143,188)(46,189,144)(47,129,190)(48,191,130)(65,128,175)(66,176,113)(67,114,161)(68,162,115)(69,116,163)(70,164,117)(71,118,165)(72,166,119)(73,120,167)(74,168,121)(75,122,169)(76,170,123)(77,124,171)(78,172,125)(79,126,173)(80,174,127)(97,240,147)(98,148,225)(99,226,149)(100,150,227)(101,228,151)(102,152,229)(103,230,153)(104,154,231)(105,232,155)(106,156,233)(107,234,157)(108,158,235)(109,236,159)(110,160,237)(111,238,145)(112,146,239), (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)(17,27)(18,26)(19,25)(20,24)(21,23)(28,32)(29,31)(33,37)(34,36)(38,48)(39,47)(40,46)(41,45)(42,44)(49,202)(50,201)(51,200)(52,199)(53,198)(54,197)(55,196)(56,195)(57,194)(58,193)(59,208)(60,207)(61,206)(62,205)(63,204)(64,203)(65,122)(66,121)(67,120)(68,119)(69,118)(70,117)(71,116)(72,115)(73,114)(74,113)(75,128)(76,127)(77,126)(78,125)(79,124)(80,123)(81,211)(82,210)(83,209)(84,224)(85,223)(86,222)(87,221)(88,220)(89,219)(90,218)(91,217)(92,216)(93,215)(94,214)(95,213)(96,212)(97,238)(98,237)(99,236)(100,235)(101,234)(102,233)(103,232)(104,231)(105,230)(106,229)(107,228)(108,227)(109,226)(110,225)(111,240)(112,239)(129,182)(130,181)(131,180)(132,179)(133,178)(134,177)(135,192)(136,191)(137,190)(138,189)(139,188)(140,187)(141,186)(142,185)(143,184)(144,183)(145,147)(148,160)(149,159)(150,158)(151,157)(152,156)(153,155)(161,167)(162,166)(163,165)(168,176)(169,175)(170,174)(171,173)>;
G:=Group( (1,164,146,43,30)(2,165,147,44,31)(3,166,148,45,32)(4,167,149,46,17)(5,168,150,47,18)(6,169,151,48,19)(7,170,152,33,20)(8,171,153,34,21)(9,172,154,35,22)(10,173,155,36,23)(11,174,156,37,24)(12,175,157,38,25)(13,176,158,39,26)(14,161,159,40,27)(15,162,160,41,28)(16,163,145,42,29)(49,78,104,178,217)(50,79,105,179,218)(51,80,106,180,219)(52,65,107,181,220)(53,66,108,182,221)(54,67,109,183,222)(55,68,110,184,223)(56,69,111,185,224)(57,70,112,186,209)(58,71,97,187,210)(59,72,98,188,211)(60,73,99,189,212)(61,74,100,190,213)(62,75,101,191,214)(63,76,102,192,215)(64,77,103,177,216)(81,208,115,237,139)(82,193,116,238,140)(83,194,117,239,141)(84,195,118,240,142)(85,196,119,225,143)(86,197,120,226,144)(87,198,121,227,129)(88,199,122,228,130)(89,200,123,229,131)(90,201,124,230,132)(91,202,125,231,133)(92,203,126,232,134)(93,204,127,233,135)(94,205,128,234,136)(95,206,113,235,137)(96,207,114,236,138), (1,194,57)(2,58,195)(3,196,59)(4,60,197)(5,198,61)(6,62,199)(7,200,63)(8,64,201)(9,202,49)(10,50,203)(11,204,51)(12,52,205)(13,206,53)(14,54,207)(15,208,55)(16,56,193)(17,212,86)(18,87,213)(19,214,88)(20,89,215)(21,216,90)(22,91,217)(23,218,92)(24,93,219)(25,220,94)(26,95,221)(27,222,96)(28,81,223)(29,224,82)(30,83,209)(31,210,84)(32,85,211)(33,131,192)(34,177,132)(35,133,178)(36,179,134)(37,135,180)(38,181,136)(39,137,182)(40,183,138)(41,139,184)(42,185,140)(43,141,186)(44,187,142)(45,143,188)(46,189,144)(47,129,190)(48,191,130)(65,128,175)(66,176,113)(67,114,161)(68,162,115)(69,116,163)(70,164,117)(71,118,165)(72,166,119)(73,120,167)(74,168,121)(75,122,169)(76,170,123)(77,124,171)(78,172,125)(79,126,173)(80,174,127)(97,240,147)(98,148,225)(99,226,149)(100,150,227)(101,228,151)(102,152,229)(103,230,153)(104,154,231)(105,232,155)(106,156,233)(107,234,157)(108,158,235)(109,236,159)(110,160,237)(111,238,145)(112,146,239), (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)(17,27)(18,26)(19,25)(20,24)(21,23)(28,32)(29,31)(33,37)(34,36)(38,48)(39,47)(40,46)(41,45)(42,44)(49,202)(50,201)(51,200)(52,199)(53,198)(54,197)(55,196)(56,195)(57,194)(58,193)(59,208)(60,207)(61,206)(62,205)(63,204)(64,203)(65,122)(66,121)(67,120)(68,119)(69,118)(70,117)(71,116)(72,115)(73,114)(74,113)(75,128)(76,127)(77,126)(78,125)(79,124)(80,123)(81,211)(82,210)(83,209)(84,224)(85,223)(86,222)(87,221)(88,220)(89,219)(90,218)(91,217)(92,216)(93,215)(94,214)(95,213)(96,212)(97,238)(98,237)(99,236)(100,235)(101,234)(102,233)(103,232)(104,231)(105,230)(106,229)(107,228)(108,227)(109,226)(110,225)(111,240)(112,239)(129,182)(130,181)(131,180)(132,179)(133,178)(134,177)(135,192)(136,191)(137,190)(138,189)(139,188)(140,187)(141,186)(142,185)(143,184)(144,183)(145,147)(148,160)(149,159)(150,158)(151,157)(152,156)(153,155)(161,167)(162,166)(163,165)(168,176)(169,175)(170,174)(171,173) );
G=PermutationGroup([[(1,164,146,43,30),(2,165,147,44,31),(3,166,148,45,32),(4,167,149,46,17),(5,168,150,47,18),(6,169,151,48,19),(7,170,152,33,20),(8,171,153,34,21),(9,172,154,35,22),(10,173,155,36,23),(11,174,156,37,24),(12,175,157,38,25),(13,176,158,39,26),(14,161,159,40,27),(15,162,160,41,28),(16,163,145,42,29),(49,78,104,178,217),(50,79,105,179,218),(51,80,106,180,219),(52,65,107,181,220),(53,66,108,182,221),(54,67,109,183,222),(55,68,110,184,223),(56,69,111,185,224),(57,70,112,186,209),(58,71,97,187,210),(59,72,98,188,211),(60,73,99,189,212),(61,74,100,190,213),(62,75,101,191,214),(63,76,102,192,215),(64,77,103,177,216),(81,208,115,237,139),(82,193,116,238,140),(83,194,117,239,141),(84,195,118,240,142),(85,196,119,225,143),(86,197,120,226,144),(87,198,121,227,129),(88,199,122,228,130),(89,200,123,229,131),(90,201,124,230,132),(91,202,125,231,133),(92,203,126,232,134),(93,204,127,233,135),(94,205,128,234,136),(95,206,113,235,137),(96,207,114,236,138)], [(1,194,57),(2,58,195),(3,196,59),(4,60,197),(5,198,61),(6,62,199),(7,200,63),(8,64,201),(9,202,49),(10,50,203),(11,204,51),(12,52,205),(13,206,53),(14,54,207),(15,208,55),(16,56,193),(17,212,86),(18,87,213),(19,214,88),(20,89,215),(21,216,90),(22,91,217),(23,218,92),(24,93,219),(25,220,94),(26,95,221),(27,222,96),(28,81,223),(29,224,82),(30,83,209),(31,210,84),(32,85,211),(33,131,192),(34,177,132),(35,133,178),(36,179,134),(37,135,180),(38,181,136),(39,137,182),(40,183,138),(41,139,184),(42,185,140),(43,141,186),(44,187,142),(45,143,188),(46,189,144),(47,129,190),(48,191,130),(65,128,175),(66,176,113),(67,114,161),(68,162,115),(69,116,163),(70,164,117),(71,118,165),(72,166,119),(73,120,167),(74,168,121),(75,122,169),(76,170,123),(77,124,171),(78,172,125),(79,126,173),(80,174,127),(97,240,147),(98,148,225),(99,226,149),(100,150,227),(101,228,151),(102,152,229),(103,230,153),(104,154,231),(105,232,155),(106,156,233),(107,234,157),(108,158,235),(109,236,159),(110,160,237),(111,238,145),(112,146,239)], [(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),(17,27),(18,26),(19,25),(20,24),(21,23),(28,32),(29,31),(33,37),(34,36),(38,48),(39,47),(40,46),(41,45),(42,44),(49,202),(50,201),(51,200),(52,199),(53,198),(54,197),(55,196),(56,195),(57,194),(58,193),(59,208),(60,207),(61,206),(62,205),(63,204),(64,203),(65,122),(66,121),(67,120),(68,119),(69,118),(70,117),(71,116),(72,115),(73,114),(74,113),(75,128),(76,127),(77,126),(78,125),(79,124),(80,123),(81,211),(82,210),(83,209),(84,224),(85,223),(86,222),(87,221),(88,220),(89,219),(90,218),(91,217),(92,216),(93,215),(94,214),(95,213),(96,212),(97,238),(98,237),(99,236),(100,235),(101,234),(102,233),(103,232),(104,231),(105,230),(106,229),(107,228),(108,227),(109,226),(110,225),(111,240),(112,239),(129,182),(130,181),(131,180),(132,179),(133,178),(134,177),(135,192),(136,191),(137,190),(138,189),(139,188),(140,187),(141,186),(142,185),(143,184),(144,183),(145,147),(148,160),(149,159),(150,158),(151,157),(152,156),(153,155),(161,167),(162,166),(163,165),(168,176),(169,175),(170,174),(171,173)]])
90 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4 | 5A | 5B | 5C | 5D | 6A | 6B | 6C | 8A | 8B | 10A | 10B | 10C | 10D | 10E | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 12 | 15A | 15B | 15C | 15D | 16A | 16B | 16C | 16D | 20A | 20B | 20C | 20D | 24A | 24B | 30A | 30B | 30C | 30D | 30E | ··· | 30L | 40A | ··· | 40H | 60A | 60B | 60C | 60D | 80A | ··· | 80P | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 15 | 15 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 20 | 20 | 24 | 24 | 30 | 30 | 30 | 30 | 30 | ··· | 30 | 40 | ··· | 40 | 60 | 60 | 60 | 60 | 80 | ··· | 80 | 120 | ··· | 120 |
| size | 1 | 1 | 8 | 24 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 8 | 8 | 2 | 2 | 1 | 1 | 1 | 1 | 8 | 8 | 8 | 8 | 24 | 24 | 24 | 24 | 4 | 2 | 2 | 2 | 2 | 6 | 6 | 6 | 6 | 2 | 2 | 2 | 2 | 4 | 4 | 2 | 2 | 2 | 2 | 8 | ··· | 8 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 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 | D16 | C5×D4 | S3×C10 | C5×D8 | C5×C3⋊D4 | C5×D16 | D4⋊S3 | C3⋊D16 | C5×D4⋊S3 | C5×C3⋊D16 |
| kernel | C5×C3⋊D16 | C5×C3⋊C16 | C5×D24 | C15×D8 | C3⋊D16 | C3⋊C16 | D24 | C3×D8 | C5×D8 | C60 | C40 | C30 | C20 | D8 | 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×C3⋊D16 ►in GL4(𝔽241) generated by
| 205 | 0 | 0 | 0 |
| 0 | 205 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 240 | 240 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 240 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 58 | 137 |
| 0 | 0 | 227 | 129 |
| 1 | 0 | 0 | 0 |
| 240 | 240 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 238 | 240 |
G:=sub<GL(4,GF(241))| [205,0,0,0,0,205,0,0,0,0,1,0,0,0,0,1],[240,1,0,0,240,0,0,0,0,0,1,0,0,0,0,1],[240,1,0,0,0,1,0,0,0,0,58,227,0,0,137,129],[1,240,0,0,0,240,0,0,0,0,1,238,0,0,0,240] >;
C5×C3⋊D16 in GAP, Magma, Sage, TeX
C_5\times C_3\rtimes D_{16} % in TeX
G:=Group("C5xC3:D16"); // GroupNames label
G:=SmallGroup(480,145);
// by ID
G=gap.SmallGroup(480,145);
# by ID
G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,309,1683,850,192,4204,2111,102,15686]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^3=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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