direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: D5×C3⋊C16, C40.48D6, C24.55D10, C120.51C22, C3⋊3(D5×C16), C15⋊5(C2×C16), (C3×D5)⋊1C16, (C6×D5).1C8, C6.11(C8×D5), C8.34(S3×D5), C15⋊3C16⋊9C2, C30.19(C2×C8), D10.4(C3⋊C8), (D5×C12).2C4, (C8×D5).11S3, (D5×C24).3C2, C12.73(C4×D5), C60.135(C2×C4), Dic5.4(C3⋊C8), (C4×D5).9Dic3, (C3×Dic5).1C8, C4.16(D5×Dic3), C5⋊2C8.7Dic3, C20.42(C2×Dic3), C5⋊3(C2×C3⋊C16), (C5×C3⋊C16)⋊4C2, C2.1(D5×C3⋊C8), C10.10(C2×C3⋊C8), (C3×C5⋊2C8).2C4, SmallGroup(480,7)
Series: Derived ►Chief ►Lower central ►Upper central
| C15 — D5×C3⋊C16 |
Generators and relations for D5×C3⋊C16
G = < a,b,c,d | a5=b2=c3=d16=1, bab=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Smallest permutation representation of D5×C3⋊C16
►On 240 points
Generators in S240
(1 173 68 34 206)(2 174 69 35 207)(3 175 70 36 208)(4 176 71 37 193)(5 161 72 38 194)(6 162 73 39 195)(7 163 74 40 196)(8 164 75 41 197)(9 165 76 42 198)(10 166 77 43 199)(11 167 78 44 200)(12 168 79 45 201)(13 169 80 46 202)(14 170 65 47 203)(15 171 66 48 204)(16 172 67 33 205)(17 159 49 96 138)(18 160 50 81 139)(19 145 51 82 140)(20 146 52 83 141)(21 147 53 84 142)(22 148 54 85 143)(23 149 55 86 144)(24 150 56 87 129)(25 151 57 88 130)(26 152 58 89 131)(27 153 59 90 132)(28 154 60 91 133)(29 155 61 92 134)(30 156 62 93 135)(31 157 63 94 136)(32 158 64 95 137)(97 116 211 238 189)(98 117 212 239 190)(99 118 213 240 191)(100 119 214 225 192)(101 120 215 226 177)(102 121 216 227 178)(103 122 217 228 179)(104 123 218 229 180)(105 124 219 230 181)(106 125 220 231 182)(107 126 221 232 183)(108 127 222 233 184)(109 128 223 234 185)(110 113 224 235 186)(111 114 209 236 187)(112 115 210 237 188)
(1 198)(2 199)(3 200)(4 201)(5 202)(6 203)(7 204)(8 205)(9 206)(10 207)(11 208)(12 193)(13 194)(14 195)(15 196)(16 197)(17 151)(18 152)(19 153)(20 154)(21 155)(22 156)(23 157)(24 158)(25 159)(26 160)(27 145)(28 146)(29 147)(30 148)(31 149)(32 150)(33 164)(34 165)(35 166)(36 167)(37 168)(38 169)(39 170)(40 171)(41 172)(42 173)(43 174)(44 175)(45 176)(46 161)(47 162)(48 163)(49 130)(50 131)(51 132)(52 133)(53 134)(54 135)(55 136)(56 137)(57 138)(58 139)(59 140)(60 141)(61 142)(62 143)(63 144)(64 129)(65 73)(66 74)(67 75)(68 76)(69 77)(70 78)(71 79)(72 80)(81 89)(82 90)(83 91)(84 92)(85 93)(86 94)(87 95)(88 96)(97 181)(98 182)(99 183)(100 184)(101 185)(102 186)(103 187)(104 188)(105 189)(106 190)(107 191)(108 192)(109 177)(110 178)(111 179)(112 180)(113 227)(114 228)(115 229)(116 230)(117 231)(118 232)(119 233)(120 234)(121 235)(122 236)(123 237)(124 238)(125 239)(126 240)(127 225)(128 226)(209 217)(210 218)(211 219)(212 220)(213 221)(214 222)(215 223)(216 224)
(1 99 145)(2 146 100)(3 101 147)(4 148 102)(5 103 149)(6 150 104)(7 105 151)(8 152 106)(9 107 153)(10 154 108)(11 109 155)(12 156 110)(13 111 157)(14 158 112)(15 97 159)(16 160 98)(17 204 189)(18 190 205)(19 206 191)(20 192 207)(21 208 177)(22 178 193)(23 194 179)(24 180 195)(25 196 181)(26 182 197)(27 198 183)(28 184 199)(29 200 185)(30 186 201)(31 202 187)(32 188 203)(33 139 239)(34 240 140)(35 141 225)(36 226 142)(37 143 227)(38 228 144)(39 129 229)(40 230 130)(41 131 231)(42 232 132)(43 133 233)(44 234 134)(45 135 235)(46 236 136)(47 137 237)(48 238 138)(49 171 116)(50 117 172)(51 173 118)(52 119 174)(53 175 120)(54 121 176)(55 161 122)(56 123 162)(57 163 124)(58 125 164)(59 165 126)(60 127 166)(61 167 128)(62 113 168)(63 169 114)(64 115 170)(65 95 210)(66 211 96)(67 81 212)(68 213 82)(69 83 214)(70 215 84)(71 85 216)(72 217 86)(73 87 218)(74 219 88)(75 89 220)(76 221 90)(77 91 222)(78 223 92)(79 93 224)(80 209 94)
(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)| (1,173,68,34,206)(2,174,69,35,207)(3,175,70,36,208)(4,176,71,37,193)(5,161,72,38,194)(6,162,73,39,195)(7,163,74,40,196)(8,164,75,41,197)(9,165,76,42,198)(10,166,77,43,199)(11,167,78,44,200)(12,168,79,45,201)(13,169,80,46,202)(14,170,65,47,203)(15,171,66,48,204)(16,172,67,33,205)(17,159,49,96,138)(18,160,50,81,139)(19,145,51,82,140)(20,146,52,83,141)(21,147,53,84,142)(22,148,54,85,143)(23,149,55,86,144)(24,150,56,87,129)(25,151,57,88,130)(26,152,58,89,131)(27,153,59,90,132)(28,154,60,91,133)(29,155,61,92,134)(30,156,62,93,135)(31,157,63,94,136)(32,158,64,95,137)(97,116,211,238,189)(98,117,212,239,190)(99,118,213,240,191)(100,119,214,225,192)(101,120,215,226,177)(102,121,216,227,178)(103,122,217,228,179)(104,123,218,229,180)(105,124,219,230,181)(106,125,220,231,182)(107,126,221,232,183)(108,127,222,233,184)(109,128,223,234,185)(110,113,224,235,186)(111,114,209,236,187)(112,115,210,237,188), (1,198)(2,199)(3,200)(4,201)(5,202)(6,203)(7,204)(8,205)(9,206)(10,207)(11,208)(12,193)(13,194)(14,195)(15,196)(16,197)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,145)(28,146)(29,147)(30,148)(31,149)(32,150)(33,164)(34,165)(35,166)(36,167)(37,168)(38,169)(39,170)(40,171)(41,172)(42,173)(43,174)(44,175)(45,176)(46,161)(47,162)(48,163)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,137)(57,138)(58,139)(59,140)(60,141)(61,142)(62,143)(63,144)(64,129)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80)(81,89)(82,90)(83,91)(84,92)(85,93)(86,94)(87,95)(88,96)(97,181)(98,182)(99,183)(100,184)(101,185)(102,186)(103,187)(104,188)(105,189)(106,190)(107,191)(108,192)(109,177)(110,178)(111,179)(112,180)(113,227)(114,228)(115,229)(116,230)(117,231)(118,232)(119,233)(120,234)(121,235)(122,236)(123,237)(124,238)(125,239)(126,240)(127,225)(128,226)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224), (1,99,145)(2,146,100)(3,101,147)(4,148,102)(5,103,149)(6,150,104)(7,105,151)(8,152,106)(9,107,153)(10,154,108)(11,109,155)(12,156,110)(13,111,157)(14,158,112)(15,97,159)(16,160,98)(17,204,189)(18,190,205)(19,206,191)(20,192,207)(21,208,177)(22,178,193)(23,194,179)(24,180,195)(25,196,181)(26,182,197)(27,198,183)(28,184,199)(29,200,185)(30,186,201)(31,202,187)(32,188,203)(33,139,239)(34,240,140)(35,141,225)(36,226,142)(37,143,227)(38,228,144)(39,129,229)(40,230,130)(41,131,231)(42,232,132)(43,133,233)(44,234,134)(45,135,235)(46,236,136)(47,137,237)(48,238,138)(49,171,116)(50,117,172)(51,173,118)(52,119,174)(53,175,120)(54,121,176)(55,161,122)(56,123,162)(57,163,124)(58,125,164)(59,165,126)(60,127,166)(61,167,128)(62,113,168)(63,169,114)(64,115,170)(65,95,210)(66,211,96)(67,81,212)(68,213,82)(69,83,214)(70,215,84)(71,85,216)(72,217,86)(73,87,218)(74,219,88)(75,89,220)(76,221,90)(77,91,222)(78,223,92)(79,93,224)(80,209,94), (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( (1,173,68,34,206)(2,174,69,35,207)(3,175,70,36,208)(4,176,71,37,193)(5,161,72,38,194)(6,162,73,39,195)(7,163,74,40,196)(8,164,75,41,197)(9,165,76,42,198)(10,166,77,43,199)(11,167,78,44,200)(12,168,79,45,201)(13,169,80,46,202)(14,170,65,47,203)(15,171,66,48,204)(16,172,67,33,205)(17,159,49,96,138)(18,160,50,81,139)(19,145,51,82,140)(20,146,52,83,141)(21,147,53,84,142)(22,148,54,85,143)(23,149,55,86,144)(24,150,56,87,129)(25,151,57,88,130)(26,152,58,89,131)(27,153,59,90,132)(28,154,60,91,133)(29,155,61,92,134)(30,156,62,93,135)(31,157,63,94,136)(32,158,64,95,137)(97,116,211,238,189)(98,117,212,239,190)(99,118,213,240,191)(100,119,214,225,192)(101,120,215,226,177)(102,121,216,227,178)(103,122,217,228,179)(104,123,218,229,180)(105,124,219,230,181)(106,125,220,231,182)(107,126,221,232,183)(108,127,222,233,184)(109,128,223,234,185)(110,113,224,235,186)(111,114,209,236,187)(112,115,210,237,188), (1,198)(2,199)(3,200)(4,201)(5,202)(6,203)(7,204)(8,205)(9,206)(10,207)(11,208)(12,193)(13,194)(14,195)(15,196)(16,197)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,145)(28,146)(29,147)(30,148)(31,149)(32,150)(33,164)(34,165)(35,166)(36,167)(37,168)(38,169)(39,170)(40,171)(41,172)(42,173)(43,174)(44,175)(45,176)(46,161)(47,162)(48,163)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,137)(57,138)(58,139)(59,140)(60,141)(61,142)(62,143)(63,144)(64,129)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80)(81,89)(82,90)(83,91)(84,92)(85,93)(86,94)(87,95)(88,96)(97,181)(98,182)(99,183)(100,184)(101,185)(102,186)(103,187)(104,188)(105,189)(106,190)(107,191)(108,192)(109,177)(110,178)(111,179)(112,180)(113,227)(114,228)(115,229)(116,230)(117,231)(118,232)(119,233)(120,234)(121,235)(122,236)(123,237)(124,238)(125,239)(126,240)(127,225)(128,226)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224), (1,99,145)(2,146,100)(3,101,147)(4,148,102)(5,103,149)(6,150,104)(7,105,151)(8,152,106)(9,107,153)(10,154,108)(11,109,155)(12,156,110)(13,111,157)(14,158,112)(15,97,159)(16,160,98)(17,204,189)(18,190,205)(19,206,191)(20,192,207)(21,208,177)(22,178,193)(23,194,179)(24,180,195)(25,196,181)(26,182,197)(27,198,183)(28,184,199)(29,200,185)(30,186,201)(31,202,187)(32,188,203)(33,139,239)(34,240,140)(35,141,225)(36,226,142)(37,143,227)(38,228,144)(39,129,229)(40,230,130)(41,131,231)(42,232,132)(43,133,233)(44,234,134)(45,135,235)(46,236,136)(47,137,237)(48,238,138)(49,171,116)(50,117,172)(51,173,118)(52,119,174)(53,175,120)(54,121,176)(55,161,122)(56,123,162)(57,163,124)(58,125,164)(59,165,126)(60,127,166)(61,167,128)(62,113,168)(63,169,114)(64,115,170)(65,95,210)(66,211,96)(67,81,212)(68,213,82)(69,83,214)(70,215,84)(71,85,216)(72,217,86)(73,87,218)(74,219,88)(75,89,220)(76,221,90)(77,91,222)(78,223,92)(79,93,224)(80,209,94), (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([[(1,173,68,34,206),(2,174,69,35,207),(3,175,70,36,208),(4,176,71,37,193),(5,161,72,38,194),(6,162,73,39,195),(7,163,74,40,196),(8,164,75,41,197),(9,165,76,42,198),(10,166,77,43,199),(11,167,78,44,200),(12,168,79,45,201),(13,169,80,46,202),(14,170,65,47,203),(15,171,66,48,204),(16,172,67,33,205),(17,159,49,96,138),(18,160,50,81,139),(19,145,51,82,140),(20,146,52,83,141),(21,147,53,84,142),(22,148,54,85,143),(23,149,55,86,144),(24,150,56,87,129),(25,151,57,88,130),(26,152,58,89,131),(27,153,59,90,132),(28,154,60,91,133),(29,155,61,92,134),(30,156,62,93,135),(31,157,63,94,136),(32,158,64,95,137),(97,116,211,238,189),(98,117,212,239,190),(99,118,213,240,191),(100,119,214,225,192),(101,120,215,226,177),(102,121,216,227,178),(103,122,217,228,179),(104,123,218,229,180),(105,124,219,230,181),(106,125,220,231,182),(107,126,221,232,183),(108,127,222,233,184),(109,128,223,234,185),(110,113,224,235,186),(111,114,209,236,187),(112,115,210,237,188)], [(1,198),(2,199),(3,200),(4,201),(5,202),(6,203),(7,204),(8,205),(9,206),(10,207),(11,208),(12,193),(13,194),(14,195),(15,196),(16,197),(17,151),(18,152),(19,153),(20,154),(21,155),(22,156),(23,157),(24,158),(25,159),(26,160),(27,145),(28,146),(29,147),(30,148),(31,149),(32,150),(33,164),(34,165),(35,166),(36,167),(37,168),(38,169),(39,170),(40,171),(41,172),(42,173),(43,174),(44,175),(45,176),(46,161),(47,162),(48,163),(49,130),(50,131),(51,132),(52,133),(53,134),(54,135),(55,136),(56,137),(57,138),(58,139),(59,140),(60,141),(61,142),(62,143),(63,144),(64,129),(65,73),(66,74),(67,75),(68,76),(69,77),(70,78),(71,79),(72,80),(81,89),(82,90),(83,91),(84,92),(85,93),(86,94),(87,95),(88,96),(97,181),(98,182),(99,183),(100,184),(101,185),(102,186),(103,187),(104,188),(105,189),(106,190),(107,191),(108,192),(109,177),(110,178),(111,179),(112,180),(113,227),(114,228),(115,229),(116,230),(117,231),(118,232),(119,233),(120,234),(121,235),(122,236),(123,237),(124,238),(125,239),(126,240),(127,225),(128,226),(209,217),(210,218),(211,219),(212,220),(213,221),(214,222),(215,223),(216,224)], [(1,99,145),(2,146,100),(3,101,147),(4,148,102),(5,103,149),(6,150,104),(7,105,151),(8,152,106),(9,107,153),(10,154,108),(11,109,155),(12,156,110),(13,111,157),(14,158,112),(15,97,159),(16,160,98),(17,204,189),(18,190,205),(19,206,191),(20,192,207),(21,208,177),(22,178,193),(23,194,179),(24,180,195),(25,196,181),(26,182,197),(27,198,183),(28,184,199),(29,200,185),(30,186,201),(31,202,187),(32,188,203),(33,139,239),(34,240,140),(35,141,225),(36,226,142),(37,143,227),(38,228,144),(39,129,229),(40,230,130),(41,131,231),(42,232,132),(43,133,233),(44,234,134),(45,135,235),(46,236,136),(47,137,237),(48,238,138),(49,171,116),(50,117,172),(51,173,118),(52,119,174),(53,175,120),(54,121,176),(55,161,122),(56,123,162),(57,163,124),(58,125,164),(59,165,126),(60,127,166),(61,167,128),(62,113,168),(63,169,114),(64,115,170),(65,95,210),(66,211,96),(67,81,212),(68,213,82),(69,83,214),(70,215,84),(71,85,216),(72,217,86),(73,87,218),(74,219,88),(75,89,220),(76,221,90),(77,91,222),(78,223,92),(79,93,224),(80,209,94)], [(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)]])
96 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 5A | 5B | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 10A | 10B | 12A | 12B | 12C | 12D | 15A | 15B | 16A | ··· | 16H | 16I | ··· | 16P | 20A | 20B | 20C | 20D | 24A | 24B | 24C | 24D | 24E | 24F | 24G | 24H | 30A | 30B | 40A | ··· | 40H | 60A | 60B | 60C | 60D | 80A | ··· | 80P | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 16 | ··· | 16 | 16 | ··· | 16 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 30 | 30 | 40 | ··· | 40 | 60 | 60 | 60 | 60 | 80 | ··· | 80 | 120 | ··· | 120 |
| size | 1 | 1 | 5 | 5 | 2 | 1 | 1 | 5 | 5 | 2 | 2 | 2 | 10 | 10 | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 2 | 2 | 2 | 2 | 10 | 10 | 4 | 4 | 3 | ··· | 3 | 15 | ··· | 15 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 4 | ··· | 4 |
96 irreducible representations
| dim | 1 | 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 | C4 | C4 | C8 | C8 | C16 | S3 | D5 | Dic3 | D6 | Dic3 | D10 | C3⋊C8 | C3⋊C8 | C4×D5 | C3⋊C16 | C8×D5 | D5×C16 | S3×D5 | D5×Dic3 | D5×C3⋊C8 | D5×C3⋊C16 |
| kernel | D5×C3⋊C16 | C5×C3⋊C16 | C15⋊3C16 | D5×C24 | C3×C5⋊2C8 | D5×C12 | C3×Dic5 | C6×D5 | C3×D5 | C8×D5 | C3⋊C16 | C5⋊2C8 | C40 | C4×D5 | C24 | Dic5 | D10 | C12 | D5 | C6 | C3 | C8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 16 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 8 | 8 | 16 | 2 | 2 | 4 | 8 |
Matrix representation of D5×C3⋊C16 ►in GL4(𝔽241) generated by
| 240 | 1 | 0 | 0 |
| 188 | 52 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 53 | 240 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 49 |
| 0 | 0 | 177 | 239 |
| 130 | 0 | 0 | 0 |
| 0 | 130 | 0 | 0 |
| 0 | 0 | 68 | 15 |
| 0 | 0 | 222 | 173 |
G:=sub<GL(4,GF(241))| [240,188,0,0,1,52,0,0,0,0,1,0,0,0,0,1],[1,53,0,0,0,240,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,1,177,0,0,49,239],[130,0,0,0,0,130,0,0,0,0,68,222,0,0,15,173] >;
D5×C3⋊C16 in GAP, Magma, Sage, TeX
D_5\times C_3\rtimes C_{16} % in TeX
G:=Group("D5xC3:C16"); // GroupNames label
G:=SmallGroup(480,7);
// by ID
G=gap.SmallGroup(480,7);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,36,58,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^2=c^3=d^16=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
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