direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D5×Dic12, C40.16D6, C24.44D10, Dic60⋊11C2, D10.24D12, Dic5.7D12, C60.120C23, C120.21C22, Dic6.18D10, Dic30.32C22, C3⋊1(D5×Q16), C15⋊1(C2×Q16), C6.5(D4×D5), (C3×D5)⋊1Q16, (C8×D5).1S3, C8.20(S3×D5), C5⋊1(C2×Dic12), (C6×D5).42D4, C5⋊Dic12⋊9C2, (D5×C24).1C2, (C4×D5).78D6, C30.13(C2×D4), C2.10(D5×D12), C10.5(C2×D12), C5⋊2C8.31D6, (C5×Dic12)⋊2C2, (D5×Dic6).2C2, C20.72(C22×S3), (C3×Dic5).46D4, (D5×C12).92C22, C12.143(C22×D5), (C5×Dic6).22C22, C4.68(C2×S3×D5), (C3×C5⋊2C8).35C22, SmallGroup(480,335)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D5×Dic12
G = < a,b,c,d | a5=b2=c24=1, d2=c12, bab=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 636 in 120 conjugacy classes, 44 normal (30 characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, C6, C6, C8, C8, C2×C4, Q8, D5, C10, Dic3, C12, C12, C2×C6, C15, C2×C8, Q16, C2×Q8, Dic5, Dic5, C20, C20, D10, C24, C24, Dic6, Dic6, C2×Dic3, C2×C12, C3×D5, C30, C2×Q16, C5⋊2C8, C40, Dic10, C4×D5, C4×D5, C5×Q8, Dic12, Dic12, C2×C24, C2×Dic6, C5×Dic3, C3×Dic5, Dic15, C60, C6×D5, C8×D5, Dic20, C5⋊Q16, C5×Q16, Q8×D5, C2×Dic12, C3×C5⋊2C8, C120, D5×Dic3, C15⋊Q8, D5×C12, C5×Dic6, Dic30, D5×Q16, C5⋊Dic12, D5×C24, C5×Dic12, Dic60, D5×Dic6, D5×Dic12
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, Q16, C2×D4, D10, D12, C22×S3, C2×Q16, C22×D5, Dic12, C2×D12, S3×D5, D4×D5, C2×Dic12, C2×S3×D5, D5×Q16, D5×D12, D5×Dic12
►On 240 points
Generators in S240
(1 231 27 212 70)(2 232 28 213 71)(3 233 29 214 72)(4 234 30 215 49)(5 235 31 216 50)(6 236 32 193 51)(7 237 33 194 52)(8 238 34 195 53)(9 239 35 196 54)(10 240 36 197 55)(11 217 37 198 56)(12 218 38 199 57)(13 219 39 200 58)(14 220 40 201 59)(15 221 41 202 60)(16 222 42 203 61)(17 223 43 204 62)(18 224 44 205 63)(19 225 45 206 64)(20 226 46 207 65)(21 227 47 208 66)(22 228 48 209 67)(23 229 25 210 68)(24 230 26 211 69)(73 97 155 179 126)(74 98 156 180 127)(75 99 157 181 128)(76 100 158 182 129)(77 101 159 183 130)(78 102 160 184 131)(79 103 161 185 132)(80 104 162 186 133)(81 105 163 187 134)(82 106 164 188 135)(83 107 165 189 136)(84 108 166 190 137)(85 109 167 191 138)(86 110 168 192 139)(87 111 145 169 140)(88 112 146 170 141)(89 113 147 171 142)(90 114 148 172 143)(91 115 149 173 144)(92 116 150 174 121)(93 117 151 175 122)(94 118 152 176 123)(95 119 153 177 124)(96 120 154 178 125)
(1 70)(2 71)(3 72)(4 49)(5 50)(6 51)(7 52)(8 53)(9 54)(10 55)(11 56)(12 57)(13 58)(14 59)(15 60)(16 61)(17 62)(18 63)(19 64)(20 65)(21 66)(22 67)(23 68)(24 69)(73 97)(74 98)(75 99)(76 100)(77 101)(78 102)(79 103)(80 104)(81 105)(82 106)(83 107)(84 108)(85 109)(86 110)(87 111)(88 112)(89 113)(90 114)(91 115)(92 116)(93 117)(94 118)(95 119)(96 120)(121 150)(122 151)(123 152)(124 153)(125 154)(126 155)(127 156)(128 157)(129 158)(130 159)(131 160)(132 161)(133 162)(134 163)(135 164)(136 165)(137 166)(138 167)(139 168)(140 145)(141 146)(142 147)(143 148)(144 149)(193 236)(194 237)(195 238)(196 239)(197 240)(198 217)(199 218)(200 219)(201 220)(202 221)(203 222)(204 223)(205 224)(206 225)(207 226)(208 227)(209 228)(210 229)(211 230)(212 231)(213 232)(214 233)(215 234)(216 235)
(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)
(1 117 13 105)(2 116 14 104)(3 115 15 103)(4 114 16 102)(5 113 17 101)(6 112 18 100)(7 111 19 99)(8 110 20 98)(9 109 21 97)(10 108 22 120)(11 107 23 119)(12 106 24 118)(25 177 37 189)(26 176 38 188)(27 175 39 187)(28 174 40 186)(29 173 41 185)(30 172 42 184)(31 171 43 183)(32 170 44 182)(33 169 45 181)(34 192 46 180)(35 191 47 179)(36 190 48 178)(49 90 61 78)(50 89 62 77)(51 88 63 76)(52 87 64 75)(53 86 65 74)(54 85 66 73)(55 84 67 96)(56 83 68 95)(57 82 69 94)(58 81 70 93)(59 80 71 92)(60 79 72 91)(121 201 133 213)(122 200 134 212)(123 199 135 211)(124 198 136 210)(125 197 137 209)(126 196 138 208)(127 195 139 207)(128 194 140 206)(129 193 141 205)(130 216 142 204)(131 215 143 203)(132 214 144 202)(145 225 157 237)(146 224 158 236)(147 223 159 235)(148 222 160 234)(149 221 161 233)(150 220 162 232)(151 219 163 231)(152 218 164 230)(153 217 165 229)(154 240 166 228)(155 239 167 227)(156 238 168 226)
G:=sub<Sym(240)| (1,231,27,212,70)(2,232,28,213,71)(3,233,29,214,72)(4,234,30,215,49)(5,235,31,216,50)(6,236,32,193,51)(7,237,33,194,52)(8,238,34,195,53)(9,239,35,196,54)(10,240,36,197,55)(11,217,37,198,56)(12,218,38,199,57)(13,219,39,200,58)(14,220,40,201,59)(15,221,41,202,60)(16,222,42,203,61)(17,223,43,204,62)(18,224,44,205,63)(19,225,45,206,64)(20,226,46,207,65)(21,227,47,208,66)(22,228,48,209,67)(23,229,25,210,68)(24,230,26,211,69)(73,97,155,179,126)(74,98,156,180,127)(75,99,157,181,128)(76,100,158,182,129)(77,101,159,183,130)(78,102,160,184,131)(79,103,161,185,132)(80,104,162,186,133)(81,105,163,187,134)(82,106,164,188,135)(83,107,165,189,136)(84,108,166,190,137)(85,109,167,191,138)(86,110,168,192,139)(87,111,145,169,140)(88,112,146,170,141)(89,113,147,171,142)(90,114,148,172,143)(91,115,149,173,144)(92,116,150,174,121)(93,117,151,175,122)(94,118,152,176,123)(95,119,153,177,124)(96,120,154,178,125), (1,70)(2,71)(3,72)(4,49)(5,50)(6,51)(7,52)(8,53)(9,54)(10,55)(11,56)(12,57)(13,58)(14,59)(15,60)(16,61)(17,62)(18,63)(19,64)(20,65)(21,66)(22,67)(23,68)(24,69)(73,97)(74,98)(75,99)(76,100)(77,101)(78,102)(79,103)(80,104)(81,105)(82,106)(83,107)(84,108)(85,109)(86,110)(87,111)(88,112)(89,113)(90,114)(91,115)(92,116)(93,117)(94,118)(95,119)(96,120)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,145)(141,146)(142,147)(143,148)(144,149)(193,236)(194,237)(195,238)(196,239)(197,240)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)(205,224)(206,225)(207,226)(208,227)(209,228)(210,229)(211,230)(212,231)(213,232)(214,233)(215,234)(216,235), (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), (1,117,13,105)(2,116,14,104)(3,115,15,103)(4,114,16,102)(5,113,17,101)(6,112,18,100)(7,111,19,99)(8,110,20,98)(9,109,21,97)(10,108,22,120)(11,107,23,119)(12,106,24,118)(25,177,37,189)(26,176,38,188)(27,175,39,187)(28,174,40,186)(29,173,41,185)(30,172,42,184)(31,171,43,183)(32,170,44,182)(33,169,45,181)(34,192,46,180)(35,191,47,179)(36,190,48,178)(49,90,61,78)(50,89,62,77)(51,88,63,76)(52,87,64,75)(53,86,65,74)(54,85,66,73)(55,84,67,96)(56,83,68,95)(57,82,69,94)(58,81,70,93)(59,80,71,92)(60,79,72,91)(121,201,133,213)(122,200,134,212)(123,199,135,211)(124,198,136,210)(125,197,137,209)(126,196,138,208)(127,195,139,207)(128,194,140,206)(129,193,141,205)(130,216,142,204)(131,215,143,203)(132,214,144,202)(145,225,157,237)(146,224,158,236)(147,223,159,235)(148,222,160,234)(149,221,161,233)(150,220,162,232)(151,219,163,231)(152,218,164,230)(153,217,165,229)(154,240,166,228)(155,239,167,227)(156,238,168,226)>;
G:=Group( (1,231,27,212,70)(2,232,28,213,71)(3,233,29,214,72)(4,234,30,215,49)(5,235,31,216,50)(6,236,32,193,51)(7,237,33,194,52)(8,238,34,195,53)(9,239,35,196,54)(10,240,36,197,55)(11,217,37,198,56)(12,218,38,199,57)(13,219,39,200,58)(14,220,40,201,59)(15,221,41,202,60)(16,222,42,203,61)(17,223,43,204,62)(18,224,44,205,63)(19,225,45,206,64)(20,226,46,207,65)(21,227,47,208,66)(22,228,48,209,67)(23,229,25,210,68)(24,230,26,211,69)(73,97,155,179,126)(74,98,156,180,127)(75,99,157,181,128)(76,100,158,182,129)(77,101,159,183,130)(78,102,160,184,131)(79,103,161,185,132)(80,104,162,186,133)(81,105,163,187,134)(82,106,164,188,135)(83,107,165,189,136)(84,108,166,190,137)(85,109,167,191,138)(86,110,168,192,139)(87,111,145,169,140)(88,112,146,170,141)(89,113,147,171,142)(90,114,148,172,143)(91,115,149,173,144)(92,116,150,174,121)(93,117,151,175,122)(94,118,152,176,123)(95,119,153,177,124)(96,120,154,178,125), (1,70)(2,71)(3,72)(4,49)(5,50)(6,51)(7,52)(8,53)(9,54)(10,55)(11,56)(12,57)(13,58)(14,59)(15,60)(16,61)(17,62)(18,63)(19,64)(20,65)(21,66)(22,67)(23,68)(24,69)(73,97)(74,98)(75,99)(76,100)(77,101)(78,102)(79,103)(80,104)(81,105)(82,106)(83,107)(84,108)(85,109)(86,110)(87,111)(88,112)(89,113)(90,114)(91,115)(92,116)(93,117)(94,118)(95,119)(96,120)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,145)(141,146)(142,147)(143,148)(144,149)(193,236)(194,237)(195,238)(196,239)(197,240)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)(205,224)(206,225)(207,226)(208,227)(209,228)(210,229)(211,230)(212,231)(213,232)(214,233)(215,234)(216,235), (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), (1,117,13,105)(2,116,14,104)(3,115,15,103)(4,114,16,102)(5,113,17,101)(6,112,18,100)(7,111,19,99)(8,110,20,98)(9,109,21,97)(10,108,22,120)(11,107,23,119)(12,106,24,118)(25,177,37,189)(26,176,38,188)(27,175,39,187)(28,174,40,186)(29,173,41,185)(30,172,42,184)(31,171,43,183)(32,170,44,182)(33,169,45,181)(34,192,46,180)(35,191,47,179)(36,190,48,178)(49,90,61,78)(50,89,62,77)(51,88,63,76)(52,87,64,75)(53,86,65,74)(54,85,66,73)(55,84,67,96)(56,83,68,95)(57,82,69,94)(58,81,70,93)(59,80,71,92)(60,79,72,91)(121,201,133,213)(122,200,134,212)(123,199,135,211)(124,198,136,210)(125,197,137,209)(126,196,138,208)(127,195,139,207)(128,194,140,206)(129,193,141,205)(130,216,142,204)(131,215,143,203)(132,214,144,202)(145,225,157,237)(146,224,158,236)(147,223,159,235)(148,222,160,234)(149,221,161,233)(150,220,162,232)(151,219,163,231)(152,218,164,230)(153,217,165,229)(154,240,166,228)(155,239,167,227)(156,238,168,226) );
G=PermutationGroup([[(1,231,27,212,70),(2,232,28,213,71),(3,233,29,214,72),(4,234,30,215,49),(5,235,31,216,50),(6,236,32,193,51),(7,237,33,194,52),(8,238,34,195,53),(9,239,35,196,54),(10,240,36,197,55),(11,217,37,198,56),(12,218,38,199,57),(13,219,39,200,58),(14,220,40,201,59),(15,221,41,202,60),(16,222,42,203,61),(17,223,43,204,62),(18,224,44,205,63),(19,225,45,206,64),(20,226,46,207,65),(21,227,47,208,66),(22,228,48,209,67),(23,229,25,210,68),(24,230,26,211,69),(73,97,155,179,126),(74,98,156,180,127),(75,99,157,181,128),(76,100,158,182,129),(77,101,159,183,130),(78,102,160,184,131),(79,103,161,185,132),(80,104,162,186,133),(81,105,163,187,134),(82,106,164,188,135),(83,107,165,189,136),(84,108,166,190,137),(85,109,167,191,138),(86,110,168,192,139),(87,111,145,169,140),(88,112,146,170,141),(89,113,147,171,142),(90,114,148,172,143),(91,115,149,173,144),(92,116,150,174,121),(93,117,151,175,122),(94,118,152,176,123),(95,119,153,177,124),(96,120,154,178,125)], [(1,70),(2,71),(3,72),(4,49),(5,50),(6,51),(7,52),(8,53),(9,54),(10,55),(11,56),(12,57),(13,58),(14,59),(15,60),(16,61),(17,62),(18,63),(19,64),(20,65),(21,66),(22,67),(23,68),(24,69),(73,97),(74,98),(75,99),(76,100),(77,101),(78,102),(79,103),(80,104),(81,105),(82,106),(83,107),(84,108),(85,109),(86,110),(87,111),(88,112),(89,113),(90,114),(91,115),(92,116),(93,117),(94,118),(95,119),(96,120),(121,150),(122,151),(123,152),(124,153),(125,154),(126,155),(127,156),(128,157),(129,158),(130,159),(131,160),(132,161),(133,162),(134,163),(135,164),(136,165),(137,166),(138,167),(139,168),(140,145),(141,146),(142,147),(143,148),(144,149),(193,236),(194,237),(195,238),(196,239),(197,240),(198,217),(199,218),(200,219),(201,220),(202,221),(203,222),(204,223),(205,224),(206,225),(207,226),(208,227),(209,228),(210,229),(211,230),(212,231),(213,232),(214,233),(215,234),(216,235)], [(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)], [(1,117,13,105),(2,116,14,104),(3,115,15,103),(4,114,16,102),(5,113,17,101),(6,112,18,100),(7,111,19,99),(8,110,20,98),(9,109,21,97),(10,108,22,120),(11,107,23,119),(12,106,24,118),(25,177,37,189),(26,176,38,188),(27,175,39,187),(28,174,40,186),(29,173,41,185),(30,172,42,184),(31,171,43,183),(32,170,44,182),(33,169,45,181),(34,192,46,180),(35,191,47,179),(36,190,48,178),(49,90,61,78),(50,89,62,77),(51,88,63,76),(52,87,64,75),(53,86,65,74),(54,85,66,73),(55,84,67,96),(56,83,68,95),(57,82,69,94),(58,81,70,93),(59,80,71,92),(60,79,72,91),(121,201,133,213),(122,200,134,212),(123,199,135,211),(124,198,136,210),(125,197,137,209),(126,196,138,208),(127,195,139,207),(128,194,140,206),(129,193,141,205),(130,216,142,204),(131,215,143,203),(132,214,144,202),(145,225,157,237),(146,224,158,236),(147,223,159,235),(148,222,160,234),(149,221,161,233),(150,220,162,232),(151,219,163,231),(152,218,164,230),(153,217,165,229),(154,240,166,228),(155,239,167,227),(156,238,168,226)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 5A | 5B | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 10A | 10B | 12A | 12B | 12C | 12D | 15A | 15B | 20A | 20B | 20C | 20D | 20E | 20F | 24A | 24B | 24C | 24D | 24E | 24F | 24G | 24H | 30A | 30B | 40A | 40B | 40C | 40D | 60A | 60B | 60C | 60D | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 30 | 30 | 40 | 40 | 40 | 40 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 5 | 5 | 2 | 2 | 10 | 12 | 12 | 60 | 60 | 2 | 2 | 2 | 10 | 10 | 2 | 2 | 10 | 10 | 2 | 2 | 2 | 2 | 10 | 10 | 4 | 4 | 4 | 4 | 24 | 24 | 24 | 24 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | + | + | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | D4 | D5 | D6 | D6 | D6 | Q16 | D10 | D10 | D12 | D12 | Dic12 | S3×D5 | D4×D5 | C2×S3×D5 | D5×Q16 | D5×D12 | D5×Dic12 |
| kernel | D5×Dic12 | C5⋊Dic12 | D5×C24 | C5×Dic12 | Dic60 | D5×Dic6 | C8×D5 | C3×Dic5 | C6×D5 | Dic12 | C5⋊2C8 | C40 | C4×D5 | C3×D5 | C24 | Dic6 | Dic5 | D10 | D5 | C8 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 4 | 2 | 4 | 2 | 2 | 8 | 2 | 2 | 2 | 4 | 4 | 8 |
Matrix representation of D5×Dic12 ►in GL4(𝔽241) generated by
| 0 | 1 | 0 | 0 |
| 240 | 189 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 123 | 131 |
| 0 | 0 | 74 | 22 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 211 | 135 |
| 0 | 0 | 129 | 30 |
G:=sub<GL(4,GF(241))| [0,240,0,0,1,189,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,123,74,0,0,131,22],[1,0,0,0,0,1,0,0,0,0,211,129,0,0,135,30] >;
D5×Dic12 in GAP, Magma, Sage, TeX
D_5\times {\rm Dic}_{12} % in TeX
G:=Group("D5xDic12"); // GroupNames label
G:=SmallGroup(480,335);
// by ID
G=gap.SmallGroup(480,335);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,135,142,346,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^2=c^24=1,d^2=c^12,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