Copied to
clipboard

## G = C15×C4⋊1D4order 480 = 25·3·5

### Direct product of C15 and C4⋊1D4

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C15×C4⋊1D4
 Chief series C1 — C2 — C22 — C2×C10 — C2×C30 — C22×C30 — D4×C30 — C15×C4⋊1D4
 Lower central C1 — C22 — C15×C4⋊1D4
 Upper central C1 — C2×C30 — C15×C4⋊1D4

Generators and relations for C15×C41D4
G = < a,b,c,d | a15=b4=c4=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >

Subgroups: 360 in 216 conjugacy classes, 104 normal (16 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×6], C22, C22 [×12], C5, C6 [×3], C6 [×4], C2×C4 [×3], D4 [×12], C23 [×4], C10 [×3], C10 [×4], C12 [×6], C2×C6, C2×C6 [×12], C15, C42, C2×D4 [×6], C20 [×6], C2×C10, C2×C10 [×12], C2×C12 [×3], C3×D4 [×12], C22×C6 [×4], C30 [×3], C30 [×4], C41D4, C2×C20 [×3], C5×D4 [×12], C22×C10 [×4], C4×C12, C6×D4 [×6], C60 [×6], C2×C30, C2×C30 [×12], C4×C20, D4×C10 [×6], C3×C41D4, C2×C60 [×3], D4×C15 [×12], C22×C30 [×4], C5×C41D4, C4×C60, D4×C30 [×6], C15×C41D4
Quotients: C1, C2 [×7], C3, C22 [×7], C5, C6 [×7], D4 [×6], C23, C10 [×7], C2×C6 [×7], C15, C2×D4 [×3], C2×C10 [×7], C3×D4 [×6], C22×C6, C30 [×7], C41D4, C5×D4 [×6], C22×C10, C6×D4 [×3], C2×C30 [×7], D4×C10 [×3], C3×C41D4, D4×C15 [×6], C22×C30, C5×C41D4, D4×C30 [×3], C15×C41D4

Smallest permutation representation of C15×C41D4
On 240 points
Generators in S240
(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 48 209 194)(2 49 210 195)(3 50 196 181)(4 51 197 182)(5 52 198 183)(6 53 199 184)(7 54 200 185)(8 55 201 186)(9 56 202 187)(10 57 203 188)(11 58 204 189)(12 59 205 190)(13 60 206 191)(14 46 207 192)(15 47 208 193)(16 176 44 112)(17 177 45 113)(18 178 31 114)(19 179 32 115)(20 180 33 116)(21 166 34 117)(22 167 35 118)(23 168 36 119)(24 169 37 120)(25 170 38 106)(26 171 39 107)(27 172 40 108)(28 173 41 109)(29 174 42 110)(30 175 43 111)(61 92 213 123)(62 93 214 124)(63 94 215 125)(64 95 216 126)(65 96 217 127)(66 97 218 128)(67 98 219 129)(68 99 220 130)(69 100 221 131)(70 101 222 132)(71 102 223 133)(72 103 224 134)(73 104 225 135)(74 105 211 121)(75 91 212 122)(76 143 157 233)(77 144 158 234)(78 145 159 235)(79 146 160 236)(80 147 161 237)(81 148 162 238)(82 149 163 239)(83 150 164 240)(84 136 165 226)(85 137 151 227)(86 138 152 228)(87 139 153 229)(88 140 154 230)(89 141 155 231)(90 142 156 232)
(1 175 77 212)(2 176 78 213)(3 177 79 214)(4 178 80 215)(5 179 81 216)(6 180 82 217)(7 166 83 218)(8 167 84 219)(9 168 85 220)(10 169 86 221)(11 170 87 222)(12 171 88 223)(13 172 89 224)(14 173 90 225)(15 174 76 211)(16 235 92 195)(17 236 93 181)(18 237 94 182)(19 238 95 183)(20 239 96 184)(21 240 97 185)(22 226 98 186)(23 227 99 187)(24 228 100 188)(25 229 101 189)(26 230 102 190)(27 231 103 191)(28 232 104 192)(29 233 105 193)(30 234 91 194)(31 147 125 51)(32 148 126 52)(33 149 127 53)(34 150 128 54)(35 136 129 55)(36 137 130 56)(37 138 131 57)(38 139 132 58)(39 140 133 59)(40 141 134 60)(41 142 135 46)(42 143 121 47)(43 144 122 48)(44 145 123 49)(45 146 124 50)(61 210 112 159)(62 196 113 160)(63 197 114 161)(64 198 115 162)(65 199 116 163)(66 200 117 164)(67 201 118 165)(68 202 119 151)(69 203 120 152)(70 204 106 153)(71 205 107 154)(72 206 108 155)(73 207 109 156)(74 208 110 157)(75 209 111 158)
(1 30)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(15 29)(31 197)(32 198)(33 199)(34 200)(35 201)(36 202)(37 203)(38 204)(39 205)(40 206)(41 207)(42 208)(43 209)(44 210)(45 196)(46 109)(47 110)(48 111)(49 112)(50 113)(51 114)(52 115)(53 116)(54 117)(55 118)(56 119)(57 120)(58 106)(59 107)(60 108)(61 145)(62 146)(63 147)(64 148)(65 149)(66 150)(67 136)(68 137)(69 138)(70 139)(71 140)(72 141)(73 142)(74 143)(75 144)(76 105)(77 91)(78 92)(79 93)(80 94)(81 95)(82 96)(83 97)(84 98)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(121 157)(122 158)(123 159)(124 160)(125 161)(126 162)(127 163)(128 164)(129 165)(130 151)(131 152)(132 153)(133 154)(134 155)(135 156)(166 185)(167 186)(168 187)(169 188)(170 189)(171 190)(172 191)(173 192)(174 193)(175 194)(176 195)(177 181)(178 182)(179 183)(180 184)(211 233)(212 234)(213 235)(214 236)(215 237)(216 238)(217 239)(218 240)(219 226)(220 227)(221 228)(222 229)(223 230)(224 231)(225 232)

G:=sub<Sym(240)| (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), (1,48,209,194)(2,49,210,195)(3,50,196,181)(4,51,197,182)(5,52,198,183)(6,53,199,184)(7,54,200,185)(8,55,201,186)(9,56,202,187)(10,57,203,188)(11,58,204,189)(12,59,205,190)(13,60,206,191)(14,46,207,192)(15,47,208,193)(16,176,44,112)(17,177,45,113)(18,178,31,114)(19,179,32,115)(20,180,33,116)(21,166,34,117)(22,167,35,118)(23,168,36,119)(24,169,37,120)(25,170,38,106)(26,171,39,107)(27,172,40,108)(28,173,41,109)(29,174,42,110)(30,175,43,111)(61,92,213,123)(62,93,214,124)(63,94,215,125)(64,95,216,126)(65,96,217,127)(66,97,218,128)(67,98,219,129)(68,99,220,130)(69,100,221,131)(70,101,222,132)(71,102,223,133)(72,103,224,134)(73,104,225,135)(74,105,211,121)(75,91,212,122)(76,143,157,233)(77,144,158,234)(78,145,159,235)(79,146,160,236)(80,147,161,237)(81,148,162,238)(82,149,163,239)(83,150,164,240)(84,136,165,226)(85,137,151,227)(86,138,152,228)(87,139,153,229)(88,140,154,230)(89,141,155,231)(90,142,156,232), (1,175,77,212)(2,176,78,213)(3,177,79,214)(4,178,80,215)(5,179,81,216)(6,180,82,217)(7,166,83,218)(8,167,84,219)(9,168,85,220)(10,169,86,221)(11,170,87,222)(12,171,88,223)(13,172,89,224)(14,173,90,225)(15,174,76,211)(16,235,92,195)(17,236,93,181)(18,237,94,182)(19,238,95,183)(20,239,96,184)(21,240,97,185)(22,226,98,186)(23,227,99,187)(24,228,100,188)(25,229,101,189)(26,230,102,190)(27,231,103,191)(28,232,104,192)(29,233,105,193)(30,234,91,194)(31,147,125,51)(32,148,126,52)(33,149,127,53)(34,150,128,54)(35,136,129,55)(36,137,130,56)(37,138,131,57)(38,139,132,58)(39,140,133,59)(40,141,134,60)(41,142,135,46)(42,143,121,47)(43,144,122,48)(44,145,123,49)(45,146,124,50)(61,210,112,159)(62,196,113,160)(63,197,114,161)(64,198,115,162)(65,199,116,163)(66,200,117,164)(67,201,118,165)(68,202,119,151)(69,203,120,152)(70,204,106,153)(71,205,107,154)(72,206,108,155)(73,207,109,156)(74,208,110,157)(75,209,111,158), (1,30)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(15,29)(31,197)(32,198)(33,199)(34,200)(35,201)(36,202)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,196)(46,109)(47,110)(48,111)(49,112)(50,113)(51,114)(52,115)(53,116)(54,117)(55,118)(56,119)(57,120)(58,106)(59,107)(60,108)(61,145)(62,146)(63,147)(64,148)(65,149)(66,150)(67,136)(68,137)(69,138)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,105)(77,91)(78,92)(79,93)(80,94)(81,95)(82,96)(83,97)(84,98)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(121,157)(122,158)(123,159)(124,160)(125,161)(126,162)(127,163)(128,164)(129,165)(130,151)(131,152)(132,153)(133,154)(134,155)(135,156)(166,185)(167,186)(168,187)(169,188)(170,189)(171,190)(172,191)(173,192)(174,193)(175,194)(176,195)(177,181)(178,182)(179,183)(180,184)(211,233)(212,234)(213,235)(214,236)(215,237)(216,238)(217,239)(218,240)(219,226)(220,227)(221,228)(222,229)(223,230)(224,231)(225,232)>;

G:=Group( (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), (1,48,209,194)(2,49,210,195)(3,50,196,181)(4,51,197,182)(5,52,198,183)(6,53,199,184)(7,54,200,185)(8,55,201,186)(9,56,202,187)(10,57,203,188)(11,58,204,189)(12,59,205,190)(13,60,206,191)(14,46,207,192)(15,47,208,193)(16,176,44,112)(17,177,45,113)(18,178,31,114)(19,179,32,115)(20,180,33,116)(21,166,34,117)(22,167,35,118)(23,168,36,119)(24,169,37,120)(25,170,38,106)(26,171,39,107)(27,172,40,108)(28,173,41,109)(29,174,42,110)(30,175,43,111)(61,92,213,123)(62,93,214,124)(63,94,215,125)(64,95,216,126)(65,96,217,127)(66,97,218,128)(67,98,219,129)(68,99,220,130)(69,100,221,131)(70,101,222,132)(71,102,223,133)(72,103,224,134)(73,104,225,135)(74,105,211,121)(75,91,212,122)(76,143,157,233)(77,144,158,234)(78,145,159,235)(79,146,160,236)(80,147,161,237)(81,148,162,238)(82,149,163,239)(83,150,164,240)(84,136,165,226)(85,137,151,227)(86,138,152,228)(87,139,153,229)(88,140,154,230)(89,141,155,231)(90,142,156,232), (1,175,77,212)(2,176,78,213)(3,177,79,214)(4,178,80,215)(5,179,81,216)(6,180,82,217)(7,166,83,218)(8,167,84,219)(9,168,85,220)(10,169,86,221)(11,170,87,222)(12,171,88,223)(13,172,89,224)(14,173,90,225)(15,174,76,211)(16,235,92,195)(17,236,93,181)(18,237,94,182)(19,238,95,183)(20,239,96,184)(21,240,97,185)(22,226,98,186)(23,227,99,187)(24,228,100,188)(25,229,101,189)(26,230,102,190)(27,231,103,191)(28,232,104,192)(29,233,105,193)(30,234,91,194)(31,147,125,51)(32,148,126,52)(33,149,127,53)(34,150,128,54)(35,136,129,55)(36,137,130,56)(37,138,131,57)(38,139,132,58)(39,140,133,59)(40,141,134,60)(41,142,135,46)(42,143,121,47)(43,144,122,48)(44,145,123,49)(45,146,124,50)(61,210,112,159)(62,196,113,160)(63,197,114,161)(64,198,115,162)(65,199,116,163)(66,200,117,164)(67,201,118,165)(68,202,119,151)(69,203,120,152)(70,204,106,153)(71,205,107,154)(72,206,108,155)(73,207,109,156)(74,208,110,157)(75,209,111,158), (1,30)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(15,29)(31,197)(32,198)(33,199)(34,200)(35,201)(36,202)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,196)(46,109)(47,110)(48,111)(49,112)(50,113)(51,114)(52,115)(53,116)(54,117)(55,118)(56,119)(57,120)(58,106)(59,107)(60,108)(61,145)(62,146)(63,147)(64,148)(65,149)(66,150)(67,136)(68,137)(69,138)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,105)(77,91)(78,92)(79,93)(80,94)(81,95)(82,96)(83,97)(84,98)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(121,157)(122,158)(123,159)(124,160)(125,161)(126,162)(127,163)(128,164)(129,165)(130,151)(131,152)(132,153)(133,154)(134,155)(135,156)(166,185)(167,186)(168,187)(169,188)(170,189)(171,190)(172,191)(173,192)(174,193)(175,194)(176,195)(177,181)(178,182)(179,183)(180,184)(211,233)(212,234)(213,235)(214,236)(215,237)(216,238)(217,239)(218,240)(219,226)(220,227)(221,228)(222,229)(223,230)(224,231)(225,232) );

G=PermutationGroup([(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)], [(1,48,209,194),(2,49,210,195),(3,50,196,181),(4,51,197,182),(5,52,198,183),(6,53,199,184),(7,54,200,185),(8,55,201,186),(9,56,202,187),(10,57,203,188),(11,58,204,189),(12,59,205,190),(13,60,206,191),(14,46,207,192),(15,47,208,193),(16,176,44,112),(17,177,45,113),(18,178,31,114),(19,179,32,115),(20,180,33,116),(21,166,34,117),(22,167,35,118),(23,168,36,119),(24,169,37,120),(25,170,38,106),(26,171,39,107),(27,172,40,108),(28,173,41,109),(29,174,42,110),(30,175,43,111),(61,92,213,123),(62,93,214,124),(63,94,215,125),(64,95,216,126),(65,96,217,127),(66,97,218,128),(67,98,219,129),(68,99,220,130),(69,100,221,131),(70,101,222,132),(71,102,223,133),(72,103,224,134),(73,104,225,135),(74,105,211,121),(75,91,212,122),(76,143,157,233),(77,144,158,234),(78,145,159,235),(79,146,160,236),(80,147,161,237),(81,148,162,238),(82,149,163,239),(83,150,164,240),(84,136,165,226),(85,137,151,227),(86,138,152,228),(87,139,153,229),(88,140,154,230),(89,141,155,231),(90,142,156,232)], [(1,175,77,212),(2,176,78,213),(3,177,79,214),(4,178,80,215),(5,179,81,216),(6,180,82,217),(7,166,83,218),(8,167,84,219),(9,168,85,220),(10,169,86,221),(11,170,87,222),(12,171,88,223),(13,172,89,224),(14,173,90,225),(15,174,76,211),(16,235,92,195),(17,236,93,181),(18,237,94,182),(19,238,95,183),(20,239,96,184),(21,240,97,185),(22,226,98,186),(23,227,99,187),(24,228,100,188),(25,229,101,189),(26,230,102,190),(27,231,103,191),(28,232,104,192),(29,233,105,193),(30,234,91,194),(31,147,125,51),(32,148,126,52),(33,149,127,53),(34,150,128,54),(35,136,129,55),(36,137,130,56),(37,138,131,57),(38,139,132,58),(39,140,133,59),(40,141,134,60),(41,142,135,46),(42,143,121,47),(43,144,122,48),(44,145,123,49),(45,146,124,50),(61,210,112,159),(62,196,113,160),(63,197,114,161),(64,198,115,162),(65,199,116,163),(66,200,117,164),(67,201,118,165),(68,202,119,151),(69,203,120,152),(70,204,106,153),(71,205,107,154),(72,206,108,155),(73,207,109,156),(74,208,110,157),(75,209,111,158)], [(1,30),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(15,29),(31,197),(32,198),(33,199),(34,200),(35,201),(36,202),(37,203),(38,204),(39,205),(40,206),(41,207),(42,208),(43,209),(44,210),(45,196),(46,109),(47,110),(48,111),(49,112),(50,113),(51,114),(52,115),(53,116),(54,117),(55,118),(56,119),(57,120),(58,106),(59,107),(60,108),(61,145),(62,146),(63,147),(64,148),(65,149),(66,150),(67,136),(68,137),(69,138),(70,139),(71,140),(72,141),(73,142),(74,143),(75,144),(76,105),(77,91),(78,92),(79,93),(80,94),(81,95),(82,96),(83,97),(84,98),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(121,157),(122,158),(123,159),(124,160),(125,161),(126,162),(127,163),(128,164),(129,165),(130,151),(131,152),(132,153),(133,154),(134,155),(135,156),(166,185),(167,186),(168,187),(169,188),(170,189),(171,190),(172,191),(173,192),(174,193),(175,194),(176,195),(177,181),(178,182),(179,183),(180,184),(211,233),(212,234),(213,235),(214,236),(215,237),(216,238),(217,239),(218,240),(219,226),(220,227),(221,228),(222,229),(223,230),(224,231),(225,232)])

210 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 3A 3B 4A ··· 4F 5A 5B 5C 5D 6A ··· 6F 6G ··· 6N 10A ··· 10L 10M ··· 10AB 12A ··· 12L 15A ··· 15H 20A ··· 20X 30A ··· 30X 30Y ··· 30BD 60A ··· 60AV order 1 2 2 2 2 2 2 2 3 3 4 ··· 4 5 5 5 5 6 ··· 6 6 ··· 6 10 ··· 10 10 ··· 10 12 ··· 12 15 ··· 15 20 ··· 20 30 ··· 30 30 ··· 30 60 ··· 60 size 1 1 1 1 4 4 4 4 1 1 2 ··· 2 1 1 1 1 1 ··· 1 4 ··· 4 1 ··· 1 4 ··· 4 2 ··· 2 1 ··· 1 2 ··· 2 1 ··· 1 4 ··· 4 2 ··· 2

210 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 type + + + + image C1 C2 C2 C3 C5 C6 C6 C10 C10 C15 C30 C30 D4 C3×D4 C5×D4 D4×C15 kernel C15×C4⋊1D4 C4×C60 D4×C30 C5×C4⋊1D4 C3×C4⋊1D4 C4×C20 D4×C10 C4×C12 C6×D4 C4⋊1D4 C42 C2×D4 C60 C20 C12 C4 # reps 1 1 6 2 4 2 12 4 24 8 8 48 6 12 24 48

Matrix representation of C15×C41D4 in GL4(𝔽61) generated by

 15 0 0 0 0 15 0 0 0 0 47 0 0 0 0 47
,
 0 60 0 0 1 0 0 0 0 0 1 60 0 0 2 60
,
 0 1 0 0 60 0 0 0 0 0 1 0 0 0 0 1
,
 60 0 0 0 0 1 0 0 0 0 60 0 0 0 59 1
G:=sub<GL(4,GF(61))| [15,0,0,0,0,15,0,0,0,0,47,0,0,0,0,47],[0,1,0,0,60,0,0,0,0,0,1,2,0,0,60,60],[0,60,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[60,0,0,0,0,1,0,0,0,0,60,59,0,0,0,1] >;

C15×C41D4 in GAP, Magma, Sage, TeX

C_{15}\times C_4\rtimes_1D_4
% in TeX

G:=Group("C15xC4:1D4");
// GroupNames label

G:=SmallGroup(480,932);
// by ID

G=gap.SmallGroup(480,932);
# by ID

G:=PCGroup([7,-2,-2,-2,-3,-5,-2,-2,1709,848,5126,1276]);
// Polycyclic

G:=Group<a,b,c,d|a^15=b^4=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽