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G = D247D5order 480 = 25·3·5

The semidirect product of D24 and D5 acting through Inn(D24)

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D247D5, C40.18D6, D10.6D12, C24.45D10, Dic6012C2, D12.22D10, C120.22C22, C60.124C23, Dic5.25D12, Dic30.36C22, (C8×D5)⋊2S3, C6.9(D4×D5), (D5×C24)⋊2C2, (C5×D24)⋊3C2, C52(C4○D24), C152(C4○D8), C8.21(S3×D5), C31(D83D5), (C4×D5).80D6, (C6×D5).44D4, C30.20(C2×D4), C10.9(C2×D12), C2.14(D5×D12), C52C8.33D6, D125D510C2, D12.D512C2, C20.77(C22×S3), (C3×Dic5).48D4, (D5×C12).94C22, (C5×D12).24C22, C12.147(C22×D5), C4.72(C2×S3×D5), (C3×C52C8).37C22, SmallGroup(480,346)

Series: Derived Chief Lower central Upper central

C1C60 — D247D5
C1C5C15C30C60D5×C12D125D5 — D247D5
C15C30C60 — D247D5
C1C2C4C8

Generators and relations for D247D5
 G = < a,b,c,d | a24=b2=c5=d2=1, bab=a-1, ac=ca, ad=da, bc=cb, dbd=a12b, dcd=c-1 >

Subgroups: 700 in 124 conjugacy classes, 40 normal (30 characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3 [×2], C6, C6, C8, C8, C2×C4 [×3], D4 [×4], Q8 [×2], D5, C10, C10 [×2], Dic3 [×2], C12, C12, D6 [×2], C2×C6, C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5, Dic5 [×2], C20, D10, C2×C10 [×2], C24, C24, Dic6 [×2], C4×S3 [×2], D12 [×2], C3⋊D4 [×2], C2×C12, C5×S3 [×2], C3×D5, C30, C4○D8, C52C8, C40, Dic10 [×2], C4×D5, C2×Dic5 [×2], C5⋊D4 [×2], C5×D4 [×2], C24⋊C2 [×2], D24, Dic12, C2×C24, C4○D12 [×2], C3×Dic5, Dic15 [×2], C60, C6×D5, S3×C10 [×2], C8×D5, Dic20, D4.D5 [×2], C5×D8, D42D5 [×2], C4○D24, C3×C52C8, C120, S3×Dic5 [×2], C15⋊D4 [×2], D5×C12, C5×D12 [×2], Dic30 [×2], D83D5, D12.D5 [×2], D5×C24, C5×D24, Dic60, D125D5 [×2], D247D5
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], D12 [×2], C22×S3, C4○D8, C22×D5, C2×D12, S3×D5, D4×D5, C4○D24, C2×S3×D5, D83D5, D5×D12, D247D5

Smallest permutation representation of D247D5
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)
(1 216)(2 215)(3 214)(4 213)(5 212)(6 211)(7 210)(8 209)(9 208)(10 207)(11 206)(12 205)(13 204)(14 203)(15 202)(16 201)(17 200)(18 199)(19 198)(20 197)(21 196)(22 195)(23 194)(24 193)(25 71)(26 70)(27 69)(28 68)(29 67)(30 66)(31 65)(32 64)(33 63)(34 62)(35 61)(36 60)(37 59)(38 58)(39 57)(40 56)(41 55)(42 54)(43 53)(44 52)(45 51)(46 50)(47 49)(48 72)(73 173)(74 172)(75 171)(76 170)(77 169)(78 192)(79 191)(80 190)(81 189)(82 188)(83 187)(84 186)(85 185)(86 184)(87 183)(88 182)(89 181)(90 180)(91 179)(92 178)(93 177)(94 176)(95 175)(96 174)(97 144)(98 143)(99 142)(100 141)(101 140)(102 139)(103 138)(104 137)(105 136)(106 135)(107 134)(108 133)(109 132)(110 131)(111 130)(112 129)(113 128)(114 127)(115 126)(116 125)(117 124)(118 123)(119 122)(120 121)(145 226)(146 225)(147 224)(148 223)(149 222)(150 221)(151 220)(152 219)(153 218)(154 217)(155 240)(156 239)(157 238)(158 237)(159 236)(160 235)(161 234)(162 233)(163 232)(164 231)(165 230)(166 229)(167 228)(168 227)
(1 226 188 62 135)(2 227 189 63 136)(3 228 190 64 137)(4 229 191 65 138)(5 230 192 66 139)(6 231 169 67 140)(7 232 170 68 141)(8 233 171 69 142)(9 234 172 70 143)(10 235 173 71 144)(11 236 174 72 121)(12 237 175 49 122)(13 238 176 50 123)(14 239 177 51 124)(15 240 178 52 125)(16 217 179 53 126)(17 218 180 54 127)(18 219 181 55 128)(19 220 182 56 129)(20 221 183 57 130)(21 222 184 58 131)(22 223 185 59 132)(23 224 186 60 133)(24 225 187 61 134)(25 97 207 160 73)(26 98 208 161 74)(27 99 209 162 75)(28 100 210 163 76)(29 101 211 164 77)(30 102 212 165 78)(31 103 213 166 79)(32 104 214 167 80)(33 105 215 168 81)(34 106 216 145 82)(35 107 193 146 83)(36 108 194 147 84)(37 109 195 148 85)(38 110 196 149 86)(39 111 197 150 87)(40 112 198 151 88)(41 113 199 152 89)(42 114 200 153 90)(43 115 201 154 91)(44 116 202 155 92)(45 117 203 156 93)(46 118 204 157 94)(47 119 205 158 95)(48 120 206 159 96)
(1 135)(2 136)(3 137)(4 138)(5 139)(6 140)(7 141)(8 142)(9 143)(10 144)(11 121)(12 122)(13 123)(14 124)(15 125)(16 126)(17 127)(18 128)(19 129)(20 130)(21 131)(22 132)(23 133)(24 134)(25 148)(26 149)(27 150)(28 151)(29 152)(30 153)(31 154)(32 155)(33 156)(34 157)(35 158)(36 159)(37 160)(38 161)(39 162)(40 163)(41 164)(42 165)(43 166)(44 167)(45 168)(46 145)(47 146)(48 147)(49 237)(50 238)(51 239)(52 240)(53 217)(54 218)(55 219)(56 220)(57 221)(58 222)(59 223)(60 224)(61 225)(62 226)(63 227)(64 228)(65 229)(66 230)(67 231)(68 232)(69 233)(70 234)(71 235)(72 236)(73 85)(74 86)(75 87)(76 88)(77 89)(78 90)(79 91)(80 92)(81 93)(82 94)(83 95)(84 96)(97 195)(98 196)(99 197)(100 198)(101 199)(102 200)(103 201)(104 202)(105 203)(106 204)(107 205)(108 206)(109 207)(110 208)(111 209)(112 210)(113 211)(114 212)(115 213)(116 214)(117 215)(118 216)(119 193)(120 194)

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

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

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

60 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B6A6B6C8A8B8C8D10A10B10C10D10E10F12A12B12C12D15A15B20A20B24A24B24C24D24E24F24G24H30A30B40A40B40C40D60A60B60C60D120A···120H
order122223444445566688881010101010101212121215152020242424242424242430304040404060606060120···120
size111012122255606022210102210102224242424221010444422221010101044444444444···4

60 irreducible representations

dim1111112222222222222444444
type++++++++++++++++++++-+-
imageC1C2C2C2C2C2S3D4D4D5D6D6D6D10D10D12D12C4○D8C4○D24S3×D5D4×D5C2×S3×D5D83D5D5×D12D247D5
kernelD247D5D12.D5D5×C24C5×D24Dic60D125D5C8×D5C3×Dic5C6×D5D24C52C8C40C4×D5C24D12Dic5D10C15C5C8C6C4C3C2C1
# reps1211121112111242248222448

Matrix representation of D247D5 in GL4(𝔽241) generated by

121000
0200
0010
0001
,
01000
217000
002400
000240
,
1000
0100
0001
0024051
,
1000
024000
0001
0010
G:=sub<GL(4,GF(241))| [121,0,0,0,0,2,0,0,0,0,1,0,0,0,0,1],[0,217,0,0,10,0,0,0,0,0,240,0,0,0,0,240],[1,0,0,0,0,1,0,0,0,0,0,240,0,0,1,51],[1,0,0,0,0,240,0,0,0,0,0,1,0,0,1,0] >;

D247D5 in GAP, Magma, Sage, TeX

D_{24}\rtimes_7D_5
% in TeX

G:=Group("D24:7D5");
// GroupNames label

G:=SmallGroup(480,346);
// by ID

G=gap.SmallGroup(480,346);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,135,142,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^24=b^2=c^5=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^12*b,d*c*d=c^-1>;
// generators/relations

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