metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D24⋊7D5, C40.18D6, D10.6D12, C24.45D10, Dic60⋊12C2, D12.22D10, C120.22C22, C60.124C23, Dic5.25D12, Dic30.36C22, (C8×D5)⋊2S3, C6.9(D4×D5), (D5×C24)⋊2C2, (C5×D24)⋊3C2, C5⋊2(C4○D24), C15⋊2(C4○D8), C8.21(S3×D5), C3⋊1(D8⋊3D5), (C4×D5).80D6, (C6×D5).44D4, C30.20(C2×D4), C10.9(C2×D12), C2.14(D5×D12), C5⋊2C8.33D6, D12⋊5D5⋊10C2, D12.D5⋊12C2, C20.77(C22×S3), (C3×Dic5).48D4, (D5×C12).94C22, (C5×D12).24C22, C12.147(C22×D5), C4.72(C2×S3×D5), (C3×C5⋊2C8).37C22, SmallGroup(480,346)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D24⋊7D5
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, C3, C4, C4, C22, C5, S3, C6, C6, C8, C8, C2×C4, D4, Q8, D5, C10, C10, Dic3, C12, C12, D6, C2×C6, C15, C2×C8, D8, SD16, Q16, C4○D4, Dic5, Dic5, C20, D10, C2×C10, C24, C24, Dic6, C4×S3, D12, C3⋊D4, C2×C12, C5×S3, C3×D5, C30, C4○D8, C5⋊2C8, C40, Dic10, C4×D5, C2×Dic5, C5⋊D4, C5×D4, C24⋊C2, D24, Dic12, C2×C24, C4○D12, C3×Dic5, Dic15, C60, C6×D5, S3×C10, C8×D5, Dic20, D4.D5, C5×D8, D4⋊2D5, C4○D24, C3×C5⋊2C8, C120, S3×Dic5, C15⋊D4, D5×C12, C5×D12, Dic30, D8⋊3D5, D12.D5, D5×C24, C5×D24, Dic60, D12⋊5D5, D24⋊7D5
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, C2×D4, D10, D12, C22×S3, C4○D8, C22×D5, C2×D12, S3×D5, D4×D5, C4○D24, C2×S3×D5, D8⋊3D5, D5×D12, D24⋊7D5
►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 89)(2 88)(3 87)(4 86)(5 85)(6 84)(7 83)(8 82)(9 81)(10 80)(11 79)(12 78)(13 77)(14 76)(15 75)(16 74)(17 73)(18 96)(19 95)(20 94)(21 93)(22 92)(23 91)(24 90)(25 197)(26 196)(27 195)(28 194)(29 193)(30 216)(31 215)(32 214)(33 213)(34 212)(35 211)(36 210)(37 209)(38 208)(39 207)(40 206)(41 205)(42 204)(43 203)(44 202)(45 201)(46 200)(47 199)(48 198)(49 115)(50 114)(51 113)(52 112)(53 111)(54 110)(55 109)(56 108)(57 107)(58 106)(59 105)(60 104)(61 103)(62 102)(63 101)(64 100)(65 99)(66 98)(67 97)(68 120)(69 119)(70 118)(71 117)(72 116)(121 168)(122 167)(123 166)(124 165)(125 164)(126 163)(127 162)(128 161)(129 160)(130 159)(131 158)(132 157)(133 156)(134 155)(135 154)(136 153)(137 152)(138 151)(139 150)(140 149)(141 148)(142 147)(143 146)(144 145)(169 230)(170 229)(171 228)(172 227)(173 226)(174 225)(175 224)(176 223)(177 222)(178 221)(179 220)(180 219)(181 218)(182 217)(183 240)(184 239)(185 238)(186 237)(187 236)(188 235)(189 234)(190 233)(191 232)(192 231)
(1 175 132 56 42)(2 176 133 57 43)(3 177 134 58 44)(4 178 135 59 45)(5 179 136 60 46)(6 180 137 61 47)(7 181 138 62 48)(8 182 139 63 25)(9 183 140 64 26)(10 184 141 65 27)(11 185 142 66 28)(12 186 143 67 29)(13 187 144 68 30)(14 188 121 69 31)(15 189 122 70 32)(16 190 123 71 33)(17 191 124 72 34)(18 192 125 49 35)(19 169 126 50 36)(20 170 127 51 37)(21 171 128 52 38)(22 172 129 53 39)(23 173 130 54 40)(24 174 131 55 41)(73 232 165 116 212)(74 233 166 117 213)(75 234 167 118 214)(76 235 168 119 215)(77 236 145 120 216)(78 237 146 97 193)(79 238 147 98 194)(80 239 148 99 195)(81 240 149 100 196)(82 217 150 101 197)(83 218 151 102 198)(84 219 152 103 199)(85 220 153 104 200)(86 221 154 105 201)(87 222 155 106 202)(88 223 156 107 203)(89 224 157 108 204)(90 225 158 109 205)(91 226 159 110 206)(92 227 160 111 207)(93 228 161 112 208)(94 229 162 113 209)(95 230 163 114 210)(96 231 164 115 211)
(1 42)(2 43)(3 44)(4 45)(5 46)(6 47)(7 48)(8 25)(9 26)(10 27)(11 28)(12 29)(13 30)(14 31)(15 32)(16 33)(17 34)(18 35)(19 36)(20 37)(21 38)(22 39)(23 40)(24 41)(49 192)(50 169)(51 170)(52 171)(53 172)(54 173)(55 174)(56 175)(57 176)(58 177)(59 178)(60 179)(61 180)(62 181)(63 182)(64 183)(65 184)(66 185)(67 186)(68 187)(69 188)(70 189)(71 190)(72 191)(73 200)(74 201)(75 202)(76 203)(77 204)(78 205)(79 206)(80 207)(81 208)(82 209)(83 210)(84 211)(85 212)(86 213)(87 214)(88 215)(89 216)(90 193)(91 194)(92 195)(93 196)(94 197)(95 198)(96 199)(97 225)(98 226)(99 227)(100 228)(101 229)(102 230)(103 231)(104 232)(105 233)(106 234)(107 235)(108 236)(109 237)(110 238)(111 239)(112 240)(113 217)(114 218)(115 219)(116 220)(117 221)(118 222)(119 223)(120 224)(145 157)(146 158)(147 159)(148 160)(149 161)(150 162)(151 163)(152 164)(153 165)(154 166)(155 167)(156 168)
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), (1,89)(2,88)(3,87)(4,86)(5,85)(6,84)(7,83)(8,82)(9,81)(10,80)(11,79)(12,78)(13,77)(14,76)(15,75)(16,74)(17,73)(18,96)(19,95)(20,94)(21,93)(22,92)(23,91)(24,90)(25,197)(26,196)(27,195)(28,194)(29,193)(30,216)(31,215)(32,214)(33,213)(34,212)(35,211)(36,210)(37,209)(38,208)(39,207)(40,206)(41,205)(42,204)(43,203)(44,202)(45,201)(46,200)(47,199)(48,198)(49,115)(50,114)(51,113)(52,112)(53,111)(54,110)(55,109)(56,108)(57,107)(58,106)(59,105)(60,104)(61,103)(62,102)(63,101)(64,100)(65,99)(66,98)(67,97)(68,120)(69,119)(70,118)(71,117)(72,116)(121,168)(122,167)(123,166)(124,165)(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)(143,146)(144,145)(169,230)(170,229)(171,228)(172,227)(173,226)(174,225)(175,224)(176,223)(177,222)(178,221)(179,220)(180,219)(181,218)(182,217)(183,240)(184,239)(185,238)(186,237)(187,236)(188,235)(189,234)(190,233)(191,232)(192,231), (1,175,132,56,42)(2,176,133,57,43)(3,177,134,58,44)(4,178,135,59,45)(5,179,136,60,46)(6,180,137,61,47)(7,181,138,62,48)(8,182,139,63,25)(9,183,140,64,26)(10,184,141,65,27)(11,185,142,66,28)(12,186,143,67,29)(13,187,144,68,30)(14,188,121,69,31)(15,189,122,70,32)(16,190,123,71,33)(17,191,124,72,34)(18,192,125,49,35)(19,169,126,50,36)(20,170,127,51,37)(21,171,128,52,38)(22,172,129,53,39)(23,173,130,54,40)(24,174,131,55,41)(73,232,165,116,212)(74,233,166,117,213)(75,234,167,118,214)(76,235,168,119,215)(77,236,145,120,216)(78,237,146,97,193)(79,238,147,98,194)(80,239,148,99,195)(81,240,149,100,196)(82,217,150,101,197)(83,218,151,102,198)(84,219,152,103,199)(85,220,153,104,200)(86,221,154,105,201)(87,222,155,106,202)(88,223,156,107,203)(89,224,157,108,204)(90,225,158,109,205)(91,226,159,110,206)(92,227,160,111,207)(93,228,161,112,208)(94,229,162,113,209)(95,230,163,114,210)(96,231,164,115,211), (1,42)(2,43)(3,44)(4,45)(5,46)(6,47)(7,48)(8,25)(9,26)(10,27)(11,28)(12,29)(13,30)(14,31)(15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(49,192)(50,169)(51,170)(52,171)(53,172)(54,173)(55,174)(56,175)(57,176)(58,177)(59,178)(60,179)(61,180)(62,181)(63,182)(64,183)(65,184)(66,185)(67,186)(68,187)(69,188)(70,189)(71,190)(72,191)(73,200)(74,201)(75,202)(76,203)(77,204)(78,205)(79,206)(80,207)(81,208)(82,209)(83,210)(84,211)(85,212)(86,213)(87,214)(88,215)(89,216)(90,193)(91,194)(92,195)(93,196)(94,197)(95,198)(96,199)(97,225)(98,226)(99,227)(100,228)(101,229)(102,230)(103,231)(104,232)(105,233)(106,234)(107,235)(108,236)(109,237)(110,238)(111,239)(112,240)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)(151,163)(152,164)(153,165)(154,166)(155,167)(156,168)>;
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), (1,89)(2,88)(3,87)(4,86)(5,85)(6,84)(7,83)(8,82)(9,81)(10,80)(11,79)(12,78)(13,77)(14,76)(15,75)(16,74)(17,73)(18,96)(19,95)(20,94)(21,93)(22,92)(23,91)(24,90)(25,197)(26,196)(27,195)(28,194)(29,193)(30,216)(31,215)(32,214)(33,213)(34,212)(35,211)(36,210)(37,209)(38,208)(39,207)(40,206)(41,205)(42,204)(43,203)(44,202)(45,201)(46,200)(47,199)(48,198)(49,115)(50,114)(51,113)(52,112)(53,111)(54,110)(55,109)(56,108)(57,107)(58,106)(59,105)(60,104)(61,103)(62,102)(63,101)(64,100)(65,99)(66,98)(67,97)(68,120)(69,119)(70,118)(71,117)(72,116)(121,168)(122,167)(123,166)(124,165)(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)(143,146)(144,145)(169,230)(170,229)(171,228)(172,227)(173,226)(174,225)(175,224)(176,223)(177,222)(178,221)(179,220)(180,219)(181,218)(182,217)(183,240)(184,239)(185,238)(186,237)(187,236)(188,235)(189,234)(190,233)(191,232)(192,231), (1,175,132,56,42)(2,176,133,57,43)(3,177,134,58,44)(4,178,135,59,45)(5,179,136,60,46)(6,180,137,61,47)(7,181,138,62,48)(8,182,139,63,25)(9,183,140,64,26)(10,184,141,65,27)(11,185,142,66,28)(12,186,143,67,29)(13,187,144,68,30)(14,188,121,69,31)(15,189,122,70,32)(16,190,123,71,33)(17,191,124,72,34)(18,192,125,49,35)(19,169,126,50,36)(20,170,127,51,37)(21,171,128,52,38)(22,172,129,53,39)(23,173,130,54,40)(24,174,131,55,41)(73,232,165,116,212)(74,233,166,117,213)(75,234,167,118,214)(76,235,168,119,215)(77,236,145,120,216)(78,237,146,97,193)(79,238,147,98,194)(80,239,148,99,195)(81,240,149,100,196)(82,217,150,101,197)(83,218,151,102,198)(84,219,152,103,199)(85,220,153,104,200)(86,221,154,105,201)(87,222,155,106,202)(88,223,156,107,203)(89,224,157,108,204)(90,225,158,109,205)(91,226,159,110,206)(92,227,160,111,207)(93,228,161,112,208)(94,229,162,113,209)(95,230,163,114,210)(96,231,164,115,211), (1,42)(2,43)(3,44)(4,45)(5,46)(6,47)(7,48)(8,25)(9,26)(10,27)(11,28)(12,29)(13,30)(14,31)(15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(49,192)(50,169)(51,170)(52,171)(53,172)(54,173)(55,174)(56,175)(57,176)(58,177)(59,178)(60,179)(61,180)(62,181)(63,182)(64,183)(65,184)(66,185)(67,186)(68,187)(69,188)(70,189)(71,190)(72,191)(73,200)(74,201)(75,202)(76,203)(77,204)(78,205)(79,206)(80,207)(81,208)(82,209)(83,210)(84,211)(85,212)(86,213)(87,214)(88,215)(89,216)(90,193)(91,194)(92,195)(93,196)(94,197)(95,198)(96,199)(97,225)(98,226)(99,227)(100,228)(101,229)(102,230)(103,231)(104,232)(105,233)(106,234)(107,235)(108,236)(109,237)(110,238)(111,239)(112,240)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)(151,163)(152,164)(153,165)(154,166)(155,167)(156,168) );
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)], [(1,89),(2,88),(3,87),(4,86),(5,85),(6,84),(7,83),(8,82),(9,81),(10,80),(11,79),(12,78),(13,77),(14,76),(15,75),(16,74),(17,73),(18,96),(19,95),(20,94),(21,93),(22,92),(23,91),(24,90),(25,197),(26,196),(27,195),(28,194),(29,193),(30,216),(31,215),(32,214),(33,213),(34,212),(35,211),(36,210),(37,209),(38,208),(39,207),(40,206),(41,205),(42,204),(43,203),(44,202),(45,201),(46,200),(47,199),(48,198),(49,115),(50,114),(51,113),(52,112),(53,111),(54,110),(55,109),(56,108),(57,107),(58,106),(59,105),(60,104),(61,103),(62,102),(63,101),(64,100),(65,99),(66,98),(67,97),(68,120),(69,119),(70,118),(71,117),(72,116),(121,168),(122,167),(123,166),(124,165),(125,164),(126,163),(127,162),(128,161),(129,160),(130,159),(131,158),(132,157),(133,156),(134,155),(135,154),(136,153),(137,152),(138,151),(139,150),(140,149),(141,148),(142,147),(143,146),(144,145),(169,230),(170,229),(171,228),(172,227),(173,226),(174,225),(175,224),(176,223),(177,222),(178,221),(179,220),(180,219),(181,218),(182,217),(183,240),(184,239),(185,238),(186,237),(187,236),(188,235),(189,234),(190,233),(191,232),(192,231)], [(1,175,132,56,42),(2,176,133,57,43),(3,177,134,58,44),(4,178,135,59,45),(5,179,136,60,46),(6,180,137,61,47),(7,181,138,62,48),(8,182,139,63,25),(9,183,140,64,26),(10,184,141,65,27),(11,185,142,66,28),(12,186,143,67,29),(13,187,144,68,30),(14,188,121,69,31),(15,189,122,70,32),(16,190,123,71,33),(17,191,124,72,34),(18,192,125,49,35),(19,169,126,50,36),(20,170,127,51,37),(21,171,128,52,38),(22,172,129,53,39),(23,173,130,54,40),(24,174,131,55,41),(73,232,165,116,212),(74,233,166,117,213),(75,234,167,118,214),(76,235,168,119,215),(77,236,145,120,216),(78,237,146,97,193),(79,238,147,98,194),(80,239,148,99,195),(81,240,149,100,196),(82,217,150,101,197),(83,218,151,102,198),(84,219,152,103,199),(85,220,153,104,200),(86,221,154,105,201),(87,222,155,106,202),(88,223,156,107,203),(89,224,157,108,204),(90,225,158,109,205),(91,226,159,110,206),(92,227,160,111,207),(93,228,161,112,208),(94,229,162,113,209),(95,230,163,114,210),(96,231,164,115,211)], [(1,42),(2,43),(3,44),(4,45),(5,46),(6,47),(7,48),(8,25),(9,26),(10,27),(11,28),(12,29),(13,30),(14,31),(15,32),(16,33),(17,34),(18,35),(19,36),(20,37),(21,38),(22,39),(23,40),(24,41),(49,192),(50,169),(51,170),(52,171),(53,172),(54,173),(55,174),(56,175),(57,176),(58,177),(59,178),(60,179),(61,180),(62,181),(63,182),(64,183),(65,184),(66,185),(67,186),(68,187),(69,188),(70,189),(71,190),(72,191),(73,200),(74,201),(75,202),(76,203),(77,204),(78,205),(79,206),(80,207),(81,208),(82,209),(83,210),(84,211),(85,212),(86,213),(87,214),(88,215),(89,216),(90,193),(91,194),(92,195),(93,196),(94,197),(95,198),(96,199),(97,225),(98,226),(99,227),(100,228),(101,229),(102,230),(103,231),(104,232),(105,233),(106,234),(107,235),(108,236),(109,237),(110,238),(111,239),(112,240),(113,217),(114,218),(115,219),(116,220),(117,221),(118,222),(119,223),(120,224),(145,157),(146,158),(147,159),(148,160),(149,161),(150,162),(151,163),(152,164),(153,165),(154,166),(155,167),(156,168)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3 | 4A | 4B | 4C | 4D | 4E | 5A | 5B | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 10A | 10B | 10C | 10D | 10E | 10F | 12A | 12B | 12C | 12D | 15A | 15B | 20A | 20B | 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 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 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 | 10 | 12 | 12 | 2 | 2 | 5 | 5 | 60 | 60 | 2 | 2 | 2 | 10 | 10 | 2 | 2 | 10 | 10 | 2 | 2 | 24 | 24 | 24 | 24 | 2 | 2 | 10 | 10 | 4 | 4 | 4 | 4 | 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 | D10 | D10 | D12 | D12 | C4○D8 | C4○D24 | S3×D5 | D4×D5 | C2×S3×D5 | D8⋊3D5 | D5×D12 | D24⋊7D5 |
| kernel | D24⋊7D5 | D12.D5 | D5×C24 | C5×D24 | Dic60 | D12⋊5D5 | C8×D5 | C3×Dic5 | C6×D5 | D24 | C5⋊2C8 | C40 | C4×D5 | C24 | D12 | Dic5 | D10 | C15 | C5 | C8 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 4 | 2 | 2 | 4 | 8 | 2 | 2 | 2 | 4 | 4 | 8 |
Matrix representation of D24⋊7D5 ►in GL4(𝔽241) generated by
| 121 | 0 | 0 | 0 |
| 0 | 2 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 10 | 0 | 0 |
| 217 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 |
| 0 | 0 | 0 | 240 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 240 | 51 |
| 1 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
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] >;
D24⋊7D5 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