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G = D12.24D10order 480 = 25·3·5

7th non-split extension by D12 of D10 acting via D10/D5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D12.24D10, C60.14C23, Dic10.8D6, Dic30.4C22, D4⋊S37D5, C3⋊C8.13D10, (C5×D4).6D6, D42D52S3, C1513(C4○D8), C35(D83D5), D4.D156C2, D4.10(S3×D5), (C6×D5).10D4, (C4×D5).45D6, C3⋊Dic203C2, C6.143(D4×D5), D125D52C2, (C3×D4).21D10, C30.176(C2×D4), C20.D63C2, C52(Q8.13D6), D10.9(C3⋊D4), C20.14(C22×S3), C153C8.3C22, (C3×Dic5).68D4, (C5×D12).4C22, (D5×C12).6C22, (D4×C15).8C22, C12.14(C22×D5), Dic5.40(C3⋊D4), (C3×Dic10).4C22, (D5×C3⋊C8)⋊3C2, C4.14(C2×S3×D5), (C5×D4⋊S3)⋊6C2, C2.25(D5×C3⋊D4), (C5×C3⋊C8).3C22, (C3×D42D5)⋊2C2, C10.46(C2×C3⋊D4), SmallGroup(480,566)

Series: Derived Chief Lower central Upper central

C1C60 — D12.24D10
C1C5C15C30C60D5×C12D125D5 — D12.24D10
C15C30C60 — D12.24D10
C1C2C4D4

Generators and relations for D12.24D10
 G = < a,b,c,d | a12=b2=c10=1, d2=a6, bab=a-1, cac-1=dad-1=a7, cbc-1=a3b, dbd-1=a9b, dcd-1=a6c-1 >

Subgroups: 604 in 124 conjugacy classes, 40 normal (all characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3, C6, C6 [×2], C8 [×2], C2×C4 [×3], D4, D4 [×3], Q8 [×2], D5, C10, C10 [×2], Dic3, C12, C12 [×2], D6, C2×C6 [×2], C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5, Dic5 [×2], C20, D10, C2×C10 [×2], C3⋊C8, C3⋊C8, Dic6, C4×S3, D12, C3⋊D4, C2×C12 [×2], C3×D4, C3×D4, C3×Q8, C5×S3, C3×D5, C30, C30, C4○D8, C52C8, C40, Dic10, Dic10, C4×D5, C2×Dic5 [×2], C5⋊D4 [×2], C5×D4, C5×D4, C2×C3⋊C8, D4⋊S3, D4.S3, Q82S3, C3⋊Q16, C4○D12, C3×C4○D4, C3×Dic5, C3×Dic5, Dic15, C60, C6×D5, S3×C10, C2×C30, C8×D5, Dic20, D4.D5 [×2], C5×D8, D42D5, D42D5, Q8.13D6, C5×C3⋊C8, C153C8, S3×Dic5, C15⋊D4, C3×Dic10, D5×C12, C6×Dic5, C3×C5⋊D4, C5×D12, Dic30, D4×C15, D83D5, D5×C3⋊C8, C20.D6, C3⋊Dic20, C5×D4⋊S3, D4.D15, D125D5, C3×D42D5, D12.24D10
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C4○D8, C22×D5, C2×C3⋊D4, S3×D5, D4×D5, Q8.13D6, C2×S3×D5, D83D5, D5×C3⋊D4, D12.24D10

Smallest permutation representation of D12.24D10
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)
(1 157)(2 168)(3 167)(4 166)(5 165)(6 164)(7 163)(8 162)(9 161)(10 160)(11 159)(12 158)(13 61)(14 72)(15 71)(16 70)(17 69)(18 68)(19 67)(20 66)(21 65)(22 64)(23 63)(24 62)(25 120)(26 119)(27 118)(28 117)(29 116)(30 115)(31 114)(32 113)(33 112)(34 111)(35 110)(36 109)(37 172)(38 171)(39 170)(40 169)(41 180)(42 179)(43 178)(44 177)(45 176)(46 175)(47 174)(48 173)(49 194)(50 193)(51 204)(52 203)(53 202)(54 201)(55 200)(56 199)(57 198)(58 197)(59 196)(60 195)(73 88)(74 87)(75 86)(76 85)(77 96)(78 95)(79 94)(80 93)(81 92)(82 91)(83 90)(84 89)(97 152)(98 151)(99 150)(100 149)(101 148)(102 147)(103 146)(104 145)(105 156)(106 155)(107 154)(108 153)(121 144)(122 143)(123 142)(124 141)(125 140)(126 139)(127 138)(128 137)(129 136)(130 135)(131 134)(132 133)(181 226)(182 225)(183 224)(184 223)(185 222)(186 221)(187 220)(188 219)(189 218)(190 217)(191 228)(192 227)(205 237)(206 236)(207 235)(208 234)(209 233)(210 232)(211 231)(212 230)(213 229)(214 240)(215 239)(216 238)
(1 19 230 127 112 60 91 43 218 156)(2 14 231 122 113 55 92 38 219 151)(3 21 232 129 114 50 93 45 220 146)(4 16 233 124 115 57 94 40 221 153)(5 23 234 131 116 52 95 47 222 148)(6 18 235 126 117 59 96 42 223 155)(7 13 236 121 118 54 85 37 224 150)(8 20 237 128 119 49 86 44 225 145)(9 15 238 123 120 56 87 39 226 152)(10 22 239 130 109 51 88 46 227 147)(11 17 240 125 110 58 89 41 228 154)(12 24 229 132 111 53 90 48 217 149)(25 196 74 179 181 106 161 68 216 139)(26 203 75 174 182 101 162 63 205 134)(27 198 76 169 183 108 163 70 206 141)(28 193 77 176 184 103 164 65 207 136)(29 200 78 171 185 98 165 72 208 143)(30 195 79 178 186 105 166 67 209 138)(31 202 80 173 187 100 167 62 210 133)(32 197 81 180 188 107 168 69 211 140)(33 204 82 175 189 102 157 64 212 135)(34 199 83 170 190 97 158 71 213 142)(35 194 84 177 191 104 159 66 214 137)(36 201 73 172 192 99 160 61 215 144)
(1 156 7 150)(2 151 8 145)(3 146 9 152)(4 153 10 147)(5 148 11 154)(6 155 12 149)(13 218 19 224)(14 225 20 219)(15 220 21 226)(16 227 22 221)(17 222 23 228)(18 217 24 223)(25 202 31 196)(26 197 32 203)(27 204 33 198)(28 199 34 193)(29 194 35 200)(30 201 36 195)(37 230 43 236)(38 237 44 231)(39 232 45 238)(40 239 46 233)(41 234 47 240)(42 229 48 235)(49 113 55 119)(50 120 56 114)(51 115 57 109)(52 110 58 116)(53 117 59 111)(54 112 60 118)(61 192 67 186)(62 187 68 181)(63 182 69 188)(64 189 70 183)(65 184 71 190)(66 191 72 185)(73 138 79 144)(74 133 80 139)(75 140 81 134)(76 135 82 141)(77 142 83 136)(78 137 84 143)(85 121 91 127)(86 128 92 122)(87 123 93 129)(88 130 94 124)(89 125 95 131)(90 132 96 126)(97 158 103 164)(98 165 104 159)(99 160 105 166)(100 167 106 161)(101 162 107 168)(102 157 108 163)(169 206 175 212)(170 213 176 207)(171 208 177 214)(172 215 178 209)(173 210 179 216)(174 205 180 211)

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

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

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

48 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B6A6B6C6D8A8B8C8D10A10B10C10D10E10F12A12B12C12D12E15A15B20A20B30A30B30C30D30E30F40A40B40C40D60A60B
order122223444445566668888101010101010121212121215152020303030303030404040406060
size11410122255206022244206630302288242441010202044444488881212121288

48 irreducible representations

dim1111111122222222222224444448
type+++++++++++++++++++++--
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C3⋊D4C3⋊D4C4○D8S3×D5D4×D5Q8.13D6C2×S3×D5D83D5D5×C3⋊D4D12.24D10
kernelD12.24D10D5×C3⋊C8C20.D6C3⋊Dic20C5×D4⋊S3D4.D15D125D5C3×D42D5D42D5C3×Dic5C6×D5D4⋊S3Dic10C4×D5C5×D4C3⋊C8D12C3×D4Dic5D10C15D4C6C5C4C3C2C1
# reps1111111111121112222242222442

Matrix representation of D12.24D10 in GL6(𝔽241)

100000
010000
0064000
0016017700
00000240
00001240
,
24000000
02400000
003021700
0016821100
0000140193
000092101
,
1901900000
512400000
00119200
00024000
000010
000001
,
1901900000
240510000
002404900
00118100
000010
000001

G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,64,160,0,0,0,0,0,177,0,0,0,0,0,0,0,1,0,0,0,0,240,240],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,30,168,0,0,0,0,217,211,0,0,0,0,0,0,140,92,0,0,0,0,193,101],[190,51,0,0,0,0,190,240,0,0,0,0,0,0,1,0,0,0,0,0,192,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[190,240,0,0,0,0,190,51,0,0,0,0,0,0,240,118,0,0,0,0,49,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;

D12.24D10 in GAP, Magma, Sage, TeX

D_{12}._{24}D_{10}
% in TeX

G:=Group("D12.24D10");
// GroupNames label

G:=SmallGroup(480,566);
// by ID

G=gap.SmallGroup(480,566);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,422,135,346,185,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^12=b^2=c^10=1,d^2=a^6,b*a*b=a^-1,c*a*c^-1=d*a*d^-1=a^7,c*b*c^-1=a^3*b,d*b*d^-1=a^9*b,d*c*d^-1=a^6*c^-1>;
// generators/relations

׿
×
𝔽