metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C40.8D6, C30.8D8, C15⋊5SD32, D24.1D5, C60.50D4, C20.2D12, C10.7D24, C24.41D10, Dic60⋊10C2, C120.18C22, C5⋊2C16⋊2S3, C3⋊1(D8.D5), C8.17(S3×D5), C5⋊2(C48⋊C2), C6.2(D4⋊D5), (C5×D24).1C2, C2.5(C5⋊D24), C4.2(C5⋊D12), C12.52(C5⋊D4), (C3×C5⋊2C16)⋊2C2, SmallGroup(480,20)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D24.D5
G = < a,b,c,d | a24=b2=c5=1, d2=a9, bab=a-1, ac=ca, ad=da, bc=cb, dbd-1=a21b, dcd-1=c-1 >
24C2
12C22
60C4
8S3
24C10
6D4
30Q8
4D6
20Dic3
12Dic5
12C2×C10
3D8
5C16
15Q16
2D12
10Dic6
15SD32
5C48
Smallest permutation representation of D24.D5
►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 24)(2 23)(3 22)(4 21)(5 20)(6 19)(7 18)(8 17)(9 16)(10 15)(11 14)(12 13)(25 27)(28 48)(29 47)(30 46)(31 45)(32 44)(33 43)(34 42)(35 41)(36 40)(37 39)(49 61)(50 60)(51 59)(52 58)(53 57)(54 56)(62 72)(63 71)(64 70)(65 69)(66 68)(73 74)(75 96)(76 95)(77 94)(78 93)(79 92)(80 91)(81 90)(82 89)(83 88)(84 87)(85 86)(97 111)(98 110)(99 109)(100 108)(101 107)(102 106)(103 105)(112 120)(113 119)(114 118)(115 117)(121 138)(122 137)(123 136)(124 135)(125 134)(126 133)(127 132)(128 131)(129 130)(139 144)(140 143)(141 142)(146 168)(147 167)(148 166)(149 165)(150 164)(151 163)(152 162)(153 161)(154 160)(155 159)(156 158)(169 192)(170 191)(171 190)(172 189)(173 188)(174 187)(175 186)(176 185)(177 184)(178 183)(179 182)(180 181)(193 213)(194 212)(195 211)(196 210)(197 209)(198 208)(199 207)(200 206)(201 205)(202 204)(214 216)(217 222)(218 221)(219 220)(223 240)(224 239)(225 238)(226 237)(227 236)(228 235)(229 234)(230 233)(231 232)
(1 74 232 130 169)(2 75 233 131 170)(3 76 234 132 171)(4 77 235 133 172)(5 78 236 134 173)(6 79 237 135 174)(7 80 238 136 175)(8 81 239 137 176)(9 82 240 138 177)(10 83 217 139 178)(11 84 218 140 179)(12 85 219 141 180)(13 86 220 142 181)(14 87 221 143 182)(15 88 222 144 183)(16 89 223 121 184)(17 90 224 122 185)(18 91 225 123 186)(19 92 226 124 187)(20 93 227 125 188)(21 94 228 126 189)(22 95 229 127 190)(23 96 230 128 191)(24 73 231 129 192)(25 115 202 168 66)(26 116 203 145 67)(27 117 204 146 68)(28 118 205 147 69)(29 119 206 148 70)(30 120 207 149 71)(31 97 208 150 72)(32 98 209 151 49)(33 99 210 152 50)(34 100 211 153 51)(35 101 212 154 52)(36 102 213 155 53)(37 103 214 156 54)(38 104 215 157 55)(39 105 216 158 56)(40 106 193 159 57)(41 107 194 160 58)(42 108 195 161 59)(43 109 196 162 60)(44 110 197 163 61)(45 111 198 164 62)(46 112 199 165 63)(47 113 200 166 64)(48 114 201 167 65)
(1 156 10 165 19 150 4 159 13 168 22 153 7 162 16 147)(2 157 11 166 20 151 5 160 14 145 23 154 8 163 17 148)(3 158 12 167 21 152 6 161 15 146 24 155 9 164 18 149)(25 127 34 136 43 121 28 130 37 139 46 124 31 133 40 142)(26 128 35 137 44 122 29 131 38 140 47 125 32 134 41 143)(27 129 36 138 45 123 30 132 39 141 48 126 33 135 42 144)(49 173 58 182 67 191 52 176 61 185 70 170 55 179 64 188)(50 174 59 183 68 192 53 177 62 186 71 171 56 180 65 189)(51 175 60 184 69 169 54 178 63 187 72 172 57 181 66 190)(73 213 82 198 91 207 76 216 85 201 94 210 79 195 88 204)(74 214 83 199 92 208 77 193 86 202 95 211 80 196 89 205)(75 215 84 200 93 209 78 194 87 203 96 212 81 197 90 206)(97 235 106 220 115 229 100 238 109 223 118 232 103 217 112 226)(98 236 107 221 116 230 101 239 110 224 119 233 104 218 113 227)(99 237 108 222 117 231 102 240 111 225 120 234 105 219 114 228)
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), (1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(25,27)(28,48)(29,47)(30,46)(31,45)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(49,61)(50,60)(51,59)(52,58)(53,57)(54,56)(62,72)(63,71)(64,70)(65,69)(66,68)(73,74)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(85,86)(97,111)(98,110)(99,109)(100,108)(101,107)(102,106)(103,105)(112,120)(113,119)(114,118)(115,117)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)(128,131)(129,130)(139,144)(140,143)(141,142)(146,168)(147,167)(148,166)(149,165)(150,164)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(169,192)(170,191)(171,190)(172,189)(173,188)(174,187)(175,186)(176,185)(177,184)(178,183)(179,182)(180,181)(193,213)(194,212)(195,211)(196,210)(197,209)(198,208)(199,207)(200,206)(201,205)(202,204)(214,216)(217,222)(218,221)(219,220)(223,240)(224,239)(225,238)(226,237)(227,236)(228,235)(229,234)(230,233)(231,232), (1,74,232,130,169)(2,75,233,131,170)(3,76,234,132,171)(4,77,235,133,172)(5,78,236,134,173)(6,79,237,135,174)(7,80,238,136,175)(8,81,239,137,176)(9,82,240,138,177)(10,83,217,139,178)(11,84,218,140,179)(12,85,219,141,180)(13,86,220,142,181)(14,87,221,143,182)(15,88,222,144,183)(16,89,223,121,184)(17,90,224,122,185)(18,91,225,123,186)(19,92,226,124,187)(20,93,227,125,188)(21,94,228,126,189)(22,95,229,127,190)(23,96,230,128,191)(24,73,231,129,192)(25,115,202,168,66)(26,116,203,145,67)(27,117,204,146,68)(28,118,205,147,69)(29,119,206,148,70)(30,120,207,149,71)(31,97,208,150,72)(32,98,209,151,49)(33,99,210,152,50)(34,100,211,153,51)(35,101,212,154,52)(36,102,213,155,53)(37,103,214,156,54)(38,104,215,157,55)(39,105,216,158,56)(40,106,193,159,57)(41,107,194,160,58)(42,108,195,161,59)(43,109,196,162,60)(44,110,197,163,61)(45,111,198,164,62)(46,112,199,165,63)(47,113,200,166,64)(48,114,201,167,65), (1,156,10,165,19,150,4,159,13,168,22,153,7,162,16,147)(2,157,11,166,20,151,5,160,14,145,23,154,8,163,17,148)(3,158,12,167,21,152,6,161,15,146,24,155,9,164,18,149)(25,127,34,136,43,121,28,130,37,139,46,124,31,133,40,142)(26,128,35,137,44,122,29,131,38,140,47,125,32,134,41,143)(27,129,36,138,45,123,30,132,39,141,48,126,33,135,42,144)(49,173,58,182,67,191,52,176,61,185,70,170,55,179,64,188)(50,174,59,183,68,192,53,177,62,186,71,171,56,180,65,189)(51,175,60,184,69,169,54,178,63,187,72,172,57,181,66,190)(73,213,82,198,91,207,76,216,85,201,94,210,79,195,88,204)(74,214,83,199,92,208,77,193,86,202,95,211,80,196,89,205)(75,215,84,200,93,209,78,194,87,203,96,212,81,197,90,206)(97,235,106,220,115,229,100,238,109,223,118,232,103,217,112,226)(98,236,107,221,116,230,101,239,110,224,119,233,104,218,113,227)(99,237,108,222,117,231,102,240,111,225,120,234,105,219,114,228)>;
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), (1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(25,27)(28,48)(29,47)(30,46)(31,45)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(49,61)(50,60)(51,59)(52,58)(53,57)(54,56)(62,72)(63,71)(64,70)(65,69)(66,68)(73,74)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(85,86)(97,111)(98,110)(99,109)(100,108)(101,107)(102,106)(103,105)(112,120)(113,119)(114,118)(115,117)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)(128,131)(129,130)(139,144)(140,143)(141,142)(146,168)(147,167)(148,166)(149,165)(150,164)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(169,192)(170,191)(171,190)(172,189)(173,188)(174,187)(175,186)(176,185)(177,184)(178,183)(179,182)(180,181)(193,213)(194,212)(195,211)(196,210)(197,209)(198,208)(199,207)(200,206)(201,205)(202,204)(214,216)(217,222)(218,221)(219,220)(223,240)(224,239)(225,238)(226,237)(227,236)(228,235)(229,234)(230,233)(231,232), (1,74,232,130,169)(2,75,233,131,170)(3,76,234,132,171)(4,77,235,133,172)(5,78,236,134,173)(6,79,237,135,174)(7,80,238,136,175)(8,81,239,137,176)(9,82,240,138,177)(10,83,217,139,178)(11,84,218,140,179)(12,85,219,141,180)(13,86,220,142,181)(14,87,221,143,182)(15,88,222,144,183)(16,89,223,121,184)(17,90,224,122,185)(18,91,225,123,186)(19,92,226,124,187)(20,93,227,125,188)(21,94,228,126,189)(22,95,229,127,190)(23,96,230,128,191)(24,73,231,129,192)(25,115,202,168,66)(26,116,203,145,67)(27,117,204,146,68)(28,118,205,147,69)(29,119,206,148,70)(30,120,207,149,71)(31,97,208,150,72)(32,98,209,151,49)(33,99,210,152,50)(34,100,211,153,51)(35,101,212,154,52)(36,102,213,155,53)(37,103,214,156,54)(38,104,215,157,55)(39,105,216,158,56)(40,106,193,159,57)(41,107,194,160,58)(42,108,195,161,59)(43,109,196,162,60)(44,110,197,163,61)(45,111,198,164,62)(46,112,199,165,63)(47,113,200,166,64)(48,114,201,167,65), (1,156,10,165,19,150,4,159,13,168,22,153,7,162,16,147)(2,157,11,166,20,151,5,160,14,145,23,154,8,163,17,148)(3,158,12,167,21,152,6,161,15,146,24,155,9,164,18,149)(25,127,34,136,43,121,28,130,37,139,46,124,31,133,40,142)(26,128,35,137,44,122,29,131,38,140,47,125,32,134,41,143)(27,129,36,138,45,123,30,132,39,141,48,126,33,135,42,144)(49,173,58,182,67,191,52,176,61,185,70,170,55,179,64,188)(50,174,59,183,68,192,53,177,62,186,71,171,56,180,65,189)(51,175,60,184,69,169,54,178,63,187,72,172,57,181,66,190)(73,213,82,198,91,207,76,216,85,201,94,210,79,195,88,204)(74,214,83,199,92,208,77,193,86,202,95,211,80,196,89,205)(75,215,84,200,93,209,78,194,87,203,96,212,81,197,90,206)(97,235,106,220,115,229,100,238,109,223,118,232,103,217,112,226)(98,236,107,221,116,230,101,239,110,224,119,233,104,218,113,227)(99,237,108,222,117,231,102,240,111,225,120,234,105,219,114,228) );
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)], [(1,24),(2,23),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13),(25,27),(28,48),(29,47),(30,46),(31,45),(32,44),(33,43),(34,42),(35,41),(36,40),(37,39),(49,61),(50,60),(51,59),(52,58),(53,57),(54,56),(62,72),(63,71),(64,70),(65,69),(66,68),(73,74),(75,96),(76,95),(77,94),(78,93),(79,92),(80,91),(81,90),(82,89),(83,88),(84,87),(85,86),(97,111),(98,110),(99,109),(100,108),(101,107),(102,106),(103,105),(112,120),(113,119),(114,118),(115,117),(121,138),(122,137),(123,136),(124,135),(125,134),(126,133),(127,132),(128,131),(129,130),(139,144),(140,143),(141,142),(146,168),(147,167),(148,166),(149,165),(150,164),(151,163),(152,162),(153,161),(154,160),(155,159),(156,158),(169,192),(170,191),(171,190),(172,189),(173,188),(174,187),(175,186),(176,185),(177,184),(178,183),(179,182),(180,181),(193,213),(194,212),(195,211),(196,210),(197,209),(198,208),(199,207),(200,206),(201,205),(202,204),(214,216),(217,222),(218,221),(219,220),(223,240),(224,239),(225,238),(226,237),(227,236),(228,235),(229,234),(230,233),(231,232)], [(1,74,232,130,169),(2,75,233,131,170),(3,76,234,132,171),(4,77,235,133,172),(5,78,236,134,173),(6,79,237,135,174),(7,80,238,136,175),(8,81,239,137,176),(9,82,240,138,177),(10,83,217,139,178),(11,84,218,140,179),(12,85,219,141,180),(13,86,220,142,181),(14,87,221,143,182),(15,88,222,144,183),(16,89,223,121,184),(17,90,224,122,185),(18,91,225,123,186),(19,92,226,124,187),(20,93,227,125,188),(21,94,228,126,189),(22,95,229,127,190),(23,96,230,128,191),(24,73,231,129,192),(25,115,202,168,66),(26,116,203,145,67),(27,117,204,146,68),(28,118,205,147,69),(29,119,206,148,70),(30,120,207,149,71),(31,97,208,150,72),(32,98,209,151,49),(33,99,210,152,50),(34,100,211,153,51),(35,101,212,154,52),(36,102,213,155,53),(37,103,214,156,54),(38,104,215,157,55),(39,105,216,158,56),(40,106,193,159,57),(41,107,194,160,58),(42,108,195,161,59),(43,109,196,162,60),(44,110,197,163,61),(45,111,198,164,62),(46,112,199,165,63),(47,113,200,166,64),(48,114,201,167,65)], [(1,156,10,165,19,150,4,159,13,168,22,153,7,162,16,147),(2,157,11,166,20,151,5,160,14,145,23,154,8,163,17,148),(3,158,12,167,21,152,6,161,15,146,24,155,9,164,18,149),(25,127,34,136,43,121,28,130,37,139,46,124,31,133,40,142),(26,128,35,137,44,122,29,131,38,140,47,125,32,134,41,143),(27,129,36,138,45,123,30,132,39,141,48,126,33,135,42,144),(49,173,58,182,67,191,52,176,61,185,70,170,55,179,64,188),(50,174,59,183,68,192,53,177,62,186,71,171,56,180,65,189),(51,175,60,184,69,169,54,178,63,187,72,172,57,181,66,190),(73,213,82,198,91,207,76,216,85,201,94,210,79,195,88,204),(74,214,83,199,92,208,77,193,86,202,95,211,80,196,89,205),(75,215,84,200,93,209,78,194,87,203,96,212,81,197,90,206),(97,235,106,220,115,229,100,238,109,223,118,232,103,217,112,226),(98,236,107,221,116,230,101,239,110,224,119,233,104,218,113,227),(99,237,108,222,117,231,102,240,111,225,120,234,105,219,114,228)]])
57 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 5A | 5B | 6 | 8A | 8B | 10A | 10B | 10C | 10D | 10E | 10F | 12A | 12B | 15A | 15B | 16A | 16B | 16C | 16D | 20A | 20B | 24A | 24B | 24C | 24D | 30A | 30B | 40A | 40B | 40C | 40D | 48A | ··· | 48H | 60A | 60B | 60C | 60D | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 5 | 5 | 6 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 24 | 24 | 24 | 24 | 30 | 30 | 40 | 40 | 40 | 40 | 48 | ··· | 48 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 24 | 2 | 2 | 120 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 24 | 24 | 24 | 24 | 2 | 2 | 4 | 4 | 10 | 10 | 10 | 10 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
57 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | S3 | D4 | D5 | D6 | D8 | D10 | D12 | SD32 | C5⋊D4 | D24 | C48⋊C2 | S3×D5 | D4⋊D5 | C5⋊D12 | D8.D5 | C5⋊D24 | D24.D5 |
| kernel | D24.D5 | C3×C5⋊2C16 | C5×D24 | Dic60 | C5⋊2C16 | C60 | D24 | C40 | C30 | C24 | C20 | C15 | C12 | C10 | C5 | C8 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 8 | 2 | 2 | 2 | 4 | 4 | 8 |
Matrix representation of D24.D5 ►in GL6(𝔽241)
| 69 | 186 | 0 | 0 | 0 | 0 |
| 151 | 194 | 0 | 0 | 0 | 0 |
| 0 | 0 | 239 | 54 | 0 | 0 |
| 0 | 0 | 174 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 69 | 186 | 0 | 0 | 0 | 0 |
| 218 | 172 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 174 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 240 | 51 |
| 122 | 36 | 0 | 0 | 0 | 0 |
| 37 | 84 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 0 | 227 | 89 |
| 0 | 0 | 0 | 0 | 98 | 14 |
G:=sub<GL(6,GF(241))| [69,151,0,0,0,0,186,194,0,0,0,0,0,0,239,174,0,0,0,0,54,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[69,218,0,0,0,0,186,172,0,0,0,0,0,0,240,174,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,240,0,0,0,0,1,51],[122,37,0,0,0,0,36,84,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,227,98,0,0,0,0,89,14] >;
D24.D5 in GAP, Magma, Sage, TeX
D_{24}.D_5 % in TeX
G:=Group("D24.D5"); // GroupNames label
G:=SmallGroup(480,20);
// by ID
G=gap.SmallGroup(480,20);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,309,135,142,346,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^24=b^2=c^5=1,d^2=a^9,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=a^21*b,d*c*d^-1=c^-1>;
// generators/relations
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