Copied to
clipboard

## G = C2×C24⋊D5order 480 = 25·3·5

### Direct product of C2 and C24⋊D5

Series: Derived Chief Lower central Upper central

 Derived series C1 — C60 — C2×C24⋊D5
 Chief series C1 — C5 — C15 — C30 — C60 — D60 — C2×D60 — C2×C24⋊D5
 Lower central C15 — C30 — C60 — C2×C24⋊D5
 Upper central C1 — C22 — C2×C4 — C2×C8

Generators and relations for C2×C24⋊D5
G = < a,b,c,d | a2=b8=c15=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b3, dcd=c-1 >

Subgroups: 1076 in 136 conjugacy classes, 55 normal (31 characteristic)
C1, C2, C2 [×2], C2 [×2], C3, C4 [×2], C4 [×2], C22, C22 [×4], C5, S3 [×2], C6, C6 [×2], C8 [×2], C2×C4, C2×C4, D4 [×3], Q8 [×3], C23, D5 [×2], C10, C10 [×2], Dic3 [×2], C12 [×2], D6 [×4], C2×C6, C15, C2×C8, SD16 [×4], C2×D4, C2×Q8, Dic5 [×2], C20 [×2], D10 [×4], C2×C10, C24 [×2], Dic6 [×3], D12 [×3], C2×Dic3, C2×C12, C22×S3, D15 [×2], C30, C30 [×2], C2×SD16, C40 [×2], Dic10 [×3], D20 [×3], C2×Dic5, C2×C20, C22×D5, C24⋊C2 [×4], C2×C24, C2×Dic6, C2×D12, Dic15 [×2], C60 [×2], D30 [×4], C2×C30, C40⋊C2 [×4], C2×C40, C2×Dic10, C2×D20, C2×C24⋊C2, C120 [×2], Dic30 [×2], Dic30, D60 [×2], D60, C2×Dic15, C2×C60, C22×D15, C2×C40⋊C2, C24⋊D5 [×4], C2×C120, C2×Dic30, C2×D60, C2×C24⋊D5
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], SD16 [×2], C2×D4, D10 [×3], D12 [×2], C22×S3, D15, C2×SD16, D20 [×2], C22×D5, C24⋊C2 [×2], C2×D12, D30 [×3], C40⋊C2 [×2], C2×D20, C2×C24⋊C2, D60 [×2], C22×D15, C2×C40⋊C2, C24⋊D5 [×2], C2×D60, C2×C24⋊D5

Smallest permutation representation of C2×C24⋊D5
On 240 points
Generators in S240
(1 130)(2 131)(3 132)(4 133)(5 134)(6 135)(7 121)(8 122)(9 123)(10 124)(11 125)(12 126)(13 127)(14 128)(15 129)(16 144)(17 145)(18 146)(19 147)(20 148)(21 149)(22 150)(23 136)(24 137)(25 138)(26 139)(27 140)(28 141)(29 142)(30 143)(31 157)(32 158)(33 159)(34 160)(35 161)(36 162)(37 163)(38 164)(39 165)(40 151)(41 152)(42 153)(43 154)(44 155)(45 156)(46 169)(47 170)(48 171)(49 172)(50 173)(51 174)(52 175)(53 176)(54 177)(55 178)(56 179)(57 180)(58 166)(59 167)(60 168)(61 184)(62 185)(63 186)(64 187)(65 188)(66 189)(67 190)(68 191)(69 192)(70 193)(71 194)(72 195)(73 181)(74 182)(75 183)(76 198)(77 199)(78 200)(79 201)(80 202)(81 203)(82 204)(83 205)(84 206)(85 207)(86 208)(87 209)(88 210)(89 196)(90 197)(91 215)(92 216)(93 217)(94 218)(95 219)(96 220)(97 221)(98 222)(99 223)(100 224)(101 225)(102 211)(103 212)(104 213)(105 214)(106 230)(107 231)(108 232)(109 233)(110 234)(111 235)(112 236)(113 237)(114 238)(115 239)(116 240)(117 226)(118 227)(119 228)(120 229)
(1 233 53 200 16 218 42 190)(2 234 54 201 17 219 43 191)(3 235 55 202 18 220 44 192)(4 236 56 203 19 221 45 193)(5 237 57 204 20 222 31 194)(6 238 58 205 21 223 32 195)(7 239 59 206 22 224 33 181)(8 240 60 207 23 225 34 182)(9 226 46 208 24 211 35 183)(10 227 47 209 25 212 36 184)(11 228 48 210 26 213 37 185)(12 229 49 196 27 214 38 186)(13 230 50 197 28 215 39 187)(14 231 51 198 29 216 40 188)(15 232 52 199 30 217 41 189)(61 124 118 170 87 138 103 162)(62 125 119 171 88 139 104 163)(63 126 120 172 89 140 105 164)(64 127 106 173 90 141 91 165)(65 128 107 174 76 142 92 151)(66 129 108 175 77 143 93 152)(67 130 109 176 78 144 94 153)(68 131 110 177 79 145 95 154)(69 132 111 178 80 146 96 155)(70 133 112 179 81 147 97 156)(71 134 113 180 82 148 98 157)(72 135 114 166 83 149 99 158)(73 121 115 167 84 150 100 159)(74 122 116 168 85 136 101 160)(75 123 117 169 86 137 102 161)
(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 15)(2 14)(3 13)(4 12)(5 11)(6 10)(7 9)(16 30)(17 29)(18 28)(19 27)(20 26)(21 25)(22 24)(31 48)(32 47)(33 46)(34 60)(35 59)(36 58)(37 57)(38 56)(39 55)(40 54)(41 53)(42 52)(43 51)(44 50)(45 49)(61 99)(62 98)(63 97)(64 96)(65 95)(66 94)(67 93)(68 92)(69 91)(70 105)(71 104)(72 103)(73 102)(74 101)(75 100)(76 110)(77 109)(78 108)(79 107)(80 106)(81 120)(82 119)(83 118)(84 117)(85 116)(86 115)(87 114)(88 113)(89 112)(90 111)(121 123)(124 135)(125 134)(126 133)(127 132)(128 131)(129 130)(137 150)(138 149)(139 148)(140 147)(141 146)(142 145)(143 144)(151 177)(152 176)(153 175)(154 174)(155 173)(156 172)(157 171)(158 170)(159 169)(160 168)(161 167)(162 166)(163 180)(164 179)(165 178)(181 211)(182 225)(183 224)(184 223)(185 222)(186 221)(187 220)(188 219)(189 218)(190 217)(191 216)(192 215)(193 214)(194 213)(195 212)(196 236)(197 235)(198 234)(199 233)(200 232)(201 231)(202 230)(203 229)(204 228)(205 227)(206 226)(207 240)(208 239)(209 238)(210 237)

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

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

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

126 conjugacy classes

 class 1 2A 2B 2C 2D 2E 3 4A 4B 4C 4D 5A 5B 6A 6B 6C 8A 8B 8C 8D 10A ··· 10F 12A 12B 12C 12D 15A 15B 15C 15D 20A ··· 20H 24A ··· 24H 30A ··· 30L 40A ··· 40P 60A ··· 60P 120A ··· 120AF order 1 2 2 2 2 2 3 4 4 4 4 5 5 6 6 6 8 8 8 8 10 ··· 10 12 12 12 12 15 15 15 15 20 ··· 20 24 ··· 24 30 ··· 30 40 ··· 40 60 ··· 60 120 ··· 120 size 1 1 1 1 60 60 2 2 2 60 60 2 2 2 2 2 2 2 2 2 2 ··· 2 2 2 2 2 2 2 2 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2

126 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 type + + + + + + + + + + + + + + + + + + + + + + image C1 C2 C2 C2 C2 S3 D4 D4 D5 D6 D6 SD16 D10 D10 D12 D12 D15 D20 D20 C24⋊C2 D30 D30 C40⋊C2 D60 D60 C24⋊D5 kernel C2×C24⋊D5 C24⋊D5 C2×C120 C2×Dic30 C2×D60 C2×C40 C60 C2×C30 C2×C24 C40 C2×C20 C30 C24 C2×C12 C20 C2×C10 C2×C8 C12 C2×C6 C10 C8 C2×C4 C6 C4 C22 C2 # reps 1 4 1 1 1 1 1 1 2 2 1 4 4 2 2 2 4 4 4 8 8 4 16 8 8 32

Matrix representation of C2×C24⋊D5 in GL5(𝔽241)

 240 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 240 0 0 0 0 0 240
,
 240 0 0 0 0 0 240 0 0 0 0 0 240 0 0 0 0 0 94 169 0 0 0 15 109
,
 1 0 0 0 0 0 131 161 0 0 0 80 148 0 0 0 0 0 51 52 0 0 0 190 0
,
 240 0 0 0 0 0 131 161 0 0 0 94 110 0 0 0 0 0 190 1 0 0 0 51 51

G:=sub<GL(5,GF(241))| [240,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,240,0,0,0,0,0,240],[240,0,0,0,0,0,240,0,0,0,0,0,240,0,0,0,0,0,94,15,0,0,0,169,109],[1,0,0,0,0,0,131,80,0,0,0,161,148,0,0,0,0,0,51,190,0,0,0,52,0],[240,0,0,0,0,0,131,94,0,0,0,161,110,0,0,0,0,0,190,51,0,0,0,1,51] >;

C2×C24⋊D5 in GAP, Magma, Sage, TeX

C_2\times C_{24}\rtimes D_5
% in TeX

G:=Group("C2xC24:D5");
// GroupNames label

G:=SmallGroup(480,867);
// by ID

G=gap.SmallGroup(480,867);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,254,58,675,80,2693,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^8=c^15=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b^3,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽