Copied to
clipboard

G = C2×C5⋊D24order 480 = 25·3·5

Direct product of C2 and C5⋊D24

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×C5⋊D24, C303D8, C102D24, C60.61D4, D1218D10, C20.13D12, D6035C22, C60.126C23, C156(C2×D8), C53(C2×D24), C61(D4⋊D5), (C2×D12)⋊1D5, C52C825D6, (C10×D12)⋊4C2, (C2×D60)⋊25C2, C30.77(C2×D4), (C2×C20).88D6, (C2×C30).45D4, (C2×C10).38D12, C10.47(C2×D12), C4.5(C5⋊D12), (C2×C12).289D10, (C5×D12)⋊20C22, C12.55(C5⋊D4), C20.88(C22×S3), (C2×C60).133C22, C12.149(C22×D5), C22.19(C5⋊D12), C31(C2×D4⋊D5), C4.74(C2×S3×D5), (C6×C52C8)⋊6C2, (C2×C52C8)⋊5S3, C6.1(C2×C5⋊D4), C2.5(C2×C5⋊D12), (C2×C4).145(S3×D5), (C3×C52C8)⋊29C22, (C2×C6).30(C5⋊D4), SmallGroup(480,378)

Series: Derived Chief Lower central Upper central

C1C60 — C2×C5⋊D24
C1C5C15C30C60C3×C52C8C5⋊D24 — C2×C5⋊D24
C15C30C60 — C2×C5⋊D24
C1C22C2×C4

Generators and relations for C2×C5⋊D24
 G = < a,b,c,d | a2=b5=c24=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >

Subgroups: 1052 in 152 conjugacy classes, 52 normal (30 characteristic)
C1, C2, C2 [×2], C2 [×4], C3, C4 [×2], C22, C22 [×8], C5, S3 [×4], C6, C6 [×2], C8 [×2], C2×C4, D4 [×6], C23 [×2], D5 [×2], C10, C10 [×2], C10 [×2], C12 [×2], D6 [×8], C2×C6, C15, C2×C8, D8 [×4], C2×D4 [×2], C20 [×2], D10 [×4], C2×C10, C2×C10 [×4], C24 [×2], D12 [×2], D12 [×4], C2×C12, C22×S3 [×2], C5×S3 [×2], D15 [×2], C30, C30 [×2], C2×D8, C52C8 [×2], D20 [×3], C2×C20, C5×D4 [×3], C22×D5, C22×C10, D24 [×4], C2×C24, C2×D12, C2×D12, C60 [×2], S3×C10 [×4], D30 [×4], C2×C30, C2×C52C8, D4⋊D5 [×4], C2×D20, D4×C10, C2×D24, C3×C52C8 [×2], C5×D12 [×2], C5×D12, D60 [×2], D60, C2×C60, S3×C2×C10, C22×D15, C2×D4⋊D5, C5⋊D24 [×4], C6×C52C8, C10×D12, C2×D60, C2×C5⋊D24
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], D8 [×2], C2×D4, D10 [×3], D12 [×2], C22×S3, C2×D8, C5⋊D4 [×2], C22×D5, D24 [×2], C2×D12, S3×D5, D4⋊D5 [×2], C2×C5⋊D4, C2×D24, C5⋊D12 [×2], C2×S3×D5, C2×D4⋊D5, C5⋊D24 [×2], C2×C5⋊D12, C2×C5⋊D24

Smallest permutation representation of C2×C5⋊D24
On 240 points
Generators in S240
(1 205)(2 206)(3 207)(4 208)(5 209)(6 210)(7 211)(8 212)(9 213)(10 214)(11 215)(12 216)(13 193)(14 194)(15 195)(16 196)(17 197)(18 198)(19 199)(20 200)(21 201)(22 202)(23 203)(24 204)(25 158)(26 159)(27 160)(28 161)(29 162)(30 163)(31 164)(32 165)(33 166)(34 167)(35 168)(36 145)(37 146)(38 147)(39 148)(40 149)(41 150)(42 151)(43 152)(44 153)(45 154)(46 155)(47 156)(48 157)(49 182)(50 183)(51 184)(52 185)(53 186)(54 187)(55 188)(56 189)(57 190)(58 191)(59 192)(60 169)(61 170)(62 171)(63 172)(64 173)(65 174)(66 175)(67 176)(68 177)(69 178)(70 179)(71 180)(72 181)(73 135)(74 136)(75 137)(76 138)(77 139)(78 140)(79 141)(80 142)(81 143)(82 144)(83 121)(84 122)(85 123)(86 124)(87 125)(88 126)(89 127)(90 128)(91 129)(92 130)(93 131)(94 132)(95 133)(96 134)(97 240)(98 217)(99 218)(100 219)(101 220)(102 221)(103 222)(104 223)(105 224)(106 225)(107 226)(108 227)(109 228)(110 229)(111 230)(112 231)(113 232)(114 233)(115 234)(116 235)(117 236)(118 237)(119 238)(120 239)
(1 105 52 126 39)(2 40 127 53 106)(3 107 54 128 41)(4 42 129 55 108)(5 109 56 130 43)(6 44 131 57 110)(7 111 58 132 45)(8 46 133 59 112)(9 113 60 134 47)(10 48 135 61 114)(11 115 62 136 25)(12 26 137 63 116)(13 117 64 138 27)(14 28 139 65 118)(15 119 66 140 29)(16 30 141 67 120)(17 97 68 142 31)(18 32 143 69 98)(19 99 70 144 33)(20 34 121 71 100)(21 101 72 122 35)(22 36 123 49 102)(23 103 50 124 37)(24 38 125 51 104)(73 170 233 214 157)(74 158 215 234 171)(75 172 235 216 159)(76 160 193 236 173)(77 174 237 194 161)(78 162 195 238 175)(79 176 239 196 163)(80 164 197 240 177)(81 178 217 198 165)(82 166 199 218 179)(83 180 219 200 167)(84 168 201 220 181)(85 182 221 202 145)(86 146 203 222 183)(87 184 223 204 147)(88 148 205 224 185)(89 186 225 206 149)(90 150 207 226 187)(91 188 227 208 151)(92 152 209 228 189)(93 190 229 210 153)(94 154 211 230 191)(95 192 231 212 155)(96 156 213 232 169)
(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 9)(2 8)(3 7)(4 6)(10 24)(11 23)(12 22)(13 21)(14 20)(15 19)(16 18)(25 103)(26 102)(27 101)(28 100)(29 99)(30 98)(31 97)(32 120)(33 119)(34 118)(35 117)(36 116)(37 115)(38 114)(39 113)(40 112)(41 111)(42 110)(43 109)(44 108)(45 107)(46 106)(47 105)(48 104)(49 137)(50 136)(51 135)(52 134)(53 133)(54 132)(55 131)(56 130)(57 129)(58 128)(59 127)(60 126)(61 125)(62 124)(63 123)(64 122)(65 121)(66 144)(67 143)(68 142)(69 141)(70 140)(71 139)(72 138)(73 184)(74 183)(75 182)(76 181)(77 180)(78 179)(79 178)(80 177)(81 176)(82 175)(83 174)(84 173)(85 172)(86 171)(87 170)(88 169)(89 192)(90 191)(91 190)(92 189)(93 188)(94 187)(95 186)(96 185)(145 235)(146 234)(147 233)(148 232)(149 231)(150 230)(151 229)(152 228)(153 227)(154 226)(155 225)(156 224)(157 223)(158 222)(159 221)(160 220)(161 219)(162 218)(163 217)(164 240)(165 239)(166 238)(167 237)(168 236)(193 201)(194 200)(195 199)(196 198)(202 216)(203 215)(204 214)(205 213)(206 212)(207 211)(208 210)

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

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

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

66 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A4B5A5B6A6B6C8A8B8C8D10A···10F10G···10N12A12B12C12D15A15B20A20B20C20D24A···24H30A···30F60A···60H
order1222222234455666888810···1010···101212121215152020202024···2430···3060···60
size11111212606022222222101010102···212···12222244444410···104···44···4

66 irreducible representations

dim1111122222222222222444444
type+++++++++++++++++++++++
imageC1C2C2C2C2S3D4D4D5D6D6D8D10D10D12D12C5⋊D4C5⋊D4D24S3×D5D4⋊D5C5⋊D12C2×S3×D5C5⋊D12C5⋊D24
kernelC2×C5⋊D24C5⋊D24C6×C52C8C10×D12C2×D60C2×C52C8C60C2×C30C2×D12C52C8C2×C20C30D12C2×C12C20C2×C10C12C2×C6C10C2×C4C6C4C4C22C2
# reps1411111122144222448242228

Matrix representation of C2×C5⋊D24 in GL6(𝔽241)

100000
010000
00240000
00024000
000010
000001
,
100000
010000
0019024000
0019124000
000010
000001
,
110000
24000000
0017221400
002216900
0000219146
00001370
,
2402400000
010000
0051100
005119000
000010
0000119240

G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,190,191,0,0,0,0,240,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,240,0,0,0,0,1,0,0,0,0,0,0,0,172,221,0,0,0,0,214,69,0,0,0,0,0,0,219,137,0,0,0,0,146,0],[240,0,0,0,0,0,240,1,0,0,0,0,0,0,51,51,0,0,0,0,1,190,0,0,0,0,0,0,1,119,0,0,0,0,0,240] >;

C2×C5⋊D24 in GAP, Magma, Sage, TeX

C_2\times C_5\rtimes D_{24}
% in TeX

G:=Group("C2xC5:D24");
// GroupNames label

G:=SmallGroup(480,378);
// by ID

G=gap.SmallGroup(480,378);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,346,80,1356,18822]);
// Polycyclic

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

׿
×
𝔽