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G = C2×C5⋊D24order 480 = 25·3·5

Direct product of C2 and C5⋊D24

Series: Derived Chief Lower central Upper central

 Derived series C1 — C60 — C2×C5⋊D24
 Chief series C1 — C5 — C15 — C30 — C60 — C3×C5⋊2C8 — C5⋊D24 — C2×C5⋊D24
 Lower central C15 — C30 — C60 — C2×C5⋊D24
 Upper central C1 — C22 — C2×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 2A 2B 2C 2D 2E 2F 2G 3 4A 4B 5A 5B 6A 6B 6C 8A 8B 8C 8D 10A ··· 10F 10G ··· 10N 12A 12B 12C 12D 15A 15B 20A 20B 20C 20D 24A ··· 24H 30A ··· 30F 60A ··· 60H order 1 2 2 2 2 2 2 2 3 4 4 5 5 6 6 6 8 8 8 8 10 ··· 10 10 ··· 10 12 12 12 12 15 15 20 20 20 20 24 ··· 24 30 ··· 30 60 ··· 60 size 1 1 1 1 12 12 60 60 2 2 2 2 2 2 2 2 10 10 10 10 2 ··· 2 12 ··· 12 2 2 2 2 4 4 4 4 4 4 10 ··· 10 4 ··· 4 4 ··· 4

66 irreducible representations

 dim 1 1 1 1 1 2 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 S3 D4 D4 D5 D6 D6 D8 D10 D10 D12 D12 C5⋊D4 C5⋊D4 D24 S3×D5 D4⋊D5 C5⋊D12 C2×S3×D5 C5⋊D12 C5⋊D24 kernel C2×C5⋊D24 C5⋊D24 C6×C5⋊2C8 C10×D12 C2×D60 C2×C5⋊2C8 C60 C2×C30 C2×D12 C5⋊2C8 C2×C20 C30 D12 C2×C12 C20 C2×C10 C12 C2×C6 C10 C2×C4 C6 C4 C4 C22 C2 # reps 1 4 1 1 1 1 1 1 2 2 1 4 4 2 2 2 4 4 8 2 4 2 2 2 8

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

 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 0 190 240 0 0 0 0 191 240 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 1 1 0 0 0 0 240 0 0 0 0 0 0 0 172 214 0 0 0 0 221 69 0 0 0 0 0 0 219 146 0 0 0 0 137 0
,
 240 240 0 0 0 0 0 1 0 0 0 0 0 0 51 1 0 0 0 0 51 190 0 0 0 0 0 0 1 0 0 0 0 0 119 240

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

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