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G = D245D5order 480 = 25·3·5

5th semidirect product of D24 and D5 acting via D5/C5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D245D5, C40.21D6, Dic205S3, D30.25D4, D12.4D10, C24.21D10, Dic10.4D6, C60.147C23, C120.38C22, Dic15.30D4, (C5×D24)⋊7C2, (C8×D15)⋊8C2, C159(C4○D8), C8.31(S3×D5), C6.36(D4×D5), C32(D83D5), C10.36(S3×D4), C30.29(C2×D4), C52(D24⋊C2), (C3×Dic20)⋊8C2, D12⋊D510C2, C20.D611C2, C20.82(C22×S3), C12.82(C22×D5), C2.14(C20⋊D6), C153C8.43C22, (C5×D12).28C22, (C4×D15).58C22, (C3×Dic10).30C22, C4.120(C2×S3×D5), SmallGroup(480,355)

Series: Derived Chief Lower central Upper central

C1C60 — D245D5
C1C5C15C30C60C3×Dic10D12⋊D5 — D245D5
C15C30C60 — D245D5
C1C2C4C8

Generators and relations for D245D5
 G = < a,b,c,d | a24=b2=c5=d2=1, bab=a-1, ac=ca, dad=a17, bc=cb, dbd=a4b, dcd=c-1 >

Subgroups: 700 in 124 conjugacy classes, 38 normal (26 characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3 [×3], C6, C8, C8, C2×C4 [×3], D4 [×4], Q8 [×2], D5, C10, C10 [×2], Dic3, C12, C12 [×2], D6 [×3], C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5 [×3], C20, D10, C2×C10 [×2], C3⋊C8, C24, C4×S3 [×3], D12 [×2], D12 [×2], C3×Q8 [×2], C5×S3 [×2], D15, C30, C4○D8, C52C8, C40, Dic10 [×2], C4×D5, C2×Dic5 [×2], C5⋊D4 [×2], C5×D4 [×2], S3×C8, D24, Q82S3 [×2], C3×Q16, Q83S3 [×2], C3×Dic5 [×2], Dic15, C60, S3×C10 [×2], D30, C8×D5, Dic20, D4.D5 [×2], C5×D8, D42D5 [×2], D24⋊C2, C153C8, C120, S3×Dic5 [×2], C5⋊D12 [×2], C3×Dic10 [×2], C5×D12 [×2], C4×D15, D83D5, C20.D6 [×2], C3×Dic20, C5×D24, C8×D15, D12⋊D5 [×2], D245D5
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C4○D8, C22×D5, S3×D4, S3×D5, D4×D5, D24⋊C2, C2×S3×D5, D83D5, C20⋊D6, D245D5

Smallest permutation representation of D245D5
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)
(1 106)(2 105)(3 104)(4 103)(5 102)(6 101)(7 100)(8 99)(9 98)(10 97)(11 120)(12 119)(13 118)(14 117)(15 116)(16 115)(17 114)(18 113)(19 112)(20 111)(21 110)(22 109)(23 108)(24 107)(25 82)(26 81)(27 80)(28 79)(29 78)(30 77)(31 76)(32 75)(33 74)(34 73)(35 96)(36 95)(37 94)(38 93)(39 92)(40 91)(41 90)(42 89)(43 88)(44 87)(45 86)(46 85)(47 84)(48 83)(49 220)(50 219)(51 218)(52 217)(53 240)(54 239)(55 238)(56 237)(57 236)(58 235)(59 234)(60 233)(61 232)(62 231)(63 230)(64 229)(65 228)(66 227)(67 226)(68 225)(69 224)(70 223)(71 222)(72 221)(121 179)(122 178)(123 177)(124 176)(125 175)(126 174)(127 173)(128 172)(129 171)(130 170)(131 169)(132 192)(133 191)(134 190)(135 189)(136 188)(137 187)(138 186)(139 185)(140 184)(141 183)(142 182)(143 181)(144 180)(145 194)(146 193)(147 216)(148 215)(149 214)(150 213)(151 212)(152 211)(153 210)(154 209)(155 208)(156 207)(157 206)(158 205)(159 204)(160 203)(161 202)(162 201)(163 200)(164 199)(165 198)(166 197)(167 196)(168 195)
(1 80 141 160 223)(2 81 142 161 224)(3 82 143 162 225)(4 83 144 163 226)(5 84 121 164 227)(6 85 122 165 228)(7 86 123 166 229)(8 87 124 167 230)(9 88 125 168 231)(10 89 126 145 232)(11 90 127 146 233)(12 91 128 147 234)(13 92 129 148 235)(14 93 130 149 236)(15 94 131 150 237)(16 95 132 151 238)(17 96 133 152 239)(18 73 134 153 240)(19 74 135 154 217)(20 75 136 155 218)(21 76 137 156 219)(22 77 138 157 220)(23 78 139 158 221)(24 79 140 159 222)(25 181 201 68 104)(26 182 202 69 105)(27 183 203 70 106)(28 184 204 71 107)(29 185 205 72 108)(30 186 206 49 109)(31 187 207 50 110)(32 188 208 51 111)(33 189 209 52 112)(34 190 210 53 113)(35 191 211 54 114)(36 192 212 55 115)(37 169 213 56 116)(38 170 214 57 117)(39 171 215 58 118)(40 172 216 59 119)(41 173 193 60 120)(42 174 194 61 97)(43 175 195 62 98)(44 176 196 63 99)(45 177 197 64 100)(46 178 198 65 101)(47 179 199 66 102)(48 180 200 67 103)
(1 223)(2 240)(3 233)(4 226)(5 219)(6 236)(7 229)(8 222)(9 239)(10 232)(11 225)(12 218)(13 235)(14 228)(15 221)(16 238)(17 231)(18 224)(19 217)(20 234)(21 227)(22 220)(23 237)(24 230)(25 213)(26 206)(27 199)(28 216)(29 209)(30 202)(31 195)(32 212)(33 205)(34 198)(35 215)(36 208)(37 201)(38 194)(39 211)(40 204)(41 197)(42 214)(43 207)(44 200)(45 193)(46 210)(47 203)(48 196)(49 105)(50 98)(51 115)(52 108)(53 101)(54 118)(55 111)(56 104)(57 97)(58 114)(59 107)(60 100)(61 117)(62 110)(63 103)(64 120)(65 113)(66 106)(67 99)(68 116)(69 109)(70 102)(71 119)(72 112)(73 161)(74 154)(75 147)(76 164)(77 157)(78 150)(79 167)(80 160)(81 153)(82 146)(83 163)(84 156)(85 149)(86 166)(87 159)(88 152)(89 145)(90 162)(91 155)(92 148)(93 165)(94 158)(95 151)(96 168)(121 137)(122 130)(124 140)(125 133)(127 143)(128 136)(131 139)(134 142)(169 181)(170 174)(171 191)(172 184)(173 177)(175 187)(176 180)(178 190)(179 183)(182 186)(185 189)(188 192)

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

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

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

51 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B 6 8A8B8C8D10A10B10C10D10E10F12A12B12C15A15B20A20B24A24B30A30B40A40B40C40D60A60B60C60D120A···120H
order12222344444556888810101010101012121215152020242430304040404060606060120···120
size11121230221515202022222303022242424244404044444444444444444···4

51 irreducible representations

dim11111122222222244444444
type+++++++++++++++++++-
imageC1C2C2C2C2C2S3D4D4D5D6D6D10D10C4○D8S3×D4S3×D5D4×D5D24⋊C2C2×S3×D5D83D5C20⋊D6D245D5
kernelD245D5C20.D6C3×Dic20C5×D24C8×D15D12⋊D5Dic20Dic15D30D24C40Dic10C24D12C15C10C8C6C5C4C3C2C1
# reps12111211121224412222448

Matrix representation of D245D5 in GL6(𝔽241)

02400000
110000
00240000
00024000
000080
0000105211
,
02400000
24000000
001000
000100
00009759
0000200144
,
100000
010000
00240100
005019000
000010
000001
,
100000
2402400000
00240000
0050100
000010
0000107240

G:=sub<GL(6,GF(241))| [0,1,0,0,0,0,240,1,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,8,105,0,0,0,0,0,211],[0,240,0,0,0,0,240,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,97,200,0,0,0,0,59,144],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,240,50,0,0,0,0,1,190,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,240,0,0,0,0,0,240,0,0,0,0,0,0,240,50,0,0,0,0,0,1,0,0,0,0,0,0,1,107,0,0,0,0,0,240] >;

D245D5 in GAP, Magma, Sage, TeX

D_{24}\rtimes_5D_5
% in TeX

G:=Group("D24:5D5");
// GroupNames label

G:=SmallGroup(480,355);
// by ID

G=gap.SmallGroup(480,355);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,135,142,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^24=b^2=c^5=d^2=1,b*a*b=a^-1,a*c=c*a,d*a*d=a^17,b*c=c*b,d*b*d=a^4*b,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽