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G = C4⋊C47D15order 480 = 25·3·5

1st semidirect product of C4⋊C4 and D15 acting through Inn(C4⋊C4)

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C4⋊C47D15, (C4×D15)⋊6C4, C20.60(C4×S3), C60.85(C2×C4), C605C418C2, (C2×C4).42D30, C12.28(C4×D5), C4.14(C4×D15), D30.34(C2×C4), (C2×C20).210D6, (C4×Dic15)⋊19C2, D303C4.5C2, (C2×C12).208D10, (C2×C60).65C22, C1527(C42⋊C2), C30.257(C4○D4), C2.4(D42D15), C2.1(Q83D15), C6.98(D42D5), (C2×C30).289C23, C30.161(C22×C4), C6.39(Q82D5), Dic15.50(C2×C4), C10.98(D42S3), C10.39(Q83S3), C22.17(C22×D15), (C22×D15).81C22, (C2×Dic15).163C22, (C5×C4⋊C4)⋊3S3, (C3×C4⋊C4)⋊3D5, (C15×C4⋊C4)⋊3C2, C6.66(C2×C4×D5), C10.98(S3×C2×C4), (C2×C4×D15).1C2, C55(C4⋊C47S3), C2.12(C2×C4×D15), C34(C4⋊C47D5), (C2×C6).285(C22×D5), (C2×C10).284(C22×S3), SmallGroup(480,857)

Series: Derived Chief Lower central Upper central

C1C30 — C4⋊C47D15
C1C5C15C30C2×C30C22×D15C2×C4×D15 — C4⋊C47D15
C15C30 — C4⋊C47D15
C1C22C4⋊C4

Generators and relations for C4⋊C47D15
 G = < a,b,c,d | a4=b4=c15=d2=1, bab-1=a-1, ac=ca, ad=da, bc=cb, dbd=a2b, dcd=c-1 >

Subgroups: 804 in 152 conjugacy classes, 63 normal (33 characteristic)
C1, C2 [×3], C2 [×2], C3, C4 [×2], C4 [×6], C22, C22 [×4], C5, S3 [×2], C6 [×3], C2×C4, C2×C4 [×2], C2×C4 [×7], C23, D5 [×2], C10 [×3], Dic3 [×4], C12 [×2], C12 [×2], D6 [×4], C2×C6, C15, C42 [×2], C22⋊C4 [×2], C4⋊C4, C4⋊C4, C22×C4, Dic5 [×4], C20 [×2], C20 [×2], D10 [×4], C2×C10, C4×S3 [×4], C2×Dic3 [×3], C2×C12, C2×C12 [×2], C22×S3, D15 [×2], C30 [×3], C42⋊C2, C4×D5 [×4], C2×Dic5 [×3], C2×C20, C2×C20 [×2], C22×D5, C4×Dic3 [×2], C4⋊Dic3, D6⋊C4 [×2], C3×C4⋊C4, S3×C2×C4, Dic15 [×2], Dic15 [×2], C60 [×2], C60 [×2], D30 [×2], D30 [×2], C2×C30, C4×Dic5 [×2], C4⋊Dic5, D10⋊C4 [×2], C5×C4⋊C4, C2×C4×D5, C4⋊C47S3, C4×D15 [×4], C2×Dic15, C2×Dic15 [×2], C2×C60, C2×C60 [×2], C22×D15, C4⋊C47D5, C4×Dic15 [×2], C605C4, D303C4 [×2], C15×C4⋊C4, C2×C4×D15, C4⋊C47D15
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], C23, D5, D6 [×3], C22×C4, C4○D4 [×2], D10 [×3], C4×S3 [×2], C22×S3, D15, C42⋊C2, C4×D5 [×2], C22×D5, S3×C2×C4, D42S3, Q83S3, D30 [×3], C2×C4×D5, D42D5, Q82D5, C4⋊C47S3, C4×D15 [×2], C22×D15, C4⋊C47D5, C2×C4×D15, D42D15, Q83D15, C4⋊C47D15

Smallest permutation representation of C4⋊C47D15
On 240 points
Generators in S240
(1 167 20 155)(2 168 21 156)(3 169 22 157)(4 170 23 158)(5 171 24 159)(6 172 25 160)(7 173 26 161)(8 174 27 162)(9 175 28 163)(10 176 29 164)(11 177 30 165)(12 178 16 151)(13 179 17 152)(14 180 18 153)(15 166 19 154)(31 147 57 121)(32 148 58 122)(33 149 59 123)(34 150 60 124)(35 136 46 125)(36 137 47 126)(37 138 48 127)(38 139 49 128)(39 140 50 129)(40 141 51 130)(41 142 52 131)(42 143 53 132)(43 144 54 133)(44 145 55 134)(45 146 56 135)(61 233 84 222)(62 234 85 223)(63 235 86 224)(64 236 87 225)(65 237 88 211)(66 238 89 212)(67 239 90 213)(68 240 76 214)(69 226 77 215)(70 227 78 216)(71 228 79 217)(72 229 80 218)(73 230 81 219)(74 231 82 220)(75 232 83 221)(91 196 117 181)(92 197 118 182)(93 198 119 183)(94 199 120 184)(95 200 106 185)(96 201 107 186)(97 202 108 187)(98 203 109 188)(99 204 110 189)(100 205 111 190)(101 206 112 191)(102 207 113 192)(103 208 114 193)(104 209 115 194)(105 210 116 195)
(1 92 35 69)(2 93 36 70)(3 94 37 71)(4 95 38 72)(5 96 39 73)(6 97 40 74)(7 98 41 75)(8 99 42 61)(9 100 43 62)(10 101 44 63)(11 102 45 64)(12 103 31 65)(13 104 32 66)(14 105 33 67)(15 91 34 68)(16 114 57 88)(17 115 58 89)(18 116 59 90)(19 117 60 76)(20 118 46 77)(21 119 47 78)(22 120 48 79)(23 106 49 80)(24 107 50 81)(25 108 51 82)(26 109 52 83)(27 110 53 84)(28 111 54 85)(29 112 55 86)(30 113 56 87)(121 237 151 208)(122 238 152 209)(123 239 153 210)(124 240 154 196)(125 226 155 197)(126 227 156 198)(127 228 157 199)(128 229 158 200)(129 230 159 201)(130 231 160 202)(131 232 161 203)(132 233 162 204)(133 234 163 205)(134 235 164 206)(135 236 165 207)(136 215 167 182)(137 216 168 183)(138 217 169 184)(139 218 170 185)(140 219 171 186)(141 220 172 187)(142 221 173 188)(143 222 174 189)(144 223 175 190)(145 224 176 191)(146 225 177 192)(147 211 178 193)(148 212 179 194)(149 213 180 195)(150 214 166 181)
(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 23)(17 22)(18 21)(19 20)(24 30)(25 29)(26 28)(31 38)(32 37)(33 36)(34 35)(39 45)(40 44)(41 43)(46 60)(47 59)(48 58)(49 57)(50 56)(51 55)(52 54)(61 84)(62 83)(63 82)(64 81)(65 80)(66 79)(67 78)(68 77)(69 76)(70 90)(71 89)(72 88)(73 87)(74 86)(75 85)(91 118)(92 117)(93 116)(94 115)(95 114)(96 113)(97 112)(98 111)(99 110)(100 109)(101 108)(102 107)(103 106)(104 120)(105 119)(121 128)(122 127)(123 126)(124 125)(129 135)(130 134)(131 133)(136 150)(137 149)(138 148)(139 147)(140 146)(141 145)(142 144)(151 158)(152 157)(153 156)(154 155)(159 165)(160 164)(161 163)(166 167)(168 180)(169 179)(170 178)(171 177)(172 176)(173 175)(181 197)(182 196)(183 210)(184 209)(185 208)(186 207)(187 206)(188 205)(189 204)(190 203)(191 202)(192 201)(193 200)(194 199)(195 198)(211 229)(212 228)(213 227)(214 226)(215 240)(216 239)(217 238)(218 237)(219 236)(220 235)(221 234)(222 233)(223 232)(224 231)(225 230)

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

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

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

90 conjugacy classes

class 1 2A2B2C2D2E 3 4A···4F4G4H4I4J4K4L4M4N5A5B6A6B6C10A···10F12A···12F15A15B15C15D20A···20L30A···30L60A···60X
order12222234···4444444445566610···1012···121515151520···2030···3060···60
size1111303022···21515151530303030222222···24···422224···42···24···4

90 irreducible representations

dim11111112222222222444444
type++++++++++++-+-+-+
imageC1C2C2C2C2C2C4S3D5D6C4○D4D10C4×S3D15C4×D5D30C4×D15D42S3Q83S3D42D5Q82D5D42D15Q83D15
kernelC4⋊C47D15C4×Dic15C605C4D303C4C15×C4⋊C4C2×C4×D15C4×D15C5×C4⋊C4C3×C4⋊C4C2×C20C30C2×C12C20C4⋊C4C12C2×C4C4C10C10C6C6C2C2
# reps1212118123464481216112244

Matrix representation of C4⋊C47D15 in GL6(𝔽61)

6000000
0600000
0060000
0006000
0000500
0000011
,
1100000
0110000
001000
000100
000001
000010
,
43170000
4300000
00473000
00312500
000010
000001
,
1600000
0600000
000100
001000
000010
0000060

G:=sub<GL(6,GF(61))| [60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,50,0,0,0,0,0,0,11],[11,0,0,0,0,0,0,11,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[43,43,0,0,0,0,17,0,0,0,0,0,0,0,47,31,0,0,0,0,30,25,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,60,60,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,60] >;

C4⋊C47D15 in GAP, Magma, Sage, TeX

C_4\rtimes C_4\rtimes_7D_{15}
% in TeX

G:=Group("C4:C4:7D15");
// GroupNames label

G:=SmallGroup(480,857);
// by ID

G=gap.SmallGroup(480,857);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,422,219,58,2693,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^4=b^4=c^15=d^2=1,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^2*b,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽