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G = C5×C12.47D4order 480 = 25·3·5

Direct product of C5 and C12.47D4

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

Aliases: C5×C12.47D4, C20.64D12, C60.225D4, C4.12(C5×D12), C12.47(C5×D4), (C2×Dic3).C20, (C2×C20).214D6, C22.5(S3×C20), C10.56(D6⋊C4), C159(C4.10D4), (C2×Dic6).6C10, M4(2).2(C5×S3), (C5×M4(2)).2S3, C4.Dic3.3C10, C20.115(C3⋊D4), C30.98(C22⋊C4), (C2×C60).343C22, (C10×Dic6).16C2, (C10×Dic3).11C4, (C3×M4(2)).2C10, (C15×M4(2)).4C2, (C2×C4).2(S3×C10), (C2×C6).3(C2×C20), C2.10(C5×D6⋊C4), C31(C5×C4.10D4), C4.22(C5×C3⋊D4), C6.9(C5×C22⋊C4), (C2×C10).64(C4×S3), (C2×C12).13(C2×C10), (C2×C30).127(C2×C4), (C5×C4.Dic3).7C2, SmallGroup(480,143)

Series: Derived Chief Lower central Upper central

C1C2×C6 — C5×C12.47D4
C1C3C6C2×C6C2×C12C2×C60C10×Dic6 — C5×C12.47D4
C3C6C2×C6 — C5×C12.47D4
C1C10C2×C20C5×M4(2)

Generators and relations for C5×C12.47D4
 G = < a,b,c,d | a5=b12=1, c4=d2=b6, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=b9c3 >

Subgroups: 164 in 76 conjugacy classes, 38 normal (34 characteristic)
C1, C2, C2, C3, C4 [×2], C4 [×2], C22, C5, C6, C6, C8 [×2], C2×C4, C2×C4 [×2], Q8 [×2], C10, C10, Dic3 [×2], C12 [×2], C2×C6, C15, M4(2), M4(2), C2×Q8, C20 [×2], C20 [×2], C2×C10, C3⋊C8, C24, Dic6 [×2], C2×Dic3 [×2], C2×C12, C30, C30, C4.10D4, C40 [×2], C2×C20, C2×C20 [×2], C5×Q8 [×2], C4.Dic3, C3×M4(2), C2×Dic6, C5×Dic3 [×2], C60 [×2], C2×C30, C5×M4(2), C5×M4(2), Q8×C10, C12.47D4, C5×C3⋊C8, C120, C5×Dic6 [×2], C10×Dic3 [×2], C2×C60, C5×C4.10D4, C5×C4.Dic3, C15×M4(2), C10×Dic6, C5×C12.47D4
Quotients: C1, C2 [×3], C4 [×2], C22, C5, S3, C2×C4, D4 [×2], C10 [×3], D6, C22⋊C4, C20 [×2], C2×C10, C4×S3, D12, C3⋊D4, C5×S3, C4.10D4, C2×C20, C5×D4 [×2], D6⋊C4, S3×C10, C5×C22⋊C4, C12.47D4, S3×C20, C5×D12, C5×C3⋊D4, C5×C4.10D4, C5×D6⋊C4, C5×C12.47D4

Smallest permutation representation of C5×C12.47D4
On 240 points
Generators in S240
(1 58 40 25 22)(2 59 41 26 23)(3 60 42 27 24)(4 49 43 28 13)(5 50 44 29 14)(6 51 45 30 15)(7 52 46 31 16)(8 53 47 32 17)(9 54 48 33 18)(10 55 37 34 19)(11 56 38 35 20)(12 57 39 36 21)(61 115 106 85 76)(62 116 107 86 77)(63 117 108 87 78)(64 118 97 88 79)(65 119 98 89 80)(66 120 99 90 81)(67 109 100 91 82)(68 110 101 92 83)(69 111 102 93 84)(70 112 103 94 73)(71 113 104 95 74)(72 114 105 96 75)(121 171 157 151 144)(122 172 158 152 133)(123 173 159 153 134)(124 174 160 154 135)(125 175 161 155 136)(126 176 162 156 137)(127 177 163 145 138)(128 178 164 146 139)(129 179 165 147 140)(130 180 166 148 141)(131 169 167 149 142)(132 170 168 150 143)(181 229 227 213 201)(182 230 228 214 202)(183 231 217 215 203)(184 232 218 216 204)(185 233 219 205 193)(186 234 220 206 194)(187 235 221 207 195)(188 236 222 208 196)(189 237 223 209 197)(190 238 224 210 198)(191 239 225 211 199)(192 240 226 212 200)
(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)
(1 181 10 184 7 187 4 190)(2 192 11 183 8 186 5 189)(3 191 12 182 9 185 6 188)(13 198 22 201 19 204 16 195)(14 197 23 200 20 203 17 194)(15 196 24 199 21 202 18 193)(25 213 34 216 31 207 28 210)(26 212 35 215 32 206 29 209)(27 211 36 214 33 205 30 208)(37 218 46 221 43 224 40 227)(38 217 47 220 44 223 41 226)(39 228 48 219 45 222 42 225)(49 238 58 229 55 232 52 235)(50 237 59 240 56 231 53 234)(51 236 60 239 57 230 54 233)(61 129 64 126 67 123 70 132)(62 128 65 125 68 122 71 131)(63 127 66 124 69 121 72 130)(73 143 76 140 79 137 82 134)(74 142 77 139 80 136 83 133)(75 141 78 138 81 135 84 144)(85 147 88 156 91 153 94 150)(86 146 89 155 92 152 95 149)(87 145 90 154 93 151 96 148)(97 162 100 159 103 168 106 165)(98 161 101 158 104 167 107 164)(99 160 102 157 105 166 108 163)(109 173 112 170 115 179 118 176)(110 172 113 169 116 178 119 175)(111 171 114 180 117 177 120 174)
(1 132 7 126)(2 131 8 125)(3 130 9 124)(4 129 10 123)(5 128 11 122)(6 127 12 121)(13 140 19 134)(14 139 20 133)(15 138 21 144)(16 137 22 143)(17 136 23 142)(18 135 24 141)(25 150 31 156)(26 149 32 155)(27 148 33 154)(28 147 34 153)(29 146 35 152)(30 145 36 151)(37 159 43 165)(38 158 44 164)(39 157 45 163)(40 168 46 162)(41 167 47 161)(42 166 48 160)(49 179 55 173)(50 178 56 172)(51 177 57 171)(52 176 58 170)(53 175 59 169)(54 174 60 180)(61 181 67 187)(62 192 68 186)(63 191 69 185)(64 190 70 184)(65 189 71 183)(66 188 72 182)(73 204 79 198)(74 203 80 197)(75 202 81 196)(76 201 82 195)(77 200 83 194)(78 199 84 193)(85 213 91 207)(86 212 92 206)(87 211 93 205)(88 210 94 216)(89 209 95 215)(90 208 96 214)(97 224 103 218)(98 223 104 217)(99 222 105 228)(100 221 106 227)(101 220 107 226)(102 219 108 225)(109 235 115 229)(110 234 116 240)(111 233 117 239)(112 232 118 238)(113 231 119 237)(114 230 120 236)

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

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

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

105 conjugacy classes

class 1 2A2B 3 4A4B4C4D5A5B5C5D6A6B8A8B8C8D10A10B10C10D10E10F10G10H12A12B12C15A15B15C15D20A···20H20I···20P24A24B24C24D30A30B30C30D30E30F30G30H40A···40H40I···40P60A···60H60I60J60K60L120A···120P
order12234444555566888810101010101010101212121515151520···2020···2024242424303030303030303040···4040···4060···6060606060120···120
size11222212121111244412121111222222422222···212···124444222244444···412···122···244444···4

105 irreducible representations

dim11111111112222222222224444
type++++++++--
imageC1C2C2C2C4C5C10C10C10C20S3D4D6D12C3⋊D4C4×S3C5×S3C5×D4S3×C10C5×D12C5×C3⋊D4S3×C20C4.10D4C12.47D4C5×C4.10D4C5×C12.47D4
kernelC5×C12.47D4C5×C4.Dic3C15×M4(2)C10×Dic6C10×Dic3C12.47D4C4.Dic3C3×M4(2)C2×Dic6C2×Dic3C5×M4(2)C60C2×C20C20C20C2×C10M4(2)C12C2×C4C4C4C22C15C5C3C1
# reps111144444161212224848881248

Matrix representation of C5×C12.47D4 in GL6(𝔽241)

8700000
0870000
001000
000100
000010
000001
,
151360000
02250000
0024023900
001100
00017701
0064642400
,
381300000
1652030000
0024001130
001064177
0017717710
006402400
,
381490000
1652030000
0064000
0017717700
0000640
00100177

G:=sub<GL(6,GF(241))| [87,0,0,0,0,0,0,87,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[15,0,0,0,0,0,136,225,0,0,0,0,0,0,240,1,0,64,0,0,239,1,177,64,0,0,0,0,0,240,0,0,0,0,1,0],[38,165,0,0,0,0,130,203,0,0,0,0,0,0,240,1,177,64,0,0,0,0,177,0,0,0,113,64,1,240,0,0,0,177,0,0],[38,165,0,0,0,0,149,203,0,0,0,0,0,0,64,177,0,1,0,0,0,177,0,0,0,0,0,0,64,0,0,0,0,0,0,177] >;

C5×C12.47D4 in GAP, Magma, Sage, TeX

C_5\times C_{12}._{47}D_4
% in TeX

G:=Group("C5xC12.47D4");
// GroupNames label

G:=SmallGroup(480,143);
// by ID

G=gap.SmallGroup(480,143);
# by ID

G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,560,589,148,2803,136,2111,15686]);
// Polycyclic

G:=Group<a,b,c,d|a^5=b^12=1,c^4=d^2=b^6,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^9*c^3>;
// generators/relations

׿
×
𝔽