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), C15⋊9(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), C3⋊1(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
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, C4, C22, C5, C6, C6, C8, C2×C4, C2×C4, Q8, C10, C10, Dic3, C12, C2×C6, C15, M4(2), M4(2), C2×Q8, C20, C20, C2×C10, C3⋊C8, C24, Dic6, C2×Dic3, C2×C12, C30, C30, C4.10D4, C40, C2×C20, C2×C20, C5×Q8, C4.Dic3, C3×M4(2), C2×Dic6, C5×Dic3, C60, C2×C30, C5×M4(2), C5×M4(2), Q8×C10, C12.47D4, C5×C3⋊C8, C120, C5×Dic6, C10×Dic3, C2×C60, C5×C4.10D4, C5×C4.Dic3, C15×M4(2), C10×Dic6, C5×C12.47D4
Quotients: C1, C2, C4, C22, C5, S3, C2×C4, D4, C10, D6, C22⋊C4, C20, C2×C10, C4×S3, D12, C3⋊D4, C5×S3, C4.10D4, C2×C20, C5×D4, 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
►On 240 points
Generators in S240
(1 52 46 31 13)(2 53 47 32 14)(3 54 48 33 15)(4 55 37 34 16)(5 56 38 35 17)(6 57 39 36 18)(7 58 40 25 19)(8 59 41 26 20)(9 60 42 27 21)(10 49 43 28 22)(11 50 44 29 23)(12 51 45 30 24)(61 112 97 88 73)(62 113 98 89 74)(63 114 99 90 75)(64 115 100 91 76)(65 116 101 92 77)(66 117 102 93 78)(67 118 103 94 79)(68 119 104 95 80)(69 120 105 96 81)(70 109 106 85 82)(71 110 107 86 83)(72 111 108 87 84)(121 170 161 146 139)(122 171 162 147 140)(123 172 163 148 141)(124 173 164 149 142)(125 174 165 150 143)(126 175 166 151 144)(127 176 167 152 133)(128 177 168 153 134)(129 178 157 154 135)(130 179 158 155 136)(131 180 159 156 137)(132 169 160 145 138)(181 239 225 206 201)(182 240 226 207 202)(183 229 227 208 203)(184 230 228 209 204)(185 231 217 210 193)(186 232 218 211 194)(187 233 219 212 195)(188 234 220 213 196)(189 235 221 214 197)(190 236 222 215 198)(191 237 223 216 199)(192 238 224 205 200)
(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)
(1 190 10 181 7 184 4 187)(2 189 11 192 8 183 5 186)(3 188 12 191 9 182 6 185)(13 198 22 201 19 204 16 195)(14 197 23 200 20 203 17 194)(15 196 24 199 21 202 18 193)(25 209 34 212 31 215 28 206)(26 208 35 211 32 214 29 205)(27 207 36 210 33 213 30 216)(37 219 46 222 43 225 40 228)(38 218 47 221 44 224 41 227)(39 217 48 220 45 223 42 226)(49 239 58 230 55 233 52 236)(50 238 59 229 56 232 53 235)(51 237 60 240 57 231 54 234)(61 122 64 131 67 128 70 125)(62 121 65 130 68 127 71 124)(63 132 66 129 69 126 72 123)(73 140 76 137 79 134 82 143)(74 139 77 136 80 133 83 142)(75 138 78 135 81 144 84 141)(85 150 88 147 91 156 94 153)(86 149 89 146 92 155 95 152)(87 148 90 145 93 154 96 151)(97 162 100 159 103 168 106 165)(98 161 101 158 104 167 107 164)(99 160 102 157 105 166 108 163)(109 174 112 171 115 180 118 177)(110 173 113 170 116 179 119 176)(111 172 114 169 117 178 120 175)
(1 125 7 131)(2 124 8 130)(3 123 9 129)(4 122 10 128)(5 121 11 127)(6 132 12 126)(13 143 19 137)(14 142 20 136)(15 141 21 135)(16 140 22 134)(17 139 23 133)(18 138 24 144)(25 156 31 150)(26 155 32 149)(27 154 33 148)(28 153 34 147)(29 152 35 146)(30 151 36 145)(37 162 43 168)(38 161 44 167)(39 160 45 166)(40 159 46 165)(41 158 47 164)(42 157 48 163)(49 177 55 171)(50 176 56 170)(51 175 57 169)(52 174 58 180)(53 173 59 179)(54 172 60 178)(61 190 67 184)(62 189 68 183)(63 188 69 182)(64 187 70 181)(65 186 71 192)(66 185 72 191)(73 198 79 204)(74 197 80 203)(75 196 81 202)(76 195 82 201)(77 194 83 200)(78 193 84 199)(85 206 91 212)(86 205 92 211)(87 216 93 210)(88 215 94 209)(89 214 95 208)(90 213 96 207)(97 222 103 228)(98 221 104 227)(99 220 105 226)(100 219 106 225)(101 218 107 224)(102 217 108 223)(109 239 115 233)(110 238 116 232)(111 237 117 231)(112 236 118 230)(113 235 119 229)(114 234 120 240)
G:=sub<Sym(240)| (1,52,46,31,13)(2,53,47,32,14)(3,54,48,33,15)(4,55,37,34,16)(5,56,38,35,17)(6,57,39,36,18)(7,58,40,25,19)(8,59,41,26,20)(9,60,42,27,21)(10,49,43,28,22)(11,50,44,29,23)(12,51,45,30,24)(61,112,97,88,73)(62,113,98,89,74)(63,114,99,90,75)(64,115,100,91,76)(65,116,101,92,77)(66,117,102,93,78)(67,118,103,94,79)(68,119,104,95,80)(69,120,105,96,81)(70,109,106,85,82)(71,110,107,86,83)(72,111,108,87,84)(121,170,161,146,139)(122,171,162,147,140)(123,172,163,148,141)(124,173,164,149,142)(125,174,165,150,143)(126,175,166,151,144)(127,176,167,152,133)(128,177,168,153,134)(129,178,157,154,135)(130,179,158,155,136)(131,180,159,156,137)(132,169,160,145,138)(181,239,225,206,201)(182,240,226,207,202)(183,229,227,208,203)(184,230,228,209,204)(185,231,217,210,193)(186,232,218,211,194)(187,233,219,212,195)(188,234,220,213,196)(189,235,221,214,197)(190,236,222,215,198)(191,237,223,216,199)(192,238,224,205,200), (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), (1,190,10,181,7,184,4,187)(2,189,11,192,8,183,5,186)(3,188,12,191,9,182,6,185)(13,198,22,201,19,204,16,195)(14,197,23,200,20,203,17,194)(15,196,24,199,21,202,18,193)(25,209,34,212,31,215,28,206)(26,208,35,211,32,214,29,205)(27,207,36,210,33,213,30,216)(37,219,46,222,43,225,40,228)(38,218,47,221,44,224,41,227)(39,217,48,220,45,223,42,226)(49,239,58,230,55,233,52,236)(50,238,59,229,56,232,53,235)(51,237,60,240,57,231,54,234)(61,122,64,131,67,128,70,125)(62,121,65,130,68,127,71,124)(63,132,66,129,69,126,72,123)(73,140,76,137,79,134,82,143)(74,139,77,136,80,133,83,142)(75,138,78,135,81,144,84,141)(85,150,88,147,91,156,94,153)(86,149,89,146,92,155,95,152)(87,148,90,145,93,154,96,151)(97,162,100,159,103,168,106,165)(98,161,101,158,104,167,107,164)(99,160,102,157,105,166,108,163)(109,174,112,171,115,180,118,177)(110,173,113,170,116,179,119,176)(111,172,114,169,117,178,120,175), (1,125,7,131)(2,124,8,130)(3,123,9,129)(4,122,10,128)(5,121,11,127)(6,132,12,126)(13,143,19,137)(14,142,20,136)(15,141,21,135)(16,140,22,134)(17,139,23,133)(18,138,24,144)(25,156,31,150)(26,155,32,149)(27,154,33,148)(28,153,34,147)(29,152,35,146)(30,151,36,145)(37,162,43,168)(38,161,44,167)(39,160,45,166)(40,159,46,165)(41,158,47,164)(42,157,48,163)(49,177,55,171)(50,176,56,170)(51,175,57,169)(52,174,58,180)(53,173,59,179)(54,172,60,178)(61,190,67,184)(62,189,68,183)(63,188,69,182)(64,187,70,181)(65,186,71,192)(66,185,72,191)(73,198,79,204)(74,197,80,203)(75,196,81,202)(76,195,82,201)(77,194,83,200)(78,193,84,199)(85,206,91,212)(86,205,92,211)(87,216,93,210)(88,215,94,209)(89,214,95,208)(90,213,96,207)(97,222,103,228)(98,221,104,227)(99,220,105,226)(100,219,106,225)(101,218,107,224)(102,217,108,223)(109,239,115,233)(110,238,116,232)(111,237,117,231)(112,236,118,230)(113,235,119,229)(114,234,120,240)>;
G:=Group( (1,52,46,31,13)(2,53,47,32,14)(3,54,48,33,15)(4,55,37,34,16)(5,56,38,35,17)(6,57,39,36,18)(7,58,40,25,19)(8,59,41,26,20)(9,60,42,27,21)(10,49,43,28,22)(11,50,44,29,23)(12,51,45,30,24)(61,112,97,88,73)(62,113,98,89,74)(63,114,99,90,75)(64,115,100,91,76)(65,116,101,92,77)(66,117,102,93,78)(67,118,103,94,79)(68,119,104,95,80)(69,120,105,96,81)(70,109,106,85,82)(71,110,107,86,83)(72,111,108,87,84)(121,170,161,146,139)(122,171,162,147,140)(123,172,163,148,141)(124,173,164,149,142)(125,174,165,150,143)(126,175,166,151,144)(127,176,167,152,133)(128,177,168,153,134)(129,178,157,154,135)(130,179,158,155,136)(131,180,159,156,137)(132,169,160,145,138)(181,239,225,206,201)(182,240,226,207,202)(183,229,227,208,203)(184,230,228,209,204)(185,231,217,210,193)(186,232,218,211,194)(187,233,219,212,195)(188,234,220,213,196)(189,235,221,214,197)(190,236,222,215,198)(191,237,223,216,199)(192,238,224,205,200), (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), (1,190,10,181,7,184,4,187)(2,189,11,192,8,183,5,186)(3,188,12,191,9,182,6,185)(13,198,22,201,19,204,16,195)(14,197,23,200,20,203,17,194)(15,196,24,199,21,202,18,193)(25,209,34,212,31,215,28,206)(26,208,35,211,32,214,29,205)(27,207,36,210,33,213,30,216)(37,219,46,222,43,225,40,228)(38,218,47,221,44,224,41,227)(39,217,48,220,45,223,42,226)(49,239,58,230,55,233,52,236)(50,238,59,229,56,232,53,235)(51,237,60,240,57,231,54,234)(61,122,64,131,67,128,70,125)(62,121,65,130,68,127,71,124)(63,132,66,129,69,126,72,123)(73,140,76,137,79,134,82,143)(74,139,77,136,80,133,83,142)(75,138,78,135,81,144,84,141)(85,150,88,147,91,156,94,153)(86,149,89,146,92,155,95,152)(87,148,90,145,93,154,96,151)(97,162,100,159,103,168,106,165)(98,161,101,158,104,167,107,164)(99,160,102,157,105,166,108,163)(109,174,112,171,115,180,118,177)(110,173,113,170,116,179,119,176)(111,172,114,169,117,178,120,175), (1,125,7,131)(2,124,8,130)(3,123,9,129)(4,122,10,128)(5,121,11,127)(6,132,12,126)(13,143,19,137)(14,142,20,136)(15,141,21,135)(16,140,22,134)(17,139,23,133)(18,138,24,144)(25,156,31,150)(26,155,32,149)(27,154,33,148)(28,153,34,147)(29,152,35,146)(30,151,36,145)(37,162,43,168)(38,161,44,167)(39,160,45,166)(40,159,46,165)(41,158,47,164)(42,157,48,163)(49,177,55,171)(50,176,56,170)(51,175,57,169)(52,174,58,180)(53,173,59,179)(54,172,60,178)(61,190,67,184)(62,189,68,183)(63,188,69,182)(64,187,70,181)(65,186,71,192)(66,185,72,191)(73,198,79,204)(74,197,80,203)(75,196,81,202)(76,195,82,201)(77,194,83,200)(78,193,84,199)(85,206,91,212)(86,205,92,211)(87,216,93,210)(88,215,94,209)(89,214,95,208)(90,213,96,207)(97,222,103,228)(98,221,104,227)(99,220,105,226)(100,219,106,225)(101,218,107,224)(102,217,108,223)(109,239,115,233)(110,238,116,232)(111,237,117,231)(112,236,118,230)(113,235,119,229)(114,234,120,240) );
G=PermutationGroup([[(1,52,46,31,13),(2,53,47,32,14),(3,54,48,33,15),(4,55,37,34,16),(5,56,38,35,17),(6,57,39,36,18),(7,58,40,25,19),(8,59,41,26,20),(9,60,42,27,21),(10,49,43,28,22),(11,50,44,29,23),(12,51,45,30,24),(61,112,97,88,73),(62,113,98,89,74),(63,114,99,90,75),(64,115,100,91,76),(65,116,101,92,77),(66,117,102,93,78),(67,118,103,94,79),(68,119,104,95,80),(69,120,105,96,81),(70,109,106,85,82),(71,110,107,86,83),(72,111,108,87,84),(121,170,161,146,139),(122,171,162,147,140),(123,172,163,148,141),(124,173,164,149,142),(125,174,165,150,143),(126,175,166,151,144),(127,176,167,152,133),(128,177,168,153,134),(129,178,157,154,135),(130,179,158,155,136),(131,180,159,156,137),(132,169,160,145,138),(181,239,225,206,201),(182,240,226,207,202),(183,229,227,208,203),(184,230,228,209,204),(185,231,217,210,193),(186,232,218,211,194),(187,233,219,212,195),(188,234,220,213,196),(189,235,221,214,197),(190,236,222,215,198),(191,237,223,216,199),(192,238,224,205,200)], [(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)], [(1,190,10,181,7,184,4,187),(2,189,11,192,8,183,5,186),(3,188,12,191,9,182,6,185),(13,198,22,201,19,204,16,195),(14,197,23,200,20,203,17,194),(15,196,24,199,21,202,18,193),(25,209,34,212,31,215,28,206),(26,208,35,211,32,214,29,205),(27,207,36,210,33,213,30,216),(37,219,46,222,43,225,40,228),(38,218,47,221,44,224,41,227),(39,217,48,220,45,223,42,226),(49,239,58,230,55,233,52,236),(50,238,59,229,56,232,53,235),(51,237,60,240,57,231,54,234),(61,122,64,131,67,128,70,125),(62,121,65,130,68,127,71,124),(63,132,66,129,69,126,72,123),(73,140,76,137,79,134,82,143),(74,139,77,136,80,133,83,142),(75,138,78,135,81,144,84,141),(85,150,88,147,91,156,94,153),(86,149,89,146,92,155,95,152),(87,148,90,145,93,154,96,151),(97,162,100,159,103,168,106,165),(98,161,101,158,104,167,107,164),(99,160,102,157,105,166,108,163),(109,174,112,171,115,180,118,177),(110,173,113,170,116,179,119,176),(111,172,114,169,117,178,120,175)], [(1,125,7,131),(2,124,8,130),(3,123,9,129),(4,122,10,128),(5,121,11,127),(6,132,12,126),(13,143,19,137),(14,142,20,136),(15,141,21,135),(16,140,22,134),(17,139,23,133),(18,138,24,144),(25,156,31,150),(26,155,32,149),(27,154,33,148),(28,153,34,147),(29,152,35,146),(30,151,36,145),(37,162,43,168),(38,161,44,167),(39,160,45,166),(40,159,46,165),(41,158,47,164),(42,157,48,163),(49,177,55,171),(50,176,56,170),(51,175,57,169),(52,174,58,180),(53,173,59,179),(54,172,60,178),(61,190,67,184),(62,189,68,183),(63,188,69,182),(64,187,70,181),(65,186,71,192),(66,185,72,191),(73,198,79,204),(74,197,80,203),(75,196,81,202),(76,195,82,201),(77,194,83,200),(78,193,84,199),(85,206,91,212),(86,205,92,211),(87,216,93,210),(88,215,94,209),(89,214,95,208),(90,213,96,207),(97,222,103,228),(98,221,104,227),(99,220,105,226),(100,219,106,225),(101,218,107,224),(102,217,108,223),(109,239,115,233),(110,238,116,232),(111,237,117,231),(112,236,118,230),(113,235,119,229),(114,234,120,240)]])
105 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 4C | 4D | 5A | 5B | 5C | 5D | 6A | 6B | 8A | 8B | 8C | 8D | 10A | 10B | 10C | 10D | 10E | 10F | 10G | 10H | 12A | 12B | 12C | 15A | 15B | 15C | 15D | 20A | ··· | 20H | 20I | ··· | 20P | 24A | 24B | 24C | 24D | 30A | 30B | 30C | 30D | 30E | 30F | 30G | 30H | 40A | ··· | 40H | 40I | ··· | 40P | 60A | ··· | 60H | 60I | 60J | 60K | 60L | 120A | ··· | 120P |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 24 | 24 | 24 | 24 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 40 | ··· | 40 | 40 | ··· | 40 | 60 | ··· | 60 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 2 | 2 | 2 | 2 | 12 | 12 | 1 | 1 | 1 | 1 | 2 | 4 | 4 | 4 | 12 | 12 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 12 | ··· | 12 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 12 | ··· | 12 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
105 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | - | ||||||||||||||||
| image | C1 | C2 | C2 | C2 | C4 | C5 | C10 | C10 | C10 | C20 | S3 | D4 | D6 | D12 | C3⋊D4 | C4×S3 | C5×S3 | C5×D4 | S3×C10 | C5×D12 | C5×C3⋊D4 | S3×C20 | C4.10D4 | C12.47D4 | C5×C4.10D4 | C5×C12.47D4 |
| kernel | C5×C12.47D4 | C5×C4.Dic3 | C15×M4(2) | C10×Dic6 | C10×Dic3 | C12.47D4 | C4.Dic3 | C3×M4(2) | C2×Dic6 | C2×Dic3 | C5×M4(2) | C60 | C2×C20 | C20 | C20 | C2×C10 | M4(2) | C12 | C2×C4 | C4 | C4 | C22 | C15 | C5 | C3 | C1 |
| # reps | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 4 | 16 | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 8 | 4 | 8 | 8 | 8 | 1 | 2 | 4 | 8 |
Matrix representation of C5×C12.47D4 ►in GL6(𝔽241)
| 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 | 136 | 0 | 0 | 0 | 0 |
| 0 | 225 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 239 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 177 | 0 | 1 |
| 0 | 0 | 64 | 64 | 240 | 0 |
| 38 | 130 | 0 | 0 | 0 | 0 |
| 165 | 203 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 | 113 | 0 |
| 0 | 0 | 1 | 0 | 64 | 177 |
| 0 | 0 | 177 | 177 | 1 | 0 |
| 0 | 0 | 64 | 0 | 240 | 0 |
| 38 | 149 | 0 | 0 | 0 | 0 |
| 165 | 203 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 0 | 0 | 0 |
| 0 | 0 | 177 | 177 | 0 | 0 |
| 0 | 0 | 0 | 0 | 64 | 0 |
| 0 | 0 | 1 | 0 | 0 | 177 |
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