direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C5×C8.D6, C40.37D6, C20.67D12, C60.146D4, Dic12⋊2C10, C120.62C22, C60.272C23, C8.1(S3×C10), C24⋊C2⋊2C10, C24.1(C2×C10), C4.15(C5×D12), C6.14(D4×C10), (C2×C30).93D4, C12.13(C5×D4), C4○D12.4C10, (C2×Dic6)⋊8C10, D12.8(C2×C10), C2.16(C10×D12), C10.85(C2×D12), C30.301(C2×D4), (C2×C20).241D6, (C2×C10).28D12, M4(2)⋊2(C5×S3), (C5×M4(2))⋊6S3, C22.6(C5×D12), (C5×Dic12)⋊10C2, (C10×Dic6)⋊24C2, (C3×M4(2))⋊2C10, C15⋊27(C8.C22), (C15×M4(2))⋊8C2, Dic6.8(C2×C10), C12.33(C22×C10), (C2×C60).356C22, C20.236(C22×S3), (C5×D12).47C22, (C5×Dic6).50C22, C4.33(S3×C2×C10), (C2×C6).6(C5×D4), C3⋊1(C5×C8.C22), (C5×C24⋊C2)⋊10C2, (C2×C4).14(S3×C10), (C2×C12).29(C2×C10), (C5×C4○D12).10C2, SmallGroup(480,788)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×C8.D6
G = < a,b,c,d | a5=b8=1, c6=d2=b4, ab=ba, ac=ca, ad=da, cbc-1=b5, dbd-1=b-1, dcd-1=c5 >
Subgroups: 292 in 120 conjugacy classes, 58 normal (38 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C5, S3, C6, C6, C8, C2×C4, C2×C4, D4, Q8, C10, C10, Dic3, C12, D6, C2×C6, C15, M4(2), SD16, Q16, C2×Q8, C4○D4, C20, C20, C2×C10, C2×C10, C24, Dic6, Dic6, Dic6, C4×S3, D12, C2×Dic3, C3⋊D4, C2×C12, C5×S3, C30, C30, C8.C22, C40, C2×C20, C2×C20, C5×D4, C5×Q8, C24⋊C2, Dic12, C3×M4(2), C2×Dic6, C4○D12, C5×Dic3, C60, S3×C10, C2×C30, C5×M4(2), C5×SD16, C5×Q16, Q8×C10, C5×C4○D4, C8.D6, C120, C5×Dic6, C5×Dic6, C5×Dic6, S3×C20, C5×D12, C10×Dic3, C5×C3⋊D4, C2×C60, C5×C8.C22, C5×C24⋊C2, C5×Dic12, C15×M4(2), C10×Dic6, C5×C4○D12, C5×C8.D6
Quotients: C1, C2, C22, C5, S3, D4, C23, C10, D6, C2×D4, C2×C10, D12, C22×S3, C5×S3, C8.C22, C5×D4, C22×C10, C2×D12, S3×C10, D4×C10, C8.D6, C5×D12, S3×C2×C10, C5×C8.C22, C10×D12, C5×C8.D6
►On 240 points
Generators in S240
(1 58 39 34 23)(2 59 40 35 24)(3 60 41 36 13)(4 49 42 25 14)(5 50 43 26 15)(6 51 44 27 16)(7 52 45 28 17)(8 53 46 29 18)(9 54 47 30 19)(10 55 48 31 20)(11 56 37 32 21)(12 57 38 33 22)(61 117 100 95 79)(62 118 101 96 80)(63 119 102 85 81)(64 120 103 86 82)(65 109 104 87 83)(66 110 105 88 84)(67 111 106 89 73)(68 112 107 90 74)(69 113 108 91 75)(70 114 97 92 76)(71 115 98 93 77)(72 116 99 94 78)(121 178 163 148 142)(122 179 164 149 143)(123 180 165 150 144)(124 169 166 151 133)(125 170 167 152 134)(126 171 168 153 135)(127 172 157 154 136)(128 173 158 155 137)(129 174 159 156 138)(130 175 160 145 139)(131 176 161 146 140)(132 177 162 147 141)(181 232 223 214 202)(182 233 224 215 203)(183 234 225 216 204)(184 235 226 205 193)(185 236 227 206 194)(186 237 228 207 195)(187 238 217 208 196)(188 239 218 209 197)(189 240 219 210 198)(190 229 220 211 199)(191 230 221 212 200)(192 231 222 213 201)
(1 72 4 69 7 66 10 63)(2 67 5 64 8 61 11 70)(3 62 6 71 9 68 12 65)(13 80 16 77 19 74 22 83)(14 75 17 84 20 81 23 78)(15 82 18 79 21 76 24 73)(25 91 28 88 31 85 34 94)(26 86 29 95 32 92 35 89)(27 93 30 90 33 87 36 96)(37 97 40 106 43 103 46 100)(38 104 41 101 44 98 47 107)(39 99 42 108 45 105 48 102)(49 113 52 110 55 119 58 116)(50 120 53 117 56 114 59 111)(51 115 54 112 57 109 60 118)(121 190 130 181 127 184 124 187)(122 185 131 188 128 191 125 182)(123 192 132 183 129 186 126 189)(133 196 142 199 139 202 136 193)(134 203 143 194 140 197 137 200)(135 198 144 201 141 204 138 195)(145 214 154 205 151 208 148 211)(146 209 155 212 152 215 149 206)(147 216 156 207 153 210 150 213)(157 226 166 217 163 220 160 223)(158 221 167 224 164 227 161 218)(159 228 168 219 165 222 162 225)(169 238 178 229 175 232 172 235)(170 233 179 236 176 239 173 230)(171 240 180 231 177 234 174 237)
(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)
(1 132 7 126)(2 125 8 131)(3 130 9 124)(4 123 10 129)(5 128 11 122)(6 121 12 127)(13 139 19 133)(14 144 20 138)(15 137 21 143)(16 142 22 136)(17 135 23 141)(18 140 24 134)(25 150 31 156)(26 155 32 149)(27 148 33 154)(28 153 34 147)(29 146 35 152)(30 151 36 145)(37 164 43 158)(38 157 44 163)(39 162 45 168)(40 167 46 161)(41 160 47 166)(42 165 48 159)(49 180 55 174)(50 173 56 179)(51 178 57 172)(52 171 58 177)(53 176 59 170)(54 169 60 175)(61 185 67 191)(62 190 68 184)(63 183 69 189)(64 188 70 182)(65 181 71 187)(66 186 72 192)(73 200 79 194)(74 193 80 199)(75 198 81 204)(76 203 82 197)(77 196 83 202)(78 201 84 195)(85 216 91 210)(86 209 92 215)(87 214 93 208)(88 207 94 213)(89 212 95 206)(90 205 96 211)(97 224 103 218)(98 217 104 223)(99 222 105 228)(100 227 106 221)(101 220 107 226)(102 225 108 219)(109 232 115 238)(110 237 116 231)(111 230 117 236)(112 235 118 229)(113 240 119 234)(114 233 120 239)
G:=sub<Sym(240)| (1,58,39,34,23)(2,59,40,35,24)(3,60,41,36,13)(4,49,42,25,14)(5,50,43,26,15)(6,51,44,27,16)(7,52,45,28,17)(8,53,46,29,18)(9,54,47,30,19)(10,55,48,31,20)(11,56,37,32,21)(12,57,38,33,22)(61,117,100,95,79)(62,118,101,96,80)(63,119,102,85,81)(64,120,103,86,82)(65,109,104,87,83)(66,110,105,88,84)(67,111,106,89,73)(68,112,107,90,74)(69,113,108,91,75)(70,114,97,92,76)(71,115,98,93,77)(72,116,99,94,78)(121,178,163,148,142)(122,179,164,149,143)(123,180,165,150,144)(124,169,166,151,133)(125,170,167,152,134)(126,171,168,153,135)(127,172,157,154,136)(128,173,158,155,137)(129,174,159,156,138)(130,175,160,145,139)(131,176,161,146,140)(132,177,162,147,141)(181,232,223,214,202)(182,233,224,215,203)(183,234,225,216,204)(184,235,226,205,193)(185,236,227,206,194)(186,237,228,207,195)(187,238,217,208,196)(188,239,218,209,197)(189,240,219,210,198)(190,229,220,211,199)(191,230,221,212,200)(192,231,222,213,201), (1,72,4,69,7,66,10,63)(2,67,5,64,8,61,11,70)(3,62,6,71,9,68,12,65)(13,80,16,77,19,74,22,83)(14,75,17,84,20,81,23,78)(15,82,18,79,21,76,24,73)(25,91,28,88,31,85,34,94)(26,86,29,95,32,92,35,89)(27,93,30,90,33,87,36,96)(37,97,40,106,43,103,46,100)(38,104,41,101,44,98,47,107)(39,99,42,108,45,105,48,102)(49,113,52,110,55,119,58,116)(50,120,53,117,56,114,59,111)(51,115,54,112,57,109,60,118)(121,190,130,181,127,184,124,187)(122,185,131,188,128,191,125,182)(123,192,132,183,129,186,126,189)(133,196,142,199,139,202,136,193)(134,203,143,194,140,197,137,200)(135,198,144,201,141,204,138,195)(145,214,154,205,151,208,148,211)(146,209,155,212,152,215,149,206)(147,216,156,207,153,210,150,213)(157,226,166,217,163,220,160,223)(158,221,167,224,164,227,161,218)(159,228,168,219,165,222,162,225)(169,238,178,229,175,232,172,235)(170,233,179,236,176,239,173,230)(171,240,180,231,177,234,174,237), (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), (1,132,7,126)(2,125,8,131)(3,130,9,124)(4,123,10,129)(5,128,11,122)(6,121,12,127)(13,139,19,133)(14,144,20,138)(15,137,21,143)(16,142,22,136)(17,135,23,141)(18,140,24,134)(25,150,31,156)(26,155,32,149)(27,148,33,154)(28,153,34,147)(29,146,35,152)(30,151,36,145)(37,164,43,158)(38,157,44,163)(39,162,45,168)(40,167,46,161)(41,160,47,166)(42,165,48,159)(49,180,55,174)(50,173,56,179)(51,178,57,172)(52,171,58,177)(53,176,59,170)(54,169,60,175)(61,185,67,191)(62,190,68,184)(63,183,69,189)(64,188,70,182)(65,181,71,187)(66,186,72,192)(73,200,79,194)(74,193,80,199)(75,198,81,204)(76,203,82,197)(77,196,83,202)(78,201,84,195)(85,216,91,210)(86,209,92,215)(87,214,93,208)(88,207,94,213)(89,212,95,206)(90,205,96,211)(97,224,103,218)(98,217,104,223)(99,222,105,228)(100,227,106,221)(101,220,107,226)(102,225,108,219)(109,232,115,238)(110,237,116,231)(111,230,117,236)(112,235,118,229)(113,240,119,234)(114,233,120,239)>;
G:=Group( (1,58,39,34,23)(2,59,40,35,24)(3,60,41,36,13)(4,49,42,25,14)(5,50,43,26,15)(6,51,44,27,16)(7,52,45,28,17)(8,53,46,29,18)(9,54,47,30,19)(10,55,48,31,20)(11,56,37,32,21)(12,57,38,33,22)(61,117,100,95,79)(62,118,101,96,80)(63,119,102,85,81)(64,120,103,86,82)(65,109,104,87,83)(66,110,105,88,84)(67,111,106,89,73)(68,112,107,90,74)(69,113,108,91,75)(70,114,97,92,76)(71,115,98,93,77)(72,116,99,94,78)(121,178,163,148,142)(122,179,164,149,143)(123,180,165,150,144)(124,169,166,151,133)(125,170,167,152,134)(126,171,168,153,135)(127,172,157,154,136)(128,173,158,155,137)(129,174,159,156,138)(130,175,160,145,139)(131,176,161,146,140)(132,177,162,147,141)(181,232,223,214,202)(182,233,224,215,203)(183,234,225,216,204)(184,235,226,205,193)(185,236,227,206,194)(186,237,228,207,195)(187,238,217,208,196)(188,239,218,209,197)(189,240,219,210,198)(190,229,220,211,199)(191,230,221,212,200)(192,231,222,213,201), (1,72,4,69,7,66,10,63)(2,67,5,64,8,61,11,70)(3,62,6,71,9,68,12,65)(13,80,16,77,19,74,22,83)(14,75,17,84,20,81,23,78)(15,82,18,79,21,76,24,73)(25,91,28,88,31,85,34,94)(26,86,29,95,32,92,35,89)(27,93,30,90,33,87,36,96)(37,97,40,106,43,103,46,100)(38,104,41,101,44,98,47,107)(39,99,42,108,45,105,48,102)(49,113,52,110,55,119,58,116)(50,120,53,117,56,114,59,111)(51,115,54,112,57,109,60,118)(121,190,130,181,127,184,124,187)(122,185,131,188,128,191,125,182)(123,192,132,183,129,186,126,189)(133,196,142,199,139,202,136,193)(134,203,143,194,140,197,137,200)(135,198,144,201,141,204,138,195)(145,214,154,205,151,208,148,211)(146,209,155,212,152,215,149,206)(147,216,156,207,153,210,150,213)(157,226,166,217,163,220,160,223)(158,221,167,224,164,227,161,218)(159,228,168,219,165,222,162,225)(169,238,178,229,175,232,172,235)(170,233,179,236,176,239,173,230)(171,240,180,231,177,234,174,237), (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), (1,132,7,126)(2,125,8,131)(3,130,9,124)(4,123,10,129)(5,128,11,122)(6,121,12,127)(13,139,19,133)(14,144,20,138)(15,137,21,143)(16,142,22,136)(17,135,23,141)(18,140,24,134)(25,150,31,156)(26,155,32,149)(27,148,33,154)(28,153,34,147)(29,146,35,152)(30,151,36,145)(37,164,43,158)(38,157,44,163)(39,162,45,168)(40,167,46,161)(41,160,47,166)(42,165,48,159)(49,180,55,174)(50,173,56,179)(51,178,57,172)(52,171,58,177)(53,176,59,170)(54,169,60,175)(61,185,67,191)(62,190,68,184)(63,183,69,189)(64,188,70,182)(65,181,71,187)(66,186,72,192)(73,200,79,194)(74,193,80,199)(75,198,81,204)(76,203,82,197)(77,196,83,202)(78,201,84,195)(85,216,91,210)(86,209,92,215)(87,214,93,208)(88,207,94,213)(89,212,95,206)(90,205,96,211)(97,224,103,218)(98,217,104,223)(99,222,105,228)(100,227,106,221)(101,220,107,226)(102,225,108,219)(109,232,115,238)(110,237,116,231)(111,230,117,236)(112,235,118,229)(113,240,119,234)(114,233,120,239) );
G=PermutationGroup([[(1,58,39,34,23),(2,59,40,35,24),(3,60,41,36,13),(4,49,42,25,14),(5,50,43,26,15),(6,51,44,27,16),(7,52,45,28,17),(8,53,46,29,18),(9,54,47,30,19),(10,55,48,31,20),(11,56,37,32,21),(12,57,38,33,22),(61,117,100,95,79),(62,118,101,96,80),(63,119,102,85,81),(64,120,103,86,82),(65,109,104,87,83),(66,110,105,88,84),(67,111,106,89,73),(68,112,107,90,74),(69,113,108,91,75),(70,114,97,92,76),(71,115,98,93,77),(72,116,99,94,78),(121,178,163,148,142),(122,179,164,149,143),(123,180,165,150,144),(124,169,166,151,133),(125,170,167,152,134),(126,171,168,153,135),(127,172,157,154,136),(128,173,158,155,137),(129,174,159,156,138),(130,175,160,145,139),(131,176,161,146,140),(132,177,162,147,141),(181,232,223,214,202),(182,233,224,215,203),(183,234,225,216,204),(184,235,226,205,193),(185,236,227,206,194),(186,237,228,207,195),(187,238,217,208,196),(188,239,218,209,197),(189,240,219,210,198),(190,229,220,211,199),(191,230,221,212,200),(192,231,222,213,201)], [(1,72,4,69,7,66,10,63),(2,67,5,64,8,61,11,70),(3,62,6,71,9,68,12,65),(13,80,16,77,19,74,22,83),(14,75,17,84,20,81,23,78),(15,82,18,79,21,76,24,73),(25,91,28,88,31,85,34,94),(26,86,29,95,32,92,35,89),(27,93,30,90,33,87,36,96),(37,97,40,106,43,103,46,100),(38,104,41,101,44,98,47,107),(39,99,42,108,45,105,48,102),(49,113,52,110,55,119,58,116),(50,120,53,117,56,114,59,111),(51,115,54,112,57,109,60,118),(121,190,130,181,127,184,124,187),(122,185,131,188,128,191,125,182),(123,192,132,183,129,186,126,189),(133,196,142,199,139,202,136,193),(134,203,143,194,140,197,137,200),(135,198,144,201,141,204,138,195),(145,214,154,205,151,208,148,211),(146,209,155,212,152,215,149,206),(147,216,156,207,153,210,150,213),(157,226,166,217,163,220,160,223),(158,221,167,224,164,227,161,218),(159,228,168,219,165,222,162,225),(169,238,178,229,175,232,172,235),(170,233,179,236,176,239,173,230),(171,240,180,231,177,234,174,237)], [(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)], [(1,132,7,126),(2,125,8,131),(3,130,9,124),(4,123,10,129),(5,128,11,122),(6,121,12,127),(13,139,19,133),(14,144,20,138),(15,137,21,143),(16,142,22,136),(17,135,23,141),(18,140,24,134),(25,150,31,156),(26,155,32,149),(27,148,33,154),(28,153,34,147),(29,146,35,152),(30,151,36,145),(37,164,43,158),(38,157,44,163),(39,162,45,168),(40,167,46,161),(41,160,47,166),(42,165,48,159),(49,180,55,174),(50,173,56,179),(51,178,57,172),(52,171,58,177),(53,176,59,170),(54,169,60,175),(61,185,67,191),(62,190,68,184),(63,183,69,189),(64,188,70,182),(65,181,71,187),(66,186,72,192),(73,200,79,194),(74,193,80,199),(75,198,81,204),(76,203,82,197),(77,196,83,202),(78,201,84,195),(85,216,91,210),(86,209,92,215),(87,214,93,208),(88,207,94,213),(89,212,95,206),(90,205,96,211),(97,224,103,218),(98,217,104,223),(99,222,105,228),(100,227,106,221),(101,220,107,226),(102,225,108,219),(109,232,115,238),(110,237,116,231),(111,230,117,236),(112,235,118,229),(113,240,119,234),(114,233,120,239)]])
105 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 5A | 5B | 5C | 5D | 6A | 6B | 8A | 8B | 10A | 10B | 10C | 10D | 10E | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 12A | 12B | 12C | 15A | 15B | 15C | 15D | 20A | ··· | 20H | 20I | ··· | 20T | 24A | 24B | 24C | 24D | 30A | 30B | 30C | 30D | 30E | 30F | 30G | 30H | 40A | ··· | 40H | 60A | ··· | 60H | 60I | 60J | 60K | 60L | 120A | ··· | 120P |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 6 | 8 | 8 | 10 | 10 | 10 | 10 | 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 | 60 | ··· | 60 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 2 | 12 | 2 | 2 | 2 | 12 | 12 | 12 | 1 | 1 | 1 | 1 | 2 | 4 | 4 | 4 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 12 | 12 | 12 | 12 | 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 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
105 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C5 | C10 | C10 | C10 | C10 | C10 | S3 | D4 | D4 | D6 | D6 | D12 | D12 | C5×S3 | C5×D4 | C5×D4 | S3×C10 | S3×C10 | C5×D12 | C5×D12 | C8.C22 | C8.D6 | C5×C8.C22 | C5×C8.D6 |
| kernel | C5×C8.D6 | C5×C24⋊C2 | C5×Dic12 | C15×M4(2) | C10×Dic6 | C5×C4○D12 | C8.D6 | C24⋊C2 | Dic12 | C3×M4(2) | C2×Dic6 | C4○D12 | C5×M4(2) | C60 | C2×C30 | C40 | C2×C20 | C20 | C2×C10 | M4(2) | C12 | C2×C6 | C8 | C2×C4 | C4 | C22 | C15 | C5 | C3 | C1 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 4 | 8 | 8 | 4 | 4 | 4 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 4 | 4 | 4 | 8 | 4 | 8 | 8 | 1 | 2 | 4 | 8 |
Matrix representation of C5×C8.D6 ►in GL4(𝔽241) generated by
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 0 | 0 | 239 | 0 |
| 0 | 0 | 0 | 239 |
| 71 | 142 | 0 | 0 |
| 99 | 170 | 0 | 0 |
| 198 | 99 | 0 | 0 |
| 142 | 99 | 0 | 0 |
| 0 | 0 | 43 | 142 |
| 0 | 0 | 99 | 142 |
| 0 | 0 | 163 | 90 |
| 0 | 0 | 168 | 78 |
| 101 | 143 | 0 | 0 |
| 42 | 140 | 0 | 0 |
G:=sub<GL(4,GF(241))| [98,0,0,0,0,98,0,0,0,0,98,0,0,0,0,98],[0,0,71,99,0,0,142,170,239,0,0,0,0,239,0,0],[198,142,0,0,99,99,0,0,0,0,43,99,0,0,142,142],[0,0,101,42,0,0,143,140,163,168,0,0,90,78,0,0] >;
C5×C8.D6 in GAP, Magma, Sage, TeX
C_5\times C_8.D_6
% in TeX
G:=Group("C5xC8.D6"); // GroupNames label
G:=SmallGroup(480,788);
// by ID
G=gap.SmallGroup(480,788);
# by ID
G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-3,568,926,891,226,4204,102,15686]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^8=1,c^6=d^2=b^4,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^5,d*b*d^-1=b^-1,d*c*d^-1=c^5>;
// generators/relations