direct product, metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C5×C8.Dic3, C24.1C20, C120.15C4, C20.70D12, C60.191D4, C40.10Dic3, (C2×C24).7C10, (C2×C40).15S3, C4.18(C5×D12), C12.34(C5×D4), C30.59(C4⋊C4), (C2×C30).20Q8, C8.1(C5×Dic3), (C2×C120).22C2, C60.246(C2×C4), C12.36(C2×C20), (C2×C20).423D6, C4.8(C10×Dic3), C15⋊12(C8.C4), C20.68(C2×Dic3), (C2×C10).10Dic6, C4.Dic3.1C10, C22.2(C5×Dic6), (C2×C60).535C22, C10.21(C4⋊Dic3), C6.7(C5×C4⋊C4), C3⋊1(C5×C8.C4), (C2×C8).5(C5×S3), (C2×C6).3(C5×Q8), C2.5(C5×C4⋊Dic3), (C2×C4).73(S3×C10), (C2×C12).102(C2×C10), (C5×C4.Dic3).5C2, SmallGroup(480,138)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×C8.Dic3
G = < a,b,c,d | a5=b8=1, c6=b4, d2=b4c3, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c5 >
Subgroups: 100 in 60 conjugacy classes, 42 normal (38 characteristic)
C1, C2, C2, C3, C4 [×2], C22, C5, C6, C6, C8 [×2], C8 [×2], C2×C4, C10, C10, C12 [×2], C2×C6, C15, C2×C8, M4(2) [×2], C20 [×2], C2×C10, C3⋊C8 [×2], C24 [×2], C2×C12, C30, C30, C8.C4, C40 [×2], C40 [×2], C2×C20, C4.Dic3 [×2], C2×C24, C60 [×2], C2×C30, C2×C40, C5×M4(2) [×2], C8.Dic3, C5×C3⋊C8 [×2], C120 [×2], C2×C60, C5×C8.C4, C5×C4.Dic3 [×2], C2×C120, C5×C8.Dic3
Quotients: C1, C2 [×3], C4 [×2], C22, C5, S3, C2×C4, D4, Q8, C10 [×3], Dic3 [×2], D6, C4⋊C4, C20 [×2], C2×C10, Dic6, D12, C2×Dic3, C5×S3, C8.C4, C2×C20, C5×D4, C5×Q8, C4⋊Dic3, C5×Dic3 [×2], S3×C10, C5×C4⋊C4, C8.Dic3, C5×Dic6, C5×D12, C10×Dic3, C5×C8.C4, C5×C4⋊Dic3, C5×C8.Dic3
►On 240 points
Generators in S240
(1 55 43 34 13)(2 56 44 35 14)(3 57 45 36 15)(4 58 46 25 16)(5 59 47 26 17)(6 60 48 27 18)(7 49 37 28 19)(8 50 38 29 20)(9 51 39 30 21)(10 52 40 31 22)(11 53 41 32 23)(12 54 42 33 24)(61 115 106 94 73)(62 116 107 95 74)(63 117 108 96 75)(64 118 97 85 76)(65 119 98 86 77)(66 120 99 87 78)(67 109 100 88 79)(68 110 101 89 80)(69 111 102 90 81)(70 112 103 91 82)(71 113 104 92 83)(72 114 105 93 84)(121 172 166 155 138)(122 173 167 156 139)(123 174 168 145 140)(124 175 157 146 141)(125 176 158 147 142)(126 177 159 148 143)(127 178 160 149 144)(128 179 161 150 133)(129 180 162 151 134)(130 169 163 152 135)(131 170 164 153 136)(132 171 165 154 137)(181 229 225 212 198)(182 230 226 213 199)(183 231 227 214 200)(184 232 228 215 201)(185 233 217 216 202)(186 234 218 205 203)(187 235 219 206 204)(188 236 220 207 193)(189 237 221 208 194)(190 238 222 209 195)(191 239 223 210 196)(192 240 224 211 197)
(1 67 10 64 7 61 4 70)(2 68 11 65 8 62 5 71)(3 69 12 66 9 63 6 72)(13 79 22 76 19 73 16 82)(14 80 23 77 20 74 17 83)(15 81 24 78 21 75 18 84)(25 91 34 88 31 85 28 94)(26 92 35 89 32 86 29 95)(27 93 36 90 33 87 30 96)(37 106 46 103 43 100 40 97)(38 107 47 104 44 101 41 98)(39 108 48 105 45 102 42 99)(49 115 58 112 55 109 52 118)(50 116 59 113 56 110 53 119)(51 117 60 114 57 111 54 120)(121 184 124 187 127 190 130 181)(122 185 125 188 128 191 131 182)(123 186 126 189 129 192 132 183)(133 196 136 199 139 202 142 193)(134 197 137 200 140 203 143 194)(135 198 138 201 141 204 144 195)(145 205 148 208 151 211 154 214)(146 206 149 209 152 212 155 215)(147 207 150 210 153 213 156 216)(157 219 160 222 163 225 166 228)(158 220 161 223 164 226 167 217)(159 221 162 224 165 227 168 218)(169 229 172 232 175 235 178 238)(170 230 173 233 176 236 179 239)(171 231 174 234 177 237 180 240)
(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)
(1 132 10 129 7 126 4 123)(2 125 11 122 8 131 5 128)(3 130 12 127 9 124 6 121)(13 137 22 134 19 143 16 140)(14 142 23 139 20 136 17 133)(15 135 24 144 21 141 18 138)(25 145 34 154 31 151 28 148)(26 150 35 147 32 156 29 153)(27 155 36 152 33 149 30 146)(37 159 46 168 43 165 40 162)(38 164 47 161 44 158 41 167)(39 157 48 166 45 163 42 160)(49 177 58 174 55 171 52 180)(50 170 59 179 56 176 53 173)(51 175 60 172 57 169 54 178)(61 186 70 183 67 192 64 189)(62 191 71 188 68 185 65 182)(63 184 72 181 69 190 66 187)(73 203 82 200 79 197 76 194)(74 196 83 193 80 202 77 199)(75 201 84 198 81 195 78 204)(85 208 94 205 91 214 88 211)(86 213 95 210 92 207 89 216)(87 206 96 215 93 212 90 209)(97 221 106 218 103 227 100 224)(98 226 107 223 104 220 101 217)(99 219 108 228 105 225 102 222)(109 240 118 237 115 234 112 231)(110 233 119 230 116 239 113 236)(111 238 120 235 117 232 114 229)
G:=sub<Sym(240)| (1,55,43,34,13)(2,56,44,35,14)(3,57,45,36,15)(4,58,46,25,16)(5,59,47,26,17)(6,60,48,27,18)(7,49,37,28,19)(8,50,38,29,20)(9,51,39,30,21)(10,52,40,31,22)(11,53,41,32,23)(12,54,42,33,24)(61,115,106,94,73)(62,116,107,95,74)(63,117,108,96,75)(64,118,97,85,76)(65,119,98,86,77)(66,120,99,87,78)(67,109,100,88,79)(68,110,101,89,80)(69,111,102,90,81)(70,112,103,91,82)(71,113,104,92,83)(72,114,105,93,84)(121,172,166,155,138)(122,173,167,156,139)(123,174,168,145,140)(124,175,157,146,141)(125,176,158,147,142)(126,177,159,148,143)(127,178,160,149,144)(128,179,161,150,133)(129,180,162,151,134)(130,169,163,152,135)(131,170,164,153,136)(132,171,165,154,137)(181,229,225,212,198)(182,230,226,213,199)(183,231,227,214,200)(184,232,228,215,201)(185,233,217,216,202)(186,234,218,205,203)(187,235,219,206,204)(188,236,220,207,193)(189,237,221,208,194)(190,238,222,209,195)(191,239,223,210,196)(192,240,224,211,197), (1,67,10,64,7,61,4,70)(2,68,11,65,8,62,5,71)(3,69,12,66,9,63,6,72)(13,79,22,76,19,73,16,82)(14,80,23,77,20,74,17,83)(15,81,24,78,21,75,18,84)(25,91,34,88,31,85,28,94)(26,92,35,89,32,86,29,95)(27,93,36,90,33,87,30,96)(37,106,46,103,43,100,40,97)(38,107,47,104,44,101,41,98)(39,108,48,105,45,102,42,99)(49,115,58,112,55,109,52,118)(50,116,59,113,56,110,53,119)(51,117,60,114,57,111,54,120)(121,184,124,187,127,190,130,181)(122,185,125,188,128,191,131,182)(123,186,126,189,129,192,132,183)(133,196,136,199,139,202,142,193)(134,197,137,200,140,203,143,194)(135,198,138,201,141,204,144,195)(145,205,148,208,151,211,154,214)(146,206,149,209,152,212,155,215)(147,207,150,210,153,213,156,216)(157,219,160,222,163,225,166,228)(158,220,161,223,164,226,167,217)(159,221,162,224,165,227,168,218)(169,229,172,232,175,235,178,238)(170,230,173,233,176,236,179,239)(171,231,174,234,177,237,180,240), (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), (1,132,10,129,7,126,4,123)(2,125,11,122,8,131,5,128)(3,130,12,127,9,124,6,121)(13,137,22,134,19,143,16,140)(14,142,23,139,20,136,17,133)(15,135,24,144,21,141,18,138)(25,145,34,154,31,151,28,148)(26,150,35,147,32,156,29,153)(27,155,36,152,33,149,30,146)(37,159,46,168,43,165,40,162)(38,164,47,161,44,158,41,167)(39,157,48,166,45,163,42,160)(49,177,58,174,55,171,52,180)(50,170,59,179,56,176,53,173)(51,175,60,172,57,169,54,178)(61,186,70,183,67,192,64,189)(62,191,71,188,68,185,65,182)(63,184,72,181,69,190,66,187)(73,203,82,200,79,197,76,194)(74,196,83,193,80,202,77,199)(75,201,84,198,81,195,78,204)(85,208,94,205,91,214,88,211)(86,213,95,210,92,207,89,216)(87,206,96,215,93,212,90,209)(97,221,106,218,103,227,100,224)(98,226,107,223,104,220,101,217)(99,219,108,228,105,225,102,222)(109,240,118,237,115,234,112,231)(110,233,119,230,116,239,113,236)(111,238,120,235,117,232,114,229)>;
G:=Group( (1,55,43,34,13)(2,56,44,35,14)(3,57,45,36,15)(4,58,46,25,16)(5,59,47,26,17)(6,60,48,27,18)(7,49,37,28,19)(8,50,38,29,20)(9,51,39,30,21)(10,52,40,31,22)(11,53,41,32,23)(12,54,42,33,24)(61,115,106,94,73)(62,116,107,95,74)(63,117,108,96,75)(64,118,97,85,76)(65,119,98,86,77)(66,120,99,87,78)(67,109,100,88,79)(68,110,101,89,80)(69,111,102,90,81)(70,112,103,91,82)(71,113,104,92,83)(72,114,105,93,84)(121,172,166,155,138)(122,173,167,156,139)(123,174,168,145,140)(124,175,157,146,141)(125,176,158,147,142)(126,177,159,148,143)(127,178,160,149,144)(128,179,161,150,133)(129,180,162,151,134)(130,169,163,152,135)(131,170,164,153,136)(132,171,165,154,137)(181,229,225,212,198)(182,230,226,213,199)(183,231,227,214,200)(184,232,228,215,201)(185,233,217,216,202)(186,234,218,205,203)(187,235,219,206,204)(188,236,220,207,193)(189,237,221,208,194)(190,238,222,209,195)(191,239,223,210,196)(192,240,224,211,197), (1,67,10,64,7,61,4,70)(2,68,11,65,8,62,5,71)(3,69,12,66,9,63,6,72)(13,79,22,76,19,73,16,82)(14,80,23,77,20,74,17,83)(15,81,24,78,21,75,18,84)(25,91,34,88,31,85,28,94)(26,92,35,89,32,86,29,95)(27,93,36,90,33,87,30,96)(37,106,46,103,43,100,40,97)(38,107,47,104,44,101,41,98)(39,108,48,105,45,102,42,99)(49,115,58,112,55,109,52,118)(50,116,59,113,56,110,53,119)(51,117,60,114,57,111,54,120)(121,184,124,187,127,190,130,181)(122,185,125,188,128,191,131,182)(123,186,126,189,129,192,132,183)(133,196,136,199,139,202,142,193)(134,197,137,200,140,203,143,194)(135,198,138,201,141,204,144,195)(145,205,148,208,151,211,154,214)(146,206,149,209,152,212,155,215)(147,207,150,210,153,213,156,216)(157,219,160,222,163,225,166,228)(158,220,161,223,164,226,167,217)(159,221,162,224,165,227,168,218)(169,229,172,232,175,235,178,238)(170,230,173,233,176,236,179,239)(171,231,174,234,177,237,180,240), (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), (1,132,10,129,7,126,4,123)(2,125,11,122,8,131,5,128)(3,130,12,127,9,124,6,121)(13,137,22,134,19,143,16,140)(14,142,23,139,20,136,17,133)(15,135,24,144,21,141,18,138)(25,145,34,154,31,151,28,148)(26,150,35,147,32,156,29,153)(27,155,36,152,33,149,30,146)(37,159,46,168,43,165,40,162)(38,164,47,161,44,158,41,167)(39,157,48,166,45,163,42,160)(49,177,58,174,55,171,52,180)(50,170,59,179,56,176,53,173)(51,175,60,172,57,169,54,178)(61,186,70,183,67,192,64,189)(62,191,71,188,68,185,65,182)(63,184,72,181,69,190,66,187)(73,203,82,200,79,197,76,194)(74,196,83,193,80,202,77,199)(75,201,84,198,81,195,78,204)(85,208,94,205,91,214,88,211)(86,213,95,210,92,207,89,216)(87,206,96,215,93,212,90,209)(97,221,106,218,103,227,100,224)(98,226,107,223,104,220,101,217)(99,219,108,228,105,225,102,222)(109,240,118,237,115,234,112,231)(110,233,119,230,116,239,113,236)(111,238,120,235,117,232,114,229) );
G=PermutationGroup([(1,55,43,34,13),(2,56,44,35,14),(3,57,45,36,15),(4,58,46,25,16),(5,59,47,26,17),(6,60,48,27,18),(7,49,37,28,19),(8,50,38,29,20),(9,51,39,30,21),(10,52,40,31,22),(11,53,41,32,23),(12,54,42,33,24),(61,115,106,94,73),(62,116,107,95,74),(63,117,108,96,75),(64,118,97,85,76),(65,119,98,86,77),(66,120,99,87,78),(67,109,100,88,79),(68,110,101,89,80),(69,111,102,90,81),(70,112,103,91,82),(71,113,104,92,83),(72,114,105,93,84),(121,172,166,155,138),(122,173,167,156,139),(123,174,168,145,140),(124,175,157,146,141),(125,176,158,147,142),(126,177,159,148,143),(127,178,160,149,144),(128,179,161,150,133),(129,180,162,151,134),(130,169,163,152,135),(131,170,164,153,136),(132,171,165,154,137),(181,229,225,212,198),(182,230,226,213,199),(183,231,227,214,200),(184,232,228,215,201),(185,233,217,216,202),(186,234,218,205,203),(187,235,219,206,204),(188,236,220,207,193),(189,237,221,208,194),(190,238,222,209,195),(191,239,223,210,196),(192,240,224,211,197)], [(1,67,10,64,7,61,4,70),(2,68,11,65,8,62,5,71),(3,69,12,66,9,63,6,72),(13,79,22,76,19,73,16,82),(14,80,23,77,20,74,17,83),(15,81,24,78,21,75,18,84),(25,91,34,88,31,85,28,94),(26,92,35,89,32,86,29,95),(27,93,36,90,33,87,30,96),(37,106,46,103,43,100,40,97),(38,107,47,104,44,101,41,98),(39,108,48,105,45,102,42,99),(49,115,58,112,55,109,52,118),(50,116,59,113,56,110,53,119),(51,117,60,114,57,111,54,120),(121,184,124,187,127,190,130,181),(122,185,125,188,128,191,131,182),(123,186,126,189,129,192,132,183),(133,196,136,199,139,202,142,193),(134,197,137,200,140,203,143,194),(135,198,138,201,141,204,144,195),(145,205,148,208,151,211,154,214),(146,206,149,209,152,212,155,215),(147,207,150,210,153,213,156,216),(157,219,160,222,163,225,166,228),(158,220,161,223,164,226,167,217),(159,221,162,224,165,227,168,218),(169,229,172,232,175,235,178,238),(170,230,173,233,176,236,179,239),(171,231,174,234,177,237,180,240)], [(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)], [(1,132,10,129,7,126,4,123),(2,125,11,122,8,131,5,128),(3,130,12,127,9,124,6,121),(13,137,22,134,19,143,16,140),(14,142,23,139,20,136,17,133),(15,135,24,144,21,141,18,138),(25,145,34,154,31,151,28,148),(26,150,35,147,32,156,29,153),(27,155,36,152,33,149,30,146),(37,159,46,168,43,165,40,162),(38,164,47,161,44,158,41,167),(39,157,48,166,45,163,42,160),(49,177,58,174,55,171,52,180),(50,170,59,179,56,176,53,173),(51,175,60,172,57,169,54,178),(61,186,70,183,67,192,64,189),(62,191,71,188,68,185,65,182),(63,184,72,181,69,190,66,187),(73,203,82,200,79,197,76,194),(74,196,83,193,80,202,77,199),(75,201,84,198,81,195,78,204),(85,208,94,205,91,214,88,211),(86,213,95,210,92,207,89,216),(87,206,96,215,93,212,90,209),(97,221,106,218,103,227,100,224),(98,226,107,223,104,220,101,217),(99,219,108,228,105,225,102,222),(109,240,118,237,115,234,112,231),(110,233,119,230,116,239,113,236),(111,238,120,235,117,232,114,229)])
150 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 4C | 5A | 5B | 5C | 5D | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 10A | 10B | 10C | 10D | 10E | 10F | 10G | 10H | 12A | 12B | 12C | 12D | 15A | 15B | 15C | 15D | 20A | ··· | 20H | 20I | 20J | 20K | 20L | 24A | ··· | 24H | 30A | ··· | 30L | 40A | ··· | 40P | 40Q | ··· | 40AF | 60A | ··· | 60P | 120A | ··· | 120AF |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 20 | 20 | 20 | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 40 | ··· | 40 | 40 | ··· | 40 | 60 | ··· | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 12 | 12 | 12 | 12 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 12 | ··· | 12 | 2 | ··· | 2 | 2 | ··· | 2 |
150 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | - | + | + | - | ||||||||||||||||
| image | C1 | C2 | C2 | C4 | C5 | C10 | C10 | C20 | S3 | D4 | Q8 | Dic3 | D6 | D12 | Dic6 | C5×S3 | C8.C4 | C5×D4 | C5×Q8 | C5×Dic3 | S3×C10 | C8.Dic3 | C5×D12 | C5×Dic6 | C5×C8.C4 | C5×C8.Dic3 |
| kernel | C5×C8.Dic3 | C5×C4.Dic3 | C2×C120 | C120 | C8.Dic3 | C4.Dic3 | C2×C24 | C24 | C2×C40 | C60 | C2×C30 | C40 | C2×C20 | C20 | C2×C10 | C2×C8 | C15 | C12 | C2×C6 | C8 | C2×C4 | C5 | C4 | C22 | C3 | C1 |
| # reps | 1 | 2 | 1 | 4 | 4 | 8 | 4 | 16 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 4 | 8 | 8 | 8 | 16 | 32 |
Matrix representation of C5×C8.Dic3 ►in GL2(𝔽241) generated by
| 205 | 0 |
| 0 | 205 |
| 211 | 0 |
| 103 | 8 |
| 60 | 0 |
| 178 | 4 |
| 58 | 239 |
| 27 | 183 |
G:=sub<GL(2,GF(241))| [205,0,0,205],[211,103,0,8],[60,178,0,4],[58,27,239,183] >;
C5×C8.Dic3 in GAP, Magma, Sage, TeX
C_5\times C_8.{\rm Dic}_3 % in TeX
G:=Group("C5xC8.Dic3"); // GroupNames label
G:=SmallGroup(480,138);
// by ID
G=gap.SmallGroup(480,138);
# by ID
G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,140,589,288,136,4204,102,15686]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^8=1,c^6=b^4,d^2=b^4*c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^5>;
// generators/relations