direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C6×D5⋊C8, D10⋊3C24, D5⋊(C2×C24), C30⋊4(C2×C8), (C6×D5)⋊7C8, C10⋊1(C2×C24), C5⋊1(C22×C24), C15⋊6(C22×C8), C4.19(C6×F5), (C2×C60).22C4, C60.72(C2×C4), (C4×D5).7C12, C12.72(C2×F5), (C2×C12).22F5, (C2×C20).11C12, C20.19(C2×C12), (D5×C12).18C4, C6.45(C22×F5), C22.15(C6×F5), D10.12(C2×C12), C10.1(C22×C12), C30.83(C22×C4), (C22×D5).7C12, Dic5.14(C2×C12), Dic5.9(C22×C6), (D5×C12).137C22, (C3×Dic5).69C23, (C6×Dic5).276C22, (C2×C5⋊C8)⋊6C6, C5⋊C8⋊4(C2×C6), (C6×C5⋊C8)⋊13C2, C2.1(C2×C6×F5), (C3×D5)⋊5(C2×C8), (C2×C4×D5).17C6, (D5×C2×C6).17C4, (C3×C5⋊C8)⋊14C22, (D5×C2×C12).38C2, (C2×C6).58(C2×F5), (C2×C4).11(C3×F5), (C2×C30).56(C2×C4), (C4×D5).34(C2×C6), (C6×D5).61(C2×C4), (C2×C10).13(C2×C12), (C3×Dic5).70(C2×C4), (C2×Dic5).53(C2×C6), SmallGroup(480,1047)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — C6×D5⋊C8 |
Generators and relations for C6×D5⋊C8
G = < a,b,c,d | a6=b5=c2=d8=1, ab=ba, ac=ca, ad=da, cbc=b-1, dbd-1=b3, dcd-1=b2c >
Subgroups: 392 in 152 conjugacy classes, 92 normal (28 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, C5, C6, C6, C6, C8, C2×C4, C2×C4, C23, D5, C10, C10, C12, C12, C2×C6, C2×C6, C15, C2×C8, C22×C4, Dic5, C20, D10, C2×C10, C24, C2×C12, C2×C12, C22×C6, C3×D5, C30, C30, C22×C8, C5⋊C8, C4×D5, C2×Dic5, C2×C20, C22×D5, C2×C24, C22×C12, C3×Dic5, C60, C6×D5, C2×C30, D5⋊C8, C2×C5⋊C8, C2×C4×D5, C22×C24, C3×C5⋊C8, D5×C12, C6×Dic5, C2×C60, D5×C2×C6, C2×D5⋊C8, C3×D5⋊C8, C6×C5⋊C8, D5×C2×C12, C6×D5⋊C8
Quotients: C1, C2, C3, C4, C22, C6, C8, C2×C4, C23, C12, C2×C6, C2×C8, C22×C4, F5, C24, C2×C12, C22×C6, C22×C8, C2×F5, C2×C24, C22×C12, C3×F5, D5⋊C8, C22×F5, C22×C24, C6×F5, C2×D5⋊C8, C3×D5⋊C8, C2×C6×F5, C6×D5⋊C8
►On 240 points
Generators in S240
(1 239 101 51 145 185)(2 240 102 52 146 186)(3 233 103 53 147 187)(4 234 104 54 148 188)(5 235 97 55 149 189)(6 236 98 56 150 190)(7 237 99 49 151 191)(8 238 100 50 152 192)(9 17 57 155 111 207)(10 18 58 156 112 208)(11 19 59 157 105 201)(12 20 60 158 106 202)(13 21 61 159 107 203)(14 22 62 160 108 204)(15 23 63 153 109 205)(16 24 64 154 110 206)(25 65 79 119 215 161)(26 66 80 120 216 162)(27 67 73 113 209 163)(28 68 74 114 210 164)(29 69 75 115 211 165)(30 70 76 116 212 166)(31 71 77 117 213 167)(32 72 78 118 214 168)(33 193 169 221 85 125)(34 194 170 222 86 126)(35 195 171 223 87 127)(36 196 172 224 88 128)(37 197 173 217 81 121)(38 198 174 218 82 122)(39 199 175 219 83 123)(40 200 176 220 84 124)(41 229 95 135 137 177)(42 230 96 136 138 178)(43 231 89 129 139 179)(44 232 90 130 140 180)(45 225 91 131 141 181)(46 226 92 132 142 182)(47 227 93 133 143 183)(48 228 94 134 144 184)
(1 19 77 35 137)(2 36 20 138 78)(3 139 37 79 21)(4 80 140 22 38)(5 23 73 39 141)(6 40 24 142 74)(7 143 33 75 17)(8 76 144 18 34)(9 191 133 125 69)(10 126 192 70 134)(11 71 127 135 185)(12 136 72 186 128)(13 187 129 121 65)(14 122 188 66 130)(15 67 123 131 189)(16 132 68 190 124)(25 203 147 89 81)(26 90 204 82 148)(27 83 91 149 205)(28 150 84 206 92)(29 207 151 93 85)(30 94 208 86 152)(31 87 95 145 201)(32 146 88 202 96)(41 101 157 213 171)(42 214 102 172 158)(43 173 215 159 103)(44 160 174 104 216)(45 97 153 209 175)(46 210 98 176 154)(47 169 211 155 99)(48 156 170 100 212)(49 227 221 165 111)(50 166 228 112 222)(51 105 167 223 229)(52 224 106 230 168)(53 231 217 161 107)(54 162 232 108 218)(55 109 163 219 225)(56 220 110 226 164)(57 237 183 193 115)(58 194 238 116 184)(59 117 195 177 239)(60 178 118 240 196)(61 233 179 197 119)(62 198 234 120 180)(63 113 199 181 235)(64 182 114 236 200)
(1 229)(2 168)(3 107)(4 218)(5 225)(6 164)(7 111)(8 222)(9 99)(10 212)(11 171)(12 158)(13 103)(14 216)(15 175)(16 154)(17 49)(18 166)(19 223)(20 106)(21 53)(22 162)(23 219)(24 110)(25 179)(26 62)(27 113)(28 236)(29 183)(30 58)(31 117)(32 240)(33 221)(34 50)(35 105)(36 230)(37 217)(38 54)(39 109)(40 226)(41 185)(42 128)(43 65)(44 130)(45 189)(46 124)(47 69)(48 134)(51 137)(52 78)(55 141)(56 74)(57 151)(59 87)(60 202)(61 147)(63 83)(64 206)(66 160)(67 209)(68 98)(70 156)(71 213)(72 102)(73 163)(75 227)(76 112)(77 167)(79 231)(80 108)(81 197)(82 234)(84 182)(85 193)(86 238)(88 178)(89 119)(90 180)(91 235)(92 200)(93 115)(94 184)(95 239)(96 196)(97 131)(100 126)(101 135)(104 122)(114 150)(116 208)(118 146)(120 204)(121 173)(123 153)(125 169)(127 157)(129 215)(132 176)(133 211)(136 172)(138 224)(139 161)(140 232)(142 220)(143 165)(144 228)(145 177)(148 198)(149 181)(152 194)(155 191)(159 187)(170 192)(174 188)(186 214)(190 210)(195 201)(199 205)(203 233)(207 237)
(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)
G:=sub<Sym(240)| (1,239,101,51,145,185)(2,240,102,52,146,186)(3,233,103,53,147,187)(4,234,104,54,148,188)(5,235,97,55,149,189)(6,236,98,56,150,190)(7,237,99,49,151,191)(8,238,100,50,152,192)(9,17,57,155,111,207)(10,18,58,156,112,208)(11,19,59,157,105,201)(12,20,60,158,106,202)(13,21,61,159,107,203)(14,22,62,160,108,204)(15,23,63,153,109,205)(16,24,64,154,110,206)(25,65,79,119,215,161)(26,66,80,120,216,162)(27,67,73,113,209,163)(28,68,74,114,210,164)(29,69,75,115,211,165)(30,70,76,116,212,166)(31,71,77,117,213,167)(32,72,78,118,214,168)(33,193,169,221,85,125)(34,194,170,222,86,126)(35,195,171,223,87,127)(36,196,172,224,88,128)(37,197,173,217,81,121)(38,198,174,218,82,122)(39,199,175,219,83,123)(40,200,176,220,84,124)(41,229,95,135,137,177)(42,230,96,136,138,178)(43,231,89,129,139,179)(44,232,90,130,140,180)(45,225,91,131,141,181)(46,226,92,132,142,182)(47,227,93,133,143,183)(48,228,94,134,144,184), (1,19,77,35,137)(2,36,20,138,78)(3,139,37,79,21)(4,80,140,22,38)(5,23,73,39,141)(6,40,24,142,74)(7,143,33,75,17)(8,76,144,18,34)(9,191,133,125,69)(10,126,192,70,134)(11,71,127,135,185)(12,136,72,186,128)(13,187,129,121,65)(14,122,188,66,130)(15,67,123,131,189)(16,132,68,190,124)(25,203,147,89,81)(26,90,204,82,148)(27,83,91,149,205)(28,150,84,206,92)(29,207,151,93,85)(30,94,208,86,152)(31,87,95,145,201)(32,146,88,202,96)(41,101,157,213,171)(42,214,102,172,158)(43,173,215,159,103)(44,160,174,104,216)(45,97,153,209,175)(46,210,98,176,154)(47,169,211,155,99)(48,156,170,100,212)(49,227,221,165,111)(50,166,228,112,222)(51,105,167,223,229)(52,224,106,230,168)(53,231,217,161,107)(54,162,232,108,218)(55,109,163,219,225)(56,220,110,226,164)(57,237,183,193,115)(58,194,238,116,184)(59,117,195,177,239)(60,178,118,240,196)(61,233,179,197,119)(62,198,234,120,180)(63,113,199,181,235)(64,182,114,236,200), (1,229)(2,168)(3,107)(4,218)(5,225)(6,164)(7,111)(8,222)(9,99)(10,212)(11,171)(12,158)(13,103)(14,216)(15,175)(16,154)(17,49)(18,166)(19,223)(20,106)(21,53)(22,162)(23,219)(24,110)(25,179)(26,62)(27,113)(28,236)(29,183)(30,58)(31,117)(32,240)(33,221)(34,50)(35,105)(36,230)(37,217)(38,54)(39,109)(40,226)(41,185)(42,128)(43,65)(44,130)(45,189)(46,124)(47,69)(48,134)(51,137)(52,78)(55,141)(56,74)(57,151)(59,87)(60,202)(61,147)(63,83)(64,206)(66,160)(67,209)(68,98)(70,156)(71,213)(72,102)(73,163)(75,227)(76,112)(77,167)(79,231)(80,108)(81,197)(82,234)(84,182)(85,193)(86,238)(88,178)(89,119)(90,180)(91,235)(92,200)(93,115)(94,184)(95,239)(96,196)(97,131)(100,126)(101,135)(104,122)(114,150)(116,208)(118,146)(120,204)(121,173)(123,153)(125,169)(127,157)(129,215)(132,176)(133,211)(136,172)(138,224)(139,161)(140,232)(142,220)(143,165)(144,228)(145,177)(148,198)(149,181)(152,194)(155,191)(159,187)(170,192)(174,188)(186,214)(190,210)(195,201)(199,205)(203,233)(207,237), (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)>;
G:=Group( (1,239,101,51,145,185)(2,240,102,52,146,186)(3,233,103,53,147,187)(4,234,104,54,148,188)(5,235,97,55,149,189)(6,236,98,56,150,190)(7,237,99,49,151,191)(8,238,100,50,152,192)(9,17,57,155,111,207)(10,18,58,156,112,208)(11,19,59,157,105,201)(12,20,60,158,106,202)(13,21,61,159,107,203)(14,22,62,160,108,204)(15,23,63,153,109,205)(16,24,64,154,110,206)(25,65,79,119,215,161)(26,66,80,120,216,162)(27,67,73,113,209,163)(28,68,74,114,210,164)(29,69,75,115,211,165)(30,70,76,116,212,166)(31,71,77,117,213,167)(32,72,78,118,214,168)(33,193,169,221,85,125)(34,194,170,222,86,126)(35,195,171,223,87,127)(36,196,172,224,88,128)(37,197,173,217,81,121)(38,198,174,218,82,122)(39,199,175,219,83,123)(40,200,176,220,84,124)(41,229,95,135,137,177)(42,230,96,136,138,178)(43,231,89,129,139,179)(44,232,90,130,140,180)(45,225,91,131,141,181)(46,226,92,132,142,182)(47,227,93,133,143,183)(48,228,94,134,144,184), (1,19,77,35,137)(2,36,20,138,78)(3,139,37,79,21)(4,80,140,22,38)(5,23,73,39,141)(6,40,24,142,74)(7,143,33,75,17)(8,76,144,18,34)(9,191,133,125,69)(10,126,192,70,134)(11,71,127,135,185)(12,136,72,186,128)(13,187,129,121,65)(14,122,188,66,130)(15,67,123,131,189)(16,132,68,190,124)(25,203,147,89,81)(26,90,204,82,148)(27,83,91,149,205)(28,150,84,206,92)(29,207,151,93,85)(30,94,208,86,152)(31,87,95,145,201)(32,146,88,202,96)(41,101,157,213,171)(42,214,102,172,158)(43,173,215,159,103)(44,160,174,104,216)(45,97,153,209,175)(46,210,98,176,154)(47,169,211,155,99)(48,156,170,100,212)(49,227,221,165,111)(50,166,228,112,222)(51,105,167,223,229)(52,224,106,230,168)(53,231,217,161,107)(54,162,232,108,218)(55,109,163,219,225)(56,220,110,226,164)(57,237,183,193,115)(58,194,238,116,184)(59,117,195,177,239)(60,178,118,240,196)(61,233,179,197,119)(62,198,234,120,180)(63,113,199,181,235)(64,182,114,236,200), (1,229)(2,168)(3,107)(4,218)(5,225)(6,164)(7,111)(8,222)(9,99)(10,212)(11,171)(12,158)(13,103)(14,216)(15,175)(16,154)(17,49)(18,166)(19,223)(20,106)(21,53)(22,162)(23,219)(24,110)(25,179)(26,62)(27,113)(28,236)(29,183)(30,58)(31,117)(32,240)(33,221)(34,50)(35,105)(36,230)(37,217)(38,54)(39,109)(40,226)(41,185)(42,128)(43,65)(44,130)(45,189)(46,124)(47,69)(48,134)(51,137)(52,78)(55,141)(56,74)(57,151)(59,87)(60,202)(61,147)(63,83)(64,206)(66,160)(67,209)(68,98)(70,156)(71,213)(72,102)(73,163)(75,227)(76,112)(77,167)(79,231)(80,108)(81,197)(82,234)(84,182)(85,193)(86,238)(88,178)(89,119)(90,180)(91,235)(92,200)(93,115)(94,184)(95,239)(96,196)(97,131)(100,126)(101,135)(104,122)(114,150)(116,208)(118,146)(120,204)(121,173)(123,153)(125,169)(127,157)(129,215)(132,176)(133,211)(136,172)(138,224)(139,161)(140,232)(142,220)(143,165)(144,228)(145,177)(148,198)(149,181)(152,194)(155,191)(159,187)(170,192)(174,188)(186,214)(190,210)(195,201)(199,205)(203,233)(207,237), (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) );
G=PermutationGroup([[(1,239,101,51,145,185),(2,240,102,52,146,186),(3,233,103,53,147,187),(4,234,104,54,148,188),(5,235,97,55,149,189),(6,236,98,56,150,190),(7,237,99,49,151,191),(8,238,100,50,152,192),(9,17,57,155,111,207),(10,18,58,156,112,208),(11,19,59,157,105,201),(12,20,60,158,106,202),(13,21,61,159,107,203),(14,22,62,160,108,204),(15,23,63,153,109,205),(16,24,64,154,110,206),(25,65,79,119,215,161),(26,66,80,120,216,162),(27,67,73,113,209,163),(28,68,74,114,210,164),(29,69,75,115,211,165),(30,70,76,116,212,166),(31,71,77,117,213,167),(32,72,78,118,214,168),(33,193,169,221,85,125),(34,194,170,222,86,126),(35,195,171,223,87,127),(36,196,172,224,88,128),(37,197,173,217,81,121),(38,198,174,218,82,122),(39,199,175,219,83,123),(40,200,176,220,84,124),(41,229,95,135,137,177),(42,230,96,136,138,178),(43,231,89,129,139,179),(44,232,90,130,140,180),(45,225,91,131,141,181),(46,226,92,132,142,182),(47,227,93,133,143,183),(48,228,94,134,144,184)], [(1,19,77,35,137),(2,36,20,138,78),(3,139,37,79,21),(4,80,140,22,38),(5,23,73,39,141),(6,40,24,142,74),(7,143,33,75,17),(8,76,144,18,34),(9,191,133,125,69),(10,126,192,70,134),(11,71,127,135,185),(12,136,72,186,128),(13,187,129,121,65),(14,122,188,66,130),(15,67,123,131,189),(16,132,68,190,124),(25,203,147,89,81),(26,90,204,82,148),(27,83,91,149,205),(28,150,84,206,92),(29,207,151,93,85),(30,94,208,86,152),(31,87,95,145,201),(32,146,88,202,96),(41,101,157,213,171),(42,214,102,172,158),(43,173,215,159,103),(44,160,174,104,216),(45,97,153,209,175),(46,210,98,176,154),(47,169,211,155,99),(48,156,170,100,212),(49,227,221,165,111),(50,166,228,112,222),(51,105,167,223,229),(52,224,106,230,168),(53,231,217,161,107),(54,162,232,108,218),(55,109,163,219,225),(56,220,110,226,164),(57,237,183,193,115),(58,194,238,116,184),(59,117,195,177,239),(60,178,118,240,196),(61,233,179,197,119),(62,198,234,120,180),(63,113,199,181,235),(64,182,114,236,200)], [(1,229),(2,168),(3,107),(4,218),(5,225),(6,164),(7,111),(8,222),(9,99),(10,212),(11,171),(12,158),(13,103),(14,216),(15,175),(16,154),(17,49),(18,166),(19,223),(20,106),(21,53),(22,162),(23,219),(24,110),(25,179),(26,62),(27,113),(28,236),(29,183),(30,58),(31,117),(32,240),(33,221),(34,50),(35,105),(36,230),(37,217),(38,54),(39,109),(40,226),(41,185),(42,128),(43,65),(44,130),(45,189),(46,124),(47,69),(48,134),(51,137),(52,78),(55,141),(56,74),(57,151),(59,87),(60,202),(61,147),(63,83),(64,206),(66,160),(67,209),(68,98),(70,156),(71,213),(72,102),(73,163),(75,227),(76,112),(77,167),(79,231),(80,108),(81,197),(82,234),(84,182),(85,193),(86,238),(88,178),(89,119),(90,180),(91,235),(92,200),(93,115),(94,184),(95,239),(96,196),(97,131),(100,126),(101,135),(104,122),(114,150),(116,208),(118,146),(120,204),(121,173),(123,153),(125,169),(127,157),(129,215),(132,176),(133,211),(136,172),(138,224),(139,161),(140,232),(142,220),(143,165),(144,228),(145,177),(148,198),(149,181),(152,194),(155,191),(159,187),(170,192),(174,188),(186,214),(190,210),(195,201),(199,205),(203,233),(207,237)], [(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)]])
120 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5 | 6A | ··· | 6F | 6G | ··· | 6N | 8A | ··· | 8P | 10A | 10B | 10C | 12A | ··· | 12H | 12I | ··· | 12P | 15A | 15B | 20A | 20B | 20C | 20D | 24A | ··· | 24AF | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 6 | ··· | 6 | 6 | ··· | 6 | 8 | ··· | 8 | 10 | 10 | 10 | 12 | ··· | 12 | 12 | ··· | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 4 | 1 | ··· | 1 | 5 | ··· | 5 | 5 | ··· | 5 | 4 | 4 | 4 | 1 | ··· | 1 | 5 | ··· | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | ··· | 5 | 4 | ··· | 4 | 4 | ··· | 4 |
120 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | |||||||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C4 | C4 | C4 | C6 | C6 | C6 | C8 | C12 | C12 | C12 | C24 | F5 | C2×F5 | C2×F5 | C3×F5 | D5⋊C8 | C6×F5 | C6×F5 | C3×D5⋊C8 |
| kernel | C6×D5⋊C8 | C3×D5⋊C8 | C6×C5⋊C8 | D5×C2×C12 | C2×D5⋊C8 | D5×C12 | C2×C60 | D5×C2×C6 | D5⋊C8 | C2×C5⋊C8 | C2×C4×D5 | C6×D5 | C4×D5 | C2×C20 | C22×D5 | D10 | C2×C12 | C12 | C2×C6 | C2×C4 | C6 | C4 | C22 | C2 |
| # reps | 1 | 4 | 2 | 1 | 2 | 4 | 2 | 2 | 8 | 4 | 2 | 16 | 8 | 4 | 4 | 32 | 1 | 2 | 1 | 2 | 4 | 4 | 2 | 8 |
Matrix representation of C6×D5⋊C8 ►in GL5(𝔽241)
| 226 | 0 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 | 0 |
| 0 | 0 | 15 | 0 | 0 |
| 0 | 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 0 | 15 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 240 | 1 | 0 | 0 |
| 0 | 240 | 0 | 1 | 0 |
| 0 | 240 | 0 | 0 | 1 |
| 0 | 240 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 1 |
| 0 | 240 | 0 | 1 | 0 |
| 0 | 240 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 107 | 134 | 175 | 0 |
| 0 | 41 | 134 | 0 | 107 |
| 0 | 107 | 0 | 134 | 41 |
| 0 | 0 | 175 | 134 | 107 |
G:=sub<GL(5,GF(241))| [226,0,0,0,0,0,15,0,0,0,0,0,15,0,0,0,0,0,15,0,0,0,0,0,15],[1,0,0,0,0,0,240,240,240,240,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0],[1,0,0,0,0,0,240,240,240,240,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0],[1,0,0,0,0,0,107,41,107,0,0,134,134,0,175,0,175,0,134,134,0,0,107,41,107] >;
C6×D5⋊C8 in GAP, Magma, Sage, TeX
C_6\times D_5\rtimes C_8
% in TeX
G:=Group("C6xD5:C8"); // GroupNames label
G:=SmallGroup(480,1047);
// by ID
G=gap.SmallGroup(480,1047);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-2,-2,-5,168,268,102,9414,818]);
// Polycyclic
G:=Group<a,b,c,d|a^6=b^5=c^2=d^8=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,d*b*d^-1=b^3,d*c*d^-1=b^2*c>;
// generators/relations