direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D12⋊5D5, D12⋊26D10, C30.12C24, C60.136C23, Dic30⋊35C22, Dic15.7C23, (C4×D5)⋊14D6, (C10×D12)⋊7C2, (C2×D12)⋊15D5, C30⋊6(C4○D4), C10⋊3(C4○D12), C6⋊2(D4⋊2D5), (C2×C20).168D6, C15⋊D4⋊9C22, D6.4(C22×D5), C6.12(C23×D5), (C2×Dic30)⋊30C2, (C2×C12).310D10, (D5×C12)⋊16C22, (C5×D12)⋊22C22, (S3×C10).4C23, C10.12(S3×C23), (S3×Dic5)⋊6C22, (C22×D5).97D6, (C6×D5).39C23, C20.128(C22×S3), (C2×C30).231C23, (C2×C60).154C22, (C2×Dic5).219D6, D10.41(C22×S3), (C22×S3).59D10, C12.160(C22×D5), Dic5.55(C22×S3), (C3×Dic5).41C23, (C6×Dic5).228C22, (C2×Dic15).151C22, (C2×C4×D5)⋊3S3, (D5×C2×C12)⋊4C2, C15⋊6(C2×C4○D4), C5⋊3(C2×C4○D12), C4.86(C2×S3×D5), C3⋊2(C2×D4⋊2D5), (C2×S3×Dic5)⋊20C2, (C2×C15⋊D4)⋊18C2, C2.16(C22×S3×D5), (C2×C4).167(S3×D5), C22.100(C2×S3×D5), (S3×C2×C10).59C22, (D5×C2×C6).116C22, (C2×C6).241(C22×D5), (C2×C10).241(C22×S3), SmallGroup(480,1084)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D12⋊5D5
G = < a,b,c,d,e | a2=b12=c2=d5=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ece=b6c, ede=d-1 >
Subgroups: 1436 in 328 conjugacy classes, 116 normal (26 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, C5, S3, C6, C6, C6, C2×C4, C2×C4, D4, Q8, C23, D5, C10, C10, C10, Dic3, C12, C12, D6, D6, C2×C6, C2×C6, C15, C22×C4, C2×D4, C2×Q8, C4○D4, Dic5, Dic5, C20, D10, D10, C2×C10, C2×C10, Dic6, C4×S3, D12, C2×Dic3, C3⋊D4, C2×C12, C2×C12, C22×S3, C22×C6, C5×S3, C3×D5, C30, C30, C2×C4○D4, Dic10, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C5×D4, C22×D5, C22×C10, C2×Dic6, S3×C2×C4, C2×D12, C4○D12, C2×C3⋊D4, C22×C12, C3×Dic5, Dic15, C60, C6×D5, C6×D5, S3×C10, S3×C10, C2×C30, C2×Dic10, C2×C4×D5, D4⋊2D5, C22×Dic5, C2×C5⋊D4, D4×C10, C2×C4○D12, S3×Dic5, C15⋊D4, D5×C12, C6×Dic5, C5×D12, Dic30, C2×Dic15, C2×C60, D5×C2×C6, S3×C2×C10, C2×D4⋊2D5, D12⋊5D5, C2×S3×Dic5, C2×C15⋊D4, D5×C2×C12, C10×D12, C2×Dic30, C2×D12⋊5D5
Quotients: C1, C2, C22, S3, C23, D5, D6, C4○D4, C24, D10, C22×S3, C2×C4○D4, C22×D5, C4○D12, S3×C23, S3×D5, D4⋊2D5, C23×D5, C2×C4○D12, C2×S3×D5, C2×D4⋊2D5, D12⋊5D5, C22×S3×D5, C2×D12⋊5D5
►On 240 points
Generators in S240
(1 100)(2 101)(3 102)(4 103)(5 104)(6 105)(7 106)(8 107)(9 108)(10 97)(11 98)(12 99)(13 64)(14 65)(15 66)(16 67)(17 68)(18 69)(19 70)(20 71)(21 72)(22 61)(23 62)(24 63)(25 224)(26 225)(27 226)(28 227)(29 228)(30 217)(31 218)(32 219)(33 220)(34 221)(35 222)(36 223)(37 78)(38 79)(39 80)(40 81)(41 82)(42 83)(43 84)(44 73)(45 74)(46 75)(47 76)(48 77)(49 235)(50 236)(51 237)(52 238)(53 239)(54 240)(55 229)(56 230)(57 231)(58 232)(59 233)(60 234)(85 163)(86 164)(87 165)(88 166)(89 167)(90 168)(91 157)(92 158)(93 159)(94 160)(95 161)(96 162)(109 135)(110 136)(111 137)(112 138)(113 139)(114 140)(115 141)(116 142)(117 143)(118 144)(119 133)(120 134)(121 146)(122 147)(123 148)(124 149)(125 150)(126 151)(127 152)(128 153)(129 154)(130 155)(131 156)(132 145)(169 210)(170 211)(171 212)(172 213)(173 214)(174 215)(175 216)(176 205)(177 206)(178 207)(179 208)(180 209)(181 194)(182 195)(183 196)(184 197)(185 198)(186 199)(187 200)(188 201)(189 202)(190 203)(191 204)(192 193)
(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)
(1 200)(2 199)(3 198)(4 197)(5 196)(6 195)(7 194)(8 193)(9 204)(10 203)(11 202)(12 201)(13 235)(14 234)(15 233)(16 232)(17 231)(18 230)(19 229)(20 240)(21 239)(22 238)(23 237)(24 236)(25 176)(26 175)(27 174)(28 173)(29 172)(30 171)(31 170)(32 169)(33 180)(34 179)(35 178)(36 177)(37 129)(38 128)(39 127)(40 126)(41 125)(42 124)(43 123)(44 122)(45 121)(46 132)(47 131)(48 130)(49 64)(50 63)(51 62)(52 61)(53 72)(54 71)(55 70)(56 69)(57 68)(58 67)(59 66)(60 65)(73 147)(74 146)(75 145)(76 156)(77 155)(78 154)(79 153)(80 152)(81 151)(82 150)(83 149)(84 148)(85 134)(86 133)(87 144)(88 143)(89 142)(90 141)(91 140)(92 139)(93 138)(94 137)(95 136)(96 135)(97 190)(98 189)(99 188)(100 187)(101 186)(102 185)(103 184)(104 183)(105 182)(106 181)(107 192)(108 191)(109 162)(110 161)(111 160)(112 159)(113 158)(114 157)(115 168)(116 167)(117 166)(118 165)(119 164)(120 163)(205 224)(206 223)(207 222)(208 221)(209 220)(210 219)(211 218)(212 217)(213 228)(214 227)(215 226)(216 225)
(1 94 51 221 145)(2 95 52 222 146)(3 96 53 223 147)(4 85 54 224 148)(5 86 55 225 149)(6 87 56 226 150)(7 88 57 227 151)(8 89 58 228 152)(9 90 59 217 153)(10 91 60 218 154)(11 92 49 219 155)(12 93 50 220 156)(13 169 48 189 113)(14 170 37 190 114)(15 171 38 191 115)(16 172 39 192 116)(17 173 40 181 117)(18 174 41 182 118)(19 175 42 183 119)(20 176 43 184 120)(21 177 44 185 109)(22 178 45 186 110)(23 179 46 187 111)(24 180 47 188 112)(25 123 103 163 240)(26 124 104 164 229)(27 125 105 165 230)(28 126 106 166 231)(29 127 107 167 232)(30 128 108 168 233)(31 129 97 157 234)(32 130 98 158 235)(33 131 99 159 236)(34 132 100 160 237)(35 121 101 161 238)(36 122 102 162 239)(61 207 74 199 136)(62 208 75 200 137)(63 209 76 201 138)(64 210 77 202 139)(65 211 78 203 140)(66 212 79 204 141)(67 213 80 193 142)(68 214 81 194 143)(69 215 82 195 144)(70 216 83 196 133)(71 205 84 197 134)(72 206 73 198 135)
(1 145)(2 146)(3 147)(4 148)(5 149)(6 150)(7 151)(8 152)(9 153)(10 154)(11 155)(12 156)(13 19)(14 20)(15 21)(16 22)(17 23)(18 24)(25 163)(26 164)(27 165)(28 166)(29 167)(30 168)(31 157)(32 158)(33 159)(34 160)(35 161)(36 162)(37 184)(38 185)(39 186)(40 187)(41 188)(42 189)(43 190)(44 191)(45 192)(46 181)(47 182)(48 183)(61 67)(62 68)(63 69)(64 70)(65 71)(66 72)(73 204)(74 193)(75 194)(76 195)(77 196)(78 197)(79 198)(80 199)(81 200)(82 201)(83 202)(84 203)(85 224)(86 225)(87 226)(88 227)(89 228)(90 217)(91 218)(92 219)(93 220)(94 221)(95 222)(96 223)(97 129)(98 130)(99 131)(100 132)(101 121)(102 122)(103 123)(104 124)(105 125)(106 126)(107 127)(108 128)(109 171)(110 172)(111 173)(112 174)(113 175)(114 176)(115 177)(116 178)(117 179)(118 180)(119 169)(120 170)(133 210)(134 211)(135 212)(136 213)(137 214)(138 215)(139 216)(140 205)(141 206)(142 207)(143 208)(144 209)
G:=sub<Sym(240)| (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,97)(11,98)(12,99)(13,64)(14,65)(15,66)(16,67)(17,68)(18,69)(19,70)(20,71)(21,72)(22,61)(23,62)(24,63)(25,224)(26,225)(27,226)(28,227)(29,228)(30,217)(31,218)(32,219)(33,220)(34,221)(35,222)(36,223)(37,78)(38,79)(39,80)(40,81)(41,82)(42,83)(43,84)(44,73)(45,74)(46,75)(47,76)(48,77)(49,235)(50,236)(51,237)(52,238)(53,239)(54,240)(55,229)(56,230)(57,231)(58,232)(59,233)(60,234)(85,163)(86,164)(87,165)(88,166)(89,167)(90,168)(91,157)(92,158)(93,159)(94,160)(95,161)(96,162)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143)(118,144)(119,133)(120,134)(121,146)(122,147)(123,148)(124,149)(125,150)(126,151)(127,152)(128,153)(129,154)(130,155)(131,156)(132,145)(169,210)(170,211)(171,212)(172,213)(173,214)(174,215)(175,216)(176,205)(177,206)(178,207)(179,208)(180,209)(181,194)(182,195)(183,196)(184,197)(185,198)(186,199)(187,200)(188,201)(189,202)(190,203)(191,204)(192,193), (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), (1,200)(2,199)(3,198)(4,197)(5,196)(6,195)(7,194)(8,193)(9,204)(10,203)(11,202)(12,201)(13,235)(14,234)(15,233)(16,232)(17,231)(18,230)(19,229)(20,240)(21,239)(22,238)(23,237)(24,236)(25,176)(26,175)(27,174)(28,173)(29,172)(30,171)(31,170)(32,169)(33,180)(34,179)(35,178)(36,177)(37,129)(38,128)(39,127)(40,126)(41,125)(42,124)(43,123)(44,122)(45,121)(46,132)(47,131)(48,130)(49,64)(50,63)(51,62)(52,61)(53,72)(54,71)(55,70)(56,69)(57,68)(58,67)(59,66)(60,65)(73,147)(74,146)(75,145)(76,156)(77,155)(78,154)(79,153)(80,152)(81,151)(82,150)(83,149)(84,148)(85,134)(86,133)(87,144)(88,143)(89,142)(90,141)(91,140)(92,139)(93,138)(94,137)(95,136)(96,135)(97,190)(98,189)(99,188)(100,187)(101,186)(102,185)(103,184)(104,183)(105,182)(106,181)(107,192)(108,191)(109,162)(110,161)(111,160)(112,159)(113,158)(114,157)(115,168)(116,167)(117,166)(118,165)(119,164)(120,163)(205,224)(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,228)(214,227)(215,226)(216,225), (1,94,51,221,145)(2,95,52,222,146)(3,96,53,223,147)(4,85,54,224,148)(5,86,55,225,149)(6,87,56,226,150)(7,88,57,227,151)(8,89,58,228,152)(9,90,59,217,153)(10,91,60,218,154)(11,92,49,219,155)(12,93,50,220,156)(13,169,48,189,113)(14,170,37,190,114)(15,171,38,191,115)(16,172,39,192,116)(17,173,40,181,117)(18,174,41,182,118)(19,175,42,183,119)(20,176,43,184,120)(21,177,44,185,109)(22,178,45,186,110)(23,179,46,187,111)(24,180,47,188,112)(25,123,103,163,240)(26,124,104,164,229)(27,125,105,165,230)(28,126,106,166,231)(29,127,107,167,232)(30,128,108,168,233)(31,129,97,157,234)(32,130,98,158,235)(33,131,99,159,236)(34,132,100,160,237)(35,121,101,161,238)(36,122,102,162,239)(61,207,74,199,136)(62,208,75,200,137)(63,209,76,201,138)(64,210,77,202,139)(65,211,78,203,140)(66,212,79,204,141)(67,213,80,193,142)(68,214,81,194,143)(69,215,82,195,144)(70,216,83,196,133)(71,205,84,197,134)(72,206,73,198,135), (1,145)(2,146)(3,147)(4,148)(5,149)(6,150)(7,151)(8,152)(9,153)(10,154)(11,155)(12,156)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,163)(26,164)(27,165)(28,166)(29,167)(30,168)(31,157)(32,158)(33,159)(34,160)(35,161)(36,162)(37,184)(38,185)(39,186)(40,187)(41,188)(42,189)(43,190)(44,191)(45,192)(46,181)(47,182)(48,183)(61,67)(62,68)(63,69)(64,70)(65,71)(66,72)(73,204)(74,193)(75,194)(76,195)(77,196)(78,197)(79,198)(80,199)(81,200)(82,201)(83,202)(84,203)(85,224)(86,225)(87,226)(88,227)(89,228)(90,217)(91,218)(92,219)(93,220)(94,221)(95,222)(96,223)(97,129)(98,130)(99,131)(100,132)(101,121)(102,122)(103,123)(104,124)(105,125)(106,126)(107,127)(108,128)(109,171)(110,172)(111,173)(112,174)(113,175)(114,176)(115,177)(116,178)(117,179)(118,180)(119,169)(120,170)(133,210)(134,211)(135,212)(136,213)(137,214)(138,215)(139,216)(140,205)(141,206)(142,207)(143,208)(144,209)>;
G:=Group( (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,97)(11,98)(12,99)(13,64)(14,65)(15,66)(16,67)(17,68)(18,69)(19,70)(20,71)(21,72)(22,61)(23,62)(24,63)(25,224)(26,225)(27,226)(28,227)(29,228)(30,217)(31,218)(32,219)(33,220)(34,221)(35,222)(36,223)(37,78)(38,79)(39,80)(40,81)(41,82)(42,83)(43,84)(44,73)(45,74)(46,75)(47,76)(48,77)(49,235)(50,236)(51,237)(52,238)(53,239)(54,240)(55,229)(56,230)(57,231)(58,232)(59,233)(60,234)(85,163)(86,164)(87,165)(88,166)(89,167)(90,168)(91,157)(92,158)(93,159)(94,160)(95,161)(96,162)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143)(118,144)(119,133)(120,134)(121,146)(122,147)(123,148)(124,149)(125,150)(126,151)(127,152)(128,153)(129,154)(130,155)(131,156)(132,145)(169,210)(170,211)(171,212)(172,213)(173,214)(174,215)(175,216)(176,205)(177,206)(178,207)(179,208)(180,209)(181,194)(182,195)(183,196)(184,197)(185,198)(186,199)(187,200)(188,201)(189,202)(190,203)(191,204)(192,193), (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), (1,200)(2,199)(3,198)(4,197)(5,196)(6,195)(7,194)(8,193)(9,204)(10,203)(11,202)(12,201)(13,235)(14,234)(15,233)(16,232)(17,231)(18,230)(19,229)(20,240)(21,239)(22,238)(23,237)(24,236)(25,176)(26,175)(27,174)(28,173)(29,172)(30,171)(31,170)(32,169)(33,180)(34,179)(35,178)(36,177)(37,129)(38,128)(39,127)(40,126)(41,125)(42,124)(43,123)(44,122)(45,121)(46,132)(47,131)(48,130)(49,64)(50,63)(51,62)(52,61)(53,72)(54,71)(55,70)(56,69)(57,68)(58,67)(59,66)(60,65)(73,147)(74,146)(75,145)(76,156)(77,155)(78,154)(79,153)(80,152)(81,151)(82,150)(83,149)(84,148)(85,134)(86,133)(87,144)(88,143)(89,142)(90,141)(91,140)(92,139)(93,138)(94,137)(95,136)(96,135)(97,190)(98,189)(99,188)(100,187)(101,186)(102,185)(103,184)(104,183)(105,182)(106,181)(107,192)(108,191)(109,162)(110,161)(111,160)(112,159)(113,158)(114,157)(115,168)(116,167)(117,166)(118,165)(119,164)(120,163)(205,224)(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,228)(214,227)(215,226)(216,225), (1,94,51,221,145)(2,95,52,222,146)(3,96,53,223,147)(4,85,54,224,148)(5,86,55,225,149)(6,87,56,226,150)(7,88,57,227,151)(8,89,58,228,152)(9,90,59,217,153)(10,91,60,218,154)(11,92,49,219,155)(12,93,50,220,156)(13,169,48,189,113)(14,170,37,190,114)(15,171,38,191,115)(16,172,39,192,116)(17,173,40,181,117)(18,174,41,182,118)(19,175,42,183,119)(20,176,43,184,120)(21,177,44,185,109)(22,178,45,186,110)(23,179,46,187,111)(24,180,47,188,112)(25,123,103,163,240)(26,124,104,164,229)(27,125,105,165,230)(28,126,106,166,231)(29,127,107,167,232)(30,128,108,168,233)(31,129,97,157,234)(32,130,98,158,235)(33,131,99,159,236)(34,132,100,160,237)(35,121,101,161,238)(36,122,102,162,239)(61,207,74,199,136)(62,208,75,200,137)(63,209,76,201,138)(64,210,77,202,139)(65,211,78,203,140)(66,212,79,204,141)(67,213,80,193,142)(68,214,81,194,143)(69,215,82,195,144)(70,216,83,196,133)(71,205,84,197,134)(72,206,73,198,135), (1,145)(2,146)(3,147)(4,148)(5,149)(6,150)(7,151)(8,152)(9,153)(10,154)(11,155)(12,156)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,163)(26,164)(27,165)(28,166)(29,167)(30,168)(31,157)(32,158)(33,159)(34,160)(35,161)(36,162)(37,184)(38,185)(39,186)(40,187)(41,188)(42,189)(43,190)(44,191)(45,192)(46,181)(47,182)(48,183)(61,67)(62,68)(63,69)(64,70)(65,71)(66,72)(73,204)(74,193)(75,194)(76,195)(77,196)(78,197)(79,198)(80,199)(81,200)(82,201)(83,202)(84,203)(85,224)(86,225)(87,226)(88,227)(89,228)(90,217)(91,218)(92,219)(93,220)(94,221)(95,222)(96,223)(97,129)(98,130)(99,131)(100,132)(101,121)(102,122)(103,123)(104,124)(105,125)(106,126)(107,127)(108,128)(109,171)(110,172)(111,173)(112,174)(113,175)(114,176)(115,177)(116,178)(117,179)(118,180)(119,169)(120,170)(133,210)(134,211)(135,212)(136,213)(137,214)(138,215)(139,216)(140,205)(141,206)(142,207)(143,208)(144,209) );
G=PermutationGroup([[(1,100),(2,101),(3,102),(4,103),(5,104),(6,105),(7,106),(8,107),(9,108),(10,97),(11,98),(12,99),(13,64),(14,65),(15,66),(16,67),(17,68),(18,69),(19,70),(20,71),(21,72),(22,61),(23,62),(24,63),(25,224),(26,225),(27,226),(28,227),(29,228),(30,217),(31,218),(32,219),(33,220),(34,221),(35,222),(36,223),(37,78),(38,79),(39,80),(40,81),(41,82),(42,83),(43,84),(44,73),(45,74),(46,75),(47,76),(48,77),(49,235),(50,236),(51,237),(52,238),(53,239),(54,240),(55,229),(56,230),(57,231),(58,232),(59,233),(60,234),(85,163),(86,164),(87,165),(88,166),(89,167),(90,168),(91,157),(92,158),(93,159),(94,160),(95,161),(96,162),(109,135),(110,136),(111,137),(112,138),(113,139),(114,140),(115,141),(116,142),(117,143),(118,144),(119,133),(120,134),(121,146),(122,147),(123,148),(124,149),(125,150),(126,151),(127,152),(128,153),(129,154),(130,155),(131,156),(132,145),(169,210),(170,211),(171,212),(172,213),(173,214),(174,215),(175,216),(176,205),(177,206),(178,207),(179,208),(180,209),(181,194),(182,195),(183,196),(184,197),(185,198),(186,199),(187,200),(188,201),(189,202),(190,203),(191,204),(192,193)], [(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)], [(1,200),(2,199),(3,198),(4,197),(5,196),(6,195),(7,194),(8,193),(9,204),(10,203),(11,202),(12,201),(13,235),(14,234),(15,233),(16,232),(17,231),(18,230),(19,229),(20,240),(21,239),(22,238),(23,237),(24,236),(25,176),(26,175),(27,174),(28,173),(29,172),(30,171),(31,170),(32,169),(33,180),(34,179),(35,178),(36,177),(37,129),(38,128),(39,127),(40,126),(41,125),(42,124),(43,123),(44,122),(45,121),(46,132),(47,131),(48,130),(49,64),(50,63),(51,62),(52,61),(53,72),(54,71),(55,70),(56,69),(57,68),(58,67),(59,66),(60,65),(73,147),(74,146),(75,145),(76,156),(77,155),(78,154),(79,153),(80,152),(81,151),(82,150),(83,149),(84,148),(85,134),(86,133),(87,144),(88,143),(89,142),(90,141),(91,140),(92,139),(93,138),(94,137),(95,136),(96,135),(97,190),(98,189),(99,188),(100,187),(101,186),(102,185),(103,184),(104,183),(105,182),(106,181),(107,192),(108,191),(109,162),(110,161),(111,160),(112,159),(113,158),(114,157),(115,168),(116,167),(117,166),(118,165),(119,164),(120,163),(205,224),(206,223),(207,222),(208,221),(209,220),(210,219),(211,218),(212,217),(213,228),(214,227),(215,226),(216,225)], [(1,94,51,221,145),(2,95,52,222,146),(3,96,53,223,147),(4,85,54,224,148),(5,86,55,225,149),(6,87,56,226,150),(7,88,57,227,151),(8,89,58,228,152),(9,90,59,217,153),(10,91,60,218,154),(11,92,49,219,155),(12,93,50,220,156),(13,169,48,189,113),(14,170,37,190,114),(15,171,38,191,115),(16,172,39,192,116),(17,173,40,181,117),(18,174,41,182,118),(19,175,42,183,119),(20,176,43,184,120),(21,177,44,185,109),(22,178,45,186,110),(23,179,46,187,111),(24,180,47,188,112),(25,123,103,163,240),(26,124,104,164,229),(27,125,105,165,230),(28,126,106,166,231),(29,127,107,167,232),(30,128,108,168,233),(31,129,97,157,234),(32,130,98,158,235),(33,131,99,159,236),(34,132,100,160,237),(35,121,101,161,238),(36,122,102,162,239),(61,207,74,199,136),(62,208,75,200,137),(63,209,76,201,138),(64,210,77,202,139),(65,211,78,203,140),(66,212,79,204,141),(67,213,80,193,142),(68,214,81,194,143),(69,215,82,195,144),(70,216,83,196,133),(71,205,84,197,134),(72,206,73,198,135)], [(1,145),(2,146),(3,147),(4,148),(5,149),(6,150),(7,151),(8,152),(9,153),(10,154),(11,155),(12,156),(13,19),(14,20),(15,21),(16,22),(17,23),(18,24),(25,163),(26,164),(27,165),(28,166),(29,167),(30,168),(31,157),(32,158),(33,159),(34,160),(35,161),(36,162),(37,184),(38,185),(39,186),(40,187),(41,188),(42,189),(43,190),(44,191),(45,192),(46,181),(47,182),(48,183),(61,67),(62,68),(63,69),(64,70),(65,71),(66,72),(73,204),(74,193),(75,194),(76,195),(77,196),(78,197),(79,198),(80,199),(81,200),(82,201),(83,202),(84,203),(85,224),(86,225),(87,226),(88,227),(89,228),(90,217),(91,218),(92,219),(93,220),(94,221),(95,222),(96,223),(97,129),(98,130),(99,131),(100,132),(101,121),(102,122),(103,123),(104,124),(105,125),(106,126),(107,127),(108,128),(109,171),(110,172),(111,173),(112,174),(113,175),(114,176),(115,177),(116,178),(117,179),(118,180),(119,169),(120,170),(133,210),(134,211),(135,212),(136,213),(137,214),(138,215),(139,216),(140,205),(141,206),(142,207),(143,208),(144,209)]])
72 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 6A | 6B | 6C | 6D | 6E | 6F | 6G | 10A | ··· | 10F | 10G | ··· | 10N | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H | 15A | 15B | 20A | 20B | 20C | 20D | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 10 | ··· | 10 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 6 | 6 | 6 | 6 | 10 | 10 | 2 | 2 | 2 | 5 | 5 | 5 | 5 | 30 | 30 | 30 | 30 | 2 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 2 | ··· | 2 | 12 | ··· | 12 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 |
72 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D5 | D6 | D6 | D6 | D6 | C4○D4 | D10 | D10 | D10 | C4○D12 | S3×D5 | D4⋊2D5 | C2×S3×D5 | C2×S3×D5 | D12⋊5D5 |
| kernel | C2×D12⋊5D5 | D12⋊5D5 | C2×S3×Dic5 | C2×C15⋊D4 | D5×C2×C12 | C10×D12 | C2×Dic30 | C2×C4×D5 | C2×D12 | C4×D5 | C2×Dic5 | C2×C20 | C22×D5 | C30 | D12 | C2×C12 | C22×S3 | C10 | C2×C4 | C6 | C4 | C22 | C2 |
| # reps | 1 | 8 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 4 | 1 | 1 | 1 | 4 | 8 | 2 | 4 | 8 | 2 | 4 | 4 | 2 | 8 |
Matrix representation of C2×D12⋊5D5 ►in GL4(𝔽61) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 29 | 0 | 0 | 0 |
| 51 | 40 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 46 | 47 | 0 | 0 |
| 16 | 15 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 60 |
| 0 | 0 | 1 | 17 |
| 1 | 0 | 0 | 0 |
| 24 | 60 | 0 | 0 |
| 0 | 0 | 44 | 60 |
| 0 | 0 | 44 | 17 |
G:=sub<GL(4,GF(61))| [1,0,0,0,0,1,0,0,0,0,60,0,0,0,0,60],[29,51,0,0,0,40,0,0,0,0,60,0,0,0,0,60],[46,16,0,0,47,15,0,0,0,0,60,0,0,0,0,60],[1,0,0,0,0,1,0,0,0,0,0,1,0,0,60,17],[1,24,0,0,0,60,0,0,0,0,44,44,0,0,60,17] >;
C2×D12⋊5D5 in GAP, Magma, Sage, TeX
C_2\times D_{12}\rtimes_5D_5 % in TeX
G:=Group("C2xD12:5D5"); // GroupNames label
G:=SmallGroup(480,1084);
// by ID
G=gap.SmallGroup(480,1084);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,346,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^12=c^2=d^5=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=b^6*c,e*d*e=d^-1>;
// generators/relations