G = C15⋊26(C4×D4) order 480 = 25·3·5
2nd semidirect product of C15 and C4×D4 acting via C4×D4/C23=C22
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C15⋊26(C4×D4), C15⋊7D4⋊4C4, D30⋊16(C2×C4), C6.160(D4×D5), (C3×Dic5)⋊15D4, C30.232(C2×D4), D30⋊4C4⋊29C2, C23.42(S3×D5), Dic15⋊11(C2×C4), C6.D4⋊15D5, Dic5⋊8(C3⋊D4), C3⋊6(Dic5⋊4D4), Dic15⋊5C4⋊34C2, (C22×Dic5)⋊9S3, (C22×C6).92D10, (C22×C10).49D6, (Dic3×Dic5)⋊34C2, C10.82(C4○D12), C30.147(C4○D4), C6.55(D4⋊2D5), (C2×C30).194C23, C30.145(C22×C4), C22⋊3(D30.C2), (C2×Dic5).194D6, (C2×Dic3).122D10, C2.7(Dic3.D10), (C22×C30).56C22, (C6×Dic5).223C22, (C22×D15).63C22, (C2×Dic15).134C22, (C10×Dic3).113C22, C5⋊5(C4×C3⋊D4), (C2×C6)⋊8(C4×D5), C6.54(C2×C4×D5), C10.86(S3×C2×C4), (C2×C6×Dic5)⋊6C2, C2.7(D5×C3⋊D4), (C2×C30)⋊16(C2×C4), (C2×C10)⋊11(C4×S3), C22.85(C2×S3×D5), C10.64(C2×C3⋊D4), (C2×D30.C2)⋊14C2, (C2×C15⋊7D4).11C2, C2.18(C2×D30.C2), (C5×C6.D4)⋊11C2, (C2×C6).206(C22×D5), (C2×C10).206(C22×S3), SmallGroup(480,628)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C15⋊26(C4×D4)
G = < a,b,c,d | a15=b4=c4=d2=1, bab-1=a4, cac-1=dad=a-1, bc=cb, bd=db, dcd=c-1 >
Subgroups: 924 in 188 conjugacy classes, 64 normal (44 characteristic)
C1, C2, C2, C3, C4, C22, C22, C22, C5, S3, C6, C6, C2×C4, D4, C23, C23, D5, C10, C10, Dic3, C12, D6, C2×C6, C2×C6, C2×C6, C15, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, C4×S3, C2×Dic3, C2×Dic3, C3⋊D4, C2×C12, C22×S3, C22×C6, D15, C30, C30, C4×D4, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C22×D5, C22×C10, C4×Dic3, Dic3⋊C4, D6⋊C4, C6.D4, S3×C2×C4, C2×C3⋊D4, C22×C12, C5×Dic3, C3×Dic5, C3×Dic5, Dic15, D30, D30, C2×C30, C2×C30, C2×C30, C4×Dic5, C10.D4, D10⋊C4, C5×C22⋊C4, C2×C4×D5, C22×Dic5, C2×C5⋊D4, C4×C3⋊D4, D30.C2, C6×Dic5, C6×Dic5, C10×Dic3, C2×Dic15, C15⋊7D4, C22×D15, C22×C30, Dic5⋊4D4, Dic3×Dic5, D30⋊4C4, Dic15⋊5C4, C5×C6.D4, C2×D30.C2, C2×C6×Dic5, C2×C15⋊7D4, C15⋊26(C4×D4)
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, C23, D5, D6, C22×C4, C2×D4, C4○D4, D10, C4×S3, C3⋊D4, C22×S3, C4×D4, C4×D5, C22×D5, S3×C2×C4, C4○D12, C2×C3⋊D4, S3×D5, C2×C4×D5, D4×D5, D4⋊2D5, C4×C3⋊D4, D30.C2, C2×S3×D5, Dic5⋊4D4, Dic3.D10, C2×D30.C2, D5×C3⋊D4, C15⋊26(C4×D4)
►On 240 points
Generators in S240
(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)
(1 157 32 121)(2 161 33 125)(3 165 34 129)(4 154 35 133)(5 158 36 122)(6 162 37 126)(7 151 38 130)(8 155 39 134)(9 159 40 123)(10 163 41 127)(11 152 42 131)(12 156 43 135)(13 160 44 124)(14 164 45 128)(15 153 31 132)(16 179 60 138)(17 168 46 142)(18 172 47 146)(19 176 48 150)(20 180 49 139)(21 169 50 143)(22 173 51 147)(23 177 52 136)(24 166 53 140)(25 170 54 144)(26 174 55 148)(27 178 56 137)(28 167 57 141)(29 171 58 145)(30 175 59 149)(61 228 94 204)(62 232 95 208)(63 236 96 197)(64 240 97 201)(65 229 98 205)(66 233 99 209)(67 237 100 198)(68 226 101 202)(69 230 102 206)(70 234 103 210)(71 238 104 199)(72 227 105 203)(73 231 91 207)(74 235 92 196)(75 239 93 200)(76 215 106 184)(77 219 107 188)(78 223 108 192)(79 212 109 181)(80 216 110 185)(81 220 111 189)(82 224 112 193)(83 213 113 182)(84 217 114 186)(85 221 115 190)(86 225 116 194)(87 214 117 183)(88 218 118 187)(89 222 119 191)(90 211 120 195)
(1 95 17 118)(2 94 18 117)(3 93 19 116)(4 92 20 115)(5 91 21 114)(6 105 22 113)(7 104 23 112)(8 103 24 111)(9 102 25 110)(10 101 26 109)(11 100 27 108)(12 99 28 107)(13 98 29 106)(14 97 30 120)(15 96 16 119)(31 63 60 89)(32 62 46 88)(33 61 47 87)(34 75 48 86)(35 74 49 85)(36 73 50 84)(37 72 51 83)(38 71 52 82)(39 70 53 81)(40 69 54 80)(41 68 55 79)(42 67 56 78)(43 66 57 77)(44 65 58 76)(45 64 59 90)(121 232 142 218)(122 231 143 217)(123 230 144 216)(124 229 145 215)(125 228 146 214)(126 227 147 213)(127 226 148 212)(128 240 149 211)(129 239 150 225)(130 238 136 224)(131 237 137 223)(132 236 138 222)(133 235 139 221)(134 234 140 220)(135 233 141 219)(151 199 177 193)(152 198 178 192)(153 197 179 191)(154 196 180 190)(155 210 166 189)(156 209 167 188)(157 208 168 187)(158 207 169 186)(159 206 170 185)(160 205 171 184)(161 204 172 183)(162 203 173 182)(163 202 174 181)(164 201 175 195)(165 200 176 194)
(2 15)(3 14)(4 13)(5 12)(6 11)(7 10)(8 9)(16 18)(19 30)(20 29)(21 28)(22 27)(23 26)(24 25)(31 33)(34 45)(35 44)(36 43)(37 42)(38 41)(39 40)(47 60)(48 59)(49 58)(50 57)(51 56)(52 55)(53 54)(61 89)(62 88)(63 87)(64 86)(65 85)(66 84)(67 83)(68 82)(69 81)(70 80)(71 79)(72 78)(73 77)(74 76)(75 90)(91 107)(92 106)(93 120)(94 119)(95 118)(96 117)(97 116)(98 115)(99 114)(100 113)(101 112)(102 111)(103 110)(104 109)(105 108)(122 135)(123 134)(124 133)(125 132)(126 131)(127 130)(128 129)(136 148)(137 147)(138 146)(139 145)(140 144)(141 143)(149 150)(151 163)(152 162)(153 161)(154 160)(155 159)(156 158)(164 165)(166 170)(167 169)(171 180)(172 179)(173 178)(174 177)(175 176)(181 199)(182 198)(183 197)(184 196)(185 210)(186 209)(187 208)(188 207)(189 206)(190 205)(191 204)(192 203)(193 202)(194 201)(195 200)(211 239)(212 238)(213 237)(214 236)(215 235)(216 234)(217 233)(218 232)(219 231)(220 230)(221 229)(222 228)(223 227)(224 226)(225 240)
G:=sub<Sym(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), (1,157,32,121)(2,161,33,125)(3,165,34,129)(4,154,35,133)(5,158,36,122)(6,162,37,126)(7,151,38,130)(8,155,39,134)(9,159,40,123)(10,163,41,127)(11,152,42,131)(12,156,43,135)(13,160,44,124)(14,164,45,128)(15,153,31,132)(16,179,60,138)(17,168,46,142)(18,172,47,146)(19,176,48,150)(20,180,49,139)(21,169,50,143)(22,173,51,147)(23,177,52,136)(24,166,53,140)(25,170,54,144)(26,174,55,148)(27,178,56,137)(28,167,57,141)(29,171,58,145)(30,175,59,149)(61,228,94,204)(62,232,95,208)(63,236,96,197)(64,240,97,201)(65,229,98,205)(66,233,99,209)(67,237,100,198)(68,226,101,202)(69,230,102,206)(70,234,103,210)(71,238,104,199)(72,227,105,203)(73,231,91,207)(74,235,92,196)(75,239,93,200)(76,215,106,184)(77,219,107,188)(78,223,108,192)(79,212,109,181)(80,216,110,185)(81,220,111,189)(82,224,112,193)(83,213,113,182)(84,217,114,186)(85,221,115,190)(86,225,116,194)(87,214,117,183)(88,218,118,187)(89,222,119,191)(90,211,120,195), (1,95,17,118)(2,94,18,117)(3,93,19,116)(4,92,20,115)(5,91,21,114)(6,105,22,113)(7,104,23,112)(8,103,24,111)(9,102,25,110)(10,101,26,109)(11,100,27,108)(12,99,28,107)(13,98,29,106)(14,97,30,120)(15,96,16,119)(31,63,60,89)(32,62,46,88)(33,61,47,87)(34,75,48,86)(35,74,49,85)(36,73,50,84)(37,72,51,83)(38,71,52,82)(39,70,53,81)(40,69,54,80)(41,68,55,79)(42,67,56,78)(43,66,57,77)(44,65,58,76)(45,64,59,90)(121,232,142,218)(122,231,143,217)(123,230,144,216)(124,229,145,215)(125,228,146,214)(126,227,147,213)(127,226,148,212)(128,240,149,211)(129,239,150,225)(130,238,136,224)(131,237,137,223)(132,236,138,222)(133,235,139,221)(134,234,140,220)(135,233,141,219)(151,199,177,193)(152,198,178,192)(153,197,179,191)(154,196,180,190)(155,210,166,189)(156,209,167,188)(157,208,168,187)(158,207,169,186)(159,206,170,185)(160,205,171,184)(161,204,172,183)(162,203,173,182)(163,202,174,181)(164,201,175,195)(165,200,176,194), (2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)(16,18)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(31,33)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)(61,89)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)(75,90)(91,107)(92,106)(93,120)(94,119)(95,118)(96,117)(97,116)(98,115)(99,114)(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)(136,148)(137,147)(138,146)(139,145)(140,144)(141,143)(149,150)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(164,165)(166,170)(167,169)(171,180)(172,179)(173,178)(174,177)(175,176)(181,199)(182,198)(183,197)(184,196)(185,210)(186,209)(187,208)(188,207)(189,206)(190,205)(191,204)(192,203)(193,202)(194,201)(195,200)(211,239)(212,238)(213,237)(214,236)(215,235)(216,234)(217,233)(218,232)(219,231)(220,230)(221,229)(222,228)(223,227)(224,226)(225,240)>;
G:=Group( (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), (1,157,32,121)(2,161,33,125)(3,165,34,129)(4,154,35,133)(5,158,36,122)(6,162,37,126)(7,151,38,130)(8,155,39,134)(9,159,40,123)(10,163,41,127)(11,152,42,131)(12,156,43,135)(13,160,44,124)(14,164,45,128)(15,153,31,132)(16,179,60,138)(17,168,46,142)(18,172,47,146)(19,176,48,150)(20,180,49,139)(21,169,50,143)(22,173,51,147)(23,177,52,136)(24,166,53,140)(25,170,54,144)(26,174,55,148)(27,178,56,137)(28,167,57,141)(29,171,58,145)(30,175,59,149)(61,228,94,204)(62,232,95,208)(63,236,96,197)(64,240,97,201)(65,229,98,205)(66,233,99,209)(67,237,100,198)(68,226,101,202)(69,230,102,206)(70,234,103,210)(71,238,104,199)(72,227,105,203)(73,231,91,207)(74,235,92,196)(75,239,93,200)(76,215,106,184)(77,219,107,188)(78,223,108,192)(79,212,109,181)(80,216,110,185)(81,220,111,189)(82,224,112,193)(83,213,113,182)(84,217,114,186)(85,221,115,190)(86,225,116,194)(87,214,117,183)(88,218,118,187)(89,222,119,191)(90,211,120,195), (1,95,17,118)(2,94,18,117)(3,93,19,116)(4,92,20,115)(5,91,21,114)(6,105,22,113)(7,104,23,112)(8,103,24,111)(9,102,25,110)(10,101,26,109)(11,100,27,108)(12,99,28,107)(13,98,29,106)(14,97,30,120)(15,96,16,119)(31,63,60,89)(32,62,46,88)(33,61,47,87)(34,75,48,86)(35,74,49,85)(36,73,50,84)(37,72,51,83)(38,71,52,82)(39,70,53,81)(40,69,54,80)(41,68,55,79)(42,67,56,78)(43,66,57,77)(44,65,58,76)(45,64,59,90)(121,232,142,218)(122,231,143,217)(123,230,144,216)(124,229,145,215)(125,228,146,214)(126,227,147,213)(127,226,148,212)(128,240,149,211)(129,239,150,225)(130,238,136,224)(131,237,137,223)(132,236,138,222)(133,235,139,221)(134,234,140,220)(135,233,141,219)(151,199,177,193)(152,198,178,192)(153,197,179,191)(154,196,180,190)(155,210,166,189)(156,209,167,188)(157,208,168,187)(158,207,169,186)(159,206,170,185)(160,205,171,184)(161,204,172,183)(162,203,173,182)(163,202,174,181)(164,201,175,195)(165,200,176,194), (2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)(16,18)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(31,33)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)(61,89)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)(75,90)(91,107)(92,106)(93,120)(94,119)(95,118)(96,117)(97,116)(98,115)(99,114)(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)(136,148)(137,147)(138,146)(139,145)(140,144)(141,143)(149,150)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(164,165)(166,170)(167,169)(171,180)(172,179)(173,178)(174,177)(175,176)(181,199)(182,198)(183,197)(184,196)(185,210)(186,209)(187,208)(188,207)(189,206)(190,205)(191,204)(192,203)(193,202)(194,201)(195,200)(211,239)(212,238)(213,237)(214,236)(215,235)(216,234)(217,233)(218,232)(219,231)(220,230)(221,229)(222,228)(223,227)(224,226)(225,240) );
G=PermutationGroup([[(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)], [(1,157,32,121),(2,161,33,125),(3,165,34,129),(4,154,35,133),(5,158,36,122),(6,162,37,126),(7,151,38,130),(8,155,39,134),(9,159,40,123),(10,163,41,127),(11,152,42,131),(12,156,43,135),(13,160,44,124),(14,164,45,128),(15,153,31,132),(16,179,60,138),(17,168,46,142),(18,172,47,146),(19,176,48,150),(20,180,49,139),(21,169,50,143),(22,173,51,147),(23,177,52,136),(24,166,53,140),(25,170,54,144),(26,174,55,148),(27,178,56,137),(28,167,57,141),(29,171,58,145),(30,175,59,149),(61,228,94,204),(62,232,95,208),(63,236,96,197),(64,240,97,201),(65,229,98,205),(66,233,99,209),(67,237,100,198),(68,226,101,202),(69,230,102,206),(70,234,103,210),(71,238,104,199),(72,227,105,203),(73,231,91,207),(74,235,92,196),(75,239,93,200),(76,215,106,184),(77,219,107,188),(78,223,108,192),(79,212,109,181),(80,216,110,185),(81,220,111,189),(82,224,112,193),(83,213,113,182),(84,217,114,186),(85,221,115,190),(86,225,116,194),(87,214,117,183),(88,218,118,187),(89,222,119,191),(90,211,120,195)], [(1,95,17,118),(2,94,18,117),(3,93,19,116),(4,92,20,115),(5,91,21,114),(6,105,22,113),(7,104,23,112),(8,103,24,111),(9,102,25,110),(10,101,26,109),(11,100,27,108),(12,99,28,107),(13,98,29,106),(14,97,30,120),(15,96,16,119),(31,63,60,89),(32,62,46,88),(33,61,47,87),(34,75,48,86),(35,74,49,85),(36,73,50,84),(37,72,51,83),(38,71,52,82),(39,70,53,81),(40,69,54,80),(41,68,55,79),(42,67,56,78),(43,66,57,77),(44,65,58,76),(45,64,59,90),(121,232,142,218),(122,231,143,217),(123,230,144,216),(124,229,145,215),(125,228,146,214),(126,227,147,213),(127,226,148,212),(128,240,149,211),(129,239,150,225),(130,238,136,224),(131,237,137,223),(132,236,138,222),(133,235,139,221),(134,234,140,220),(135,233,141,219),(151,199,177,193),(152,198,178,192),(153,197,179,191),(154,196,180,190),(155,210,166,189),(156,209,167,188),(157,208,168,187),(158,207,169,186),(159,206,170,185),(160,205,171,184),(161,204,172,183),(162,203,173,182),(163,202,174,181),(164,201,175,195),(165,200,176,194)], [(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(16,18),(19,30),(20,29),(21,28),(22,27),(23,26),(24,25),(31,33),(34,45),(35,44),(36,43),(37,42),(38,41),(39,40),(47,60),(48,59),(49,58),(50,57),(51,56),(52,55),(53,54),(61,89),(62,88),(63,87),(64,86),(65,85),(66,84),(67,83),(68,82),(69,81),(70,80),(71,79),(72,78),(73,77),(74,76),(75,90),(91,107),(92,106),(93,120),(94,119),(95,118),(96,117),(97,116),(98,115),(99,114),(100,113),(101,112),(102,111),(103,110),(104,109),(105,108),(122,135),(123,134),(124,133),(125,132),(126,131),(127,130),(128,129),(136,148),(137,147),(138,146),(139,145),(140,144),(141,143),(149,150),(151,163),(152,162),(153,161),(154,160),(155,159),(156,158),(164,165),(166,170),(167,169),(171,180),(172,179),(173,178),(174,177),(175,176),(181,199),(182,198),(183,197),(184,196),(185,210),(186,209),(187,208),(188,207),(189,206),(190,205),(191,204),(192,203),(193,202),(194,201),(195,200),(211,239),(212,238),(213,237),(214,236),(215,235),(216,234),(217,233),(218,232),(219,231),(220,230),(221,229),(222,228),(223,227),(224,226),(225,240)]])
72 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 6A | ··· | 6G | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 12A | ··· | 12H | 15A | 15B | 20A | ··· | 20H | 30A | ··· | 30N |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 12 | ··· | 12 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 30 | 30 | 2 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | 6 | 10 | 10 | 30 | 30 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | 4 | 12 | ··· | 12 | 4 | ··· | 4 |
72 irreducible representations
| dim | 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 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | S3 | D4 | D5 | D6 | D6 | C4○D4 | D10 | D10 | C3⋊D4 | C4×S3 | C4×D5 | C4○D12 | S3×D5 | D4×D5 | D4⋊2D5 | D30.C2 | C2×S3×D5 | Dic3.D10 | D5×C3⋊D4 |
| kernel | C15⋊26(C4×D4) | Dic3×Dic5 | D30⋊4C4 | Dic15⋊5C4 | C5×C6.D4 | C2×D30.C2 | C2×C6×Dic5 | C2×C15⋊7D4 | C15⋊7D4 | C22×Dic5 | C3×Dic5 | C6.D4 | C2×Dic5 | C22×C10 | C30 | C2×Dic3 | C22×C6 | Dic5 | C2×C10 | C2×C6 | C10 | C23 | C6 | C6 | C22 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 2 | 2 | 2 | 1 | 2 | 4 | 2 | 4 | 4 | 8 | 4 | 2 | 2 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of C15⋊26(C4×D4) ►in GL6(𝔽61)
| 60 | 17 | 0 | 0 | 0 | 0 |
| 44 | 44 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 1 |
| 0 | 0 | 0 | 0 | 60 | 0 |
| 50 | 0 | 0 | 0 | 0 | 0 |
| 57 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 50 | 0 |
| 0 | 0 | 0 | 0 | 0 | 50 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 17 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 15 | 0 | 0 |
| 0 | 0 | 8 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 60 |
| 0 | 0 | 0 | 0 | 60 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 17 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 8 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(61))| [60,44,0,0,0,0,17,44,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,60,0,0,0,0,1,0],[50,57,0,0,0,0,0,11,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,50,0,0,0,0,0,0,50],[1,17,0,0,0,0,0,60,0,0,0,0,0,0,1,8,0,0,0,0,15,60,0,0,0,0,0,0,0,60,0,0,0,0,60,0],[1,17,0,0,0,0,0,60,0,0,0,0,0,0,1,8,0,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
C15⋊26(C4×D4) in GAP, Magma, Sage, TeX
C_{15}\rtimes_{26}(C_4\times D_4) % in TeX
G:=Group("C15:26(C4xD4)"); // GroupNames label
G:=SmallGroup(480,628);
// by ID
G=gap.SmallGroup(480,628);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,64,219,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^15=b^4=c^4=d^2=1,b*a*b^-1=a^4,c*a*c^-1=d*a*d=a^-1,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations