metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic15⋊14D4, C15⋊8(C4×D4), D6⋊2(C4×D5), D6⋊C4⋊10D5, C5⋊D12⋊4C4, C6.58(D4×D5), D30⋊23(C2×C4), Dic5⋊3(C4×S3), C10.60(S3×D4), C5⋊3(Dic3⋊5D4), C30.128(C2×D4), (C2×C20).197D6, D30⋊4C4⋊11C2, C30.53(C4○D4), C10.D4⋊14S3, (C2×C12).195D10, C3⋊2(Dic5⋊4D4), (C2×C30).96C23, C30.57(C22×C4), (Dic3×Dic5)⋊18C2, C2.4(D12⋊D5), C6.11(D4⋊2D5), C2.3(D10⋊D6), (C2×C60).167C22, (C2×Dic3).97D10, (C2×Dic5).105D6, (C22×S3).35D10, C10.31(Q8⋊3S3), (C6×Dic5).56C22, (C10×Dic3).56C22, (C2×Dic15).205C22, (C22×D15).104C22, C2.27(C4×S3×D5), C6.25(C2×C4×D5), (C2×C4×D15)⋊10C2, C10.58(S3×C2×C4), (C2×S3×Dic5)⋊2C2, (S3×C10)⋊9(C2×C4), (C5×D6⋊C4)⋊10C2, C22.51(C2×S3×D5), (C3×Dic5)⋊3(C2×C4), (C2×C4).180(S3×D5), (C2×C5⋊D12).6C2, (S3×C2×C10).13C22, (C3×C10.D4)⋊14C2, (C2×C6).108(C22×D5), (C2×C10).108(C22×S3), SmallGroup(480,482)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic15⋊14D4
G = < a,b,c,d | a30=c4=d2=1, b2=a15, bab-1=a-1, cac-1=a19, dad=a11, bc=cb, bd=db, dcd=c-1 >
Subgroups: 1004 in 188 conjugacy classes, 60 normal (44 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, S3, C6, C2×C4, C2×C4, D4, C23, D5, C10, C10, Dic3, C12, D6, D6, C2×C6, C15, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C4×S3, D12, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C22×S3, C22×S3, C5×S3, D15, C30, C4×D4, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×C10, C4×Dic3, D6⋊C4, D6⋊C4, C3×C4⋊C4, S3×C2×C4, C2×D12, C5×Dic3, C3×Dic5, C3×Dic5, Dic15, C60, S3×C10, S3×C10, D30, D30, C2×C30, C4×Dic5, C10.D4, D10⋊C4, C5×C22⋊C4, C2×C4×D5, C22×Dic5, C2×C5⋊D4, Dic3⋊5D4, S3×Dic5, C5⋊D12, C6×Dic5, C10×Dic3, C4×D15, C2×Dic15, C2×C60, S3×C2×C10, C22×D15, Dic5⋊4D4, Dic3×Dic5, D30⋊4C4, C3×C10.D4, C5×D6⋊C4, C2×S3×Dic5, C2×C5⋊D12, C2×C4×D15, Dic15⋊14D4
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, C23, D5, D6, C22×C4, C2×D4, C4○D4, D10, C4×S3, C22×S3, C4×D4, C4×D5, C22×D5, S3×C2×C4, S3×D4, Q8⋊3S3, S3×D5, C2×C4×D5, D4×D5, D4⋊2D5, Dic3⋊5D4, C2×S3×D5, Dic5⋊4D4, D12⋊D5, C4×S3×D5, D10⋊D6, Dic15⋊14D4
►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)
(1 104 16 119)(2 103 17 118)(3 102 18 117)(4 101 19 116)(5 100 20 115)(6 99 21 114)(7 98 22 113)(8 97 23 112)(9 96 24 111)(10 95 25 110)(11 94 26 109)(12 93 27 108)(13 92 28 107)(14 91 29 106)(15 120 30 105)(31 75 46 90)(32 74 47 89)(33 73 48 88)(34 72 49 87)(35 71 50 86)(36 70 51 85)(37 69 52 84)(38 68 53 83)(39 67 54 82)(40 66 55 81)(41 65 56 80)(42 64 57 79)(43 63 58 78)(44 62 59 77)(45 61 60 76)(121 224 136 239)(122 223 137 238)(123 222 138 237)(124 221 139 236)(125 220 140 235)(126 219 141 234)(127 218 142 233)(128 217 143 232)(129 216 144 231)(130 215 145 230)(131 214 146 229)(132 213 147 228)(133 212 148 227)(134 211 149 226)(135 240 150 225)(151 200 166 185)(152 199 167 184)(153 198 168 183)(154 197 169 182)(155 196 170 181)(156 195 171 210)(157 194 172 209)(158 193 173 208)(159 192 174 207)(160 191 175 206)(161 190 176 205)(162 189 177 204)(163 188 178 203)(164 187 179 202)(165 186 180 201)
(1 134 53 156)(2 123 54 175)(3 142 55 164)(4 131 56 153)(5 150 57 172)(6 139 58 161)(7 128 59 180)(8 147 60 169)(9 136 31 158)(10 125 32 177)(11 144 33 166)(12 133 34 155)(13 122 35 174)(14 141 36 163)(15 130 37 152)(16 149 38 171)(17 138 39 160)(18 127 40 179)(19 146 41 168)(20 135 42 157)(21 124 43 176)(22 143 44 165)(23 132 45 154)(24 121 46 173)(25 140 47 162)(26 129 48 151)(27 148 49 170)(28 137 50 159)(29 126 51 178)(30 145 52 167)(61 197 112 213)(62 186 113 232)(63 205 114 221)(64 194 115 240)(65 183 116 229)(66 202 117 218)(67 191 118 237)(68 210 119 226)(69 199 120 215)(70 188 91 234)(71 207 92 223)(72 196 93 212)(73 185 94 231)(74 204 95 220)(75 193 96 239)(76 182 97 228)(77 201 98 217)(78 190 99 236)(79 209 100 225)(80 198 101 214)(81 187 102 233)(82 206 103 222)(83 195 104 211)(84 184 105 230)(85 203 106 219)(86 192 107 238)(87 181 108 227)(88 200 109 216)(89 189 110 235)(90 208 111 224)
(1 149)(2 130)(3 141)(4 122)(5 133)(6 144)(7 125)(8 136)(9 147)(10 128)(11 139)(12 150)(13 131)(14 142)(15 123)(16 134)(17 145)(18 126)(19 137)(20 148)(21 129)(22 140)(23 121)(24 132)(25 143)(26 124)(27 135)(28 146)(29 127)(30 138)(31 169)(32 180)(33 161)(34 172)(35 153)(36 164)(37 175)(38 156)(39 167)(40 178)(41 159)(42 170)(43 151)(44 162)(45 173)(46 154)(47 165)(48 176)(49 157)(50 168)(51 179)(52 160)(53 171)(54 152)(55 163)(56 174)(57 155)(58 166)(59 177)(60 158)(61 208)(62 189)(63 200)(64 181)(65 192)(66 203)(67 184)(68 195)(69 206)(70 187)(71 198)(72 209)(73 190)(74 201)(75 182)(76 193)(77 204)(78 185)(79 196)(80 207)(81 188)(82 199)(83 210)(84 191)(85 202)(86 183)(87 194)(88 205)(89 186)(90 197)(91 233)(92 214)(93 225)(94 236)(95 217)(96 228)(97 239)(98 220)(99 231)(100 212)(101 223)(102 234)(103 215)(104 226)(105 237)(106 218)(107 229)(108 240)(109 221)(110 232)(111 213)(112 224)(113 235)(114 216)(115 227)(116 238)(117 219)(118 230)(119 211)(120 222)
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), (1,104,16,119)(2,103,17,118)(3,102,18,117)(4,101,19,116)(5,100,20,115)(6,99,21,114)(7,98,22,113)(8,97,23,112)(9,96,24,111)(10,95,25,110)(11,94,26,109)(12,93,27,108)(13,92,28,107)(14,91,29,106)(15,120,30,105)(31,75,46,90)(32,74,47,89)(33,73,48,88)(34,72,49,87)(35,71,50,86)(36,70,51,85)(37,69,52,84)(38,68,53,83)(39,67,54,82)(40,66,55,81)(41,65,56,80)(42,64,57,79)(43,63,58,78)(44,62,59,77)(45,61,60,76)(121,224,136,239)(122,223,137,238)(123,222,138,237)(124,221,139,236)(125,220,140,235)(126,219,141,234)(127,218,142,233)(128,217,143,232)(129,216,144,231)(130,215,145,230)(131,214,146,229)(132,213,147,228)(133,212,148,227)(134,211,149,226)(135,240,150,225)(151,200,166,185)(152,199,167,184)(153,198,168,183)(154,197,169,182)(155,196,170,181)(156,195,171,210)(157,194,172,209)(158,193,173,208)(159,192,174,207)(160,191,175,206)(161,190,176,205)(162,189,177,204)(163,188,178,203)(164,187,179,202)(165,186,180,201), (1,134,53,156)(2,123,54,175)(3,142,55,164)(4,131,56,153)(5,150,57,172)(6,139,58,161)(7,128,59,180)(8,147,60,169)(9,136,31,158)(10,125,32,177)(11,144,33,166)(12,133,34,155)(13,122,35,174)(14,141,36,163)(15,130,37,152)(16,149,38,171)(17,138,39,160)(18,127,40,179)(19,146,41,168)(20,135,42,157)(21,124,43,176)(22,143,44,165)(23,132,45,154)(24,121,46,173)(25,140,47,162)(26,129,48,151)(27,148,49,170)(28,137,50,159)(29,126,51,178)(30,145,52,167)(61,197,112,213)(62,186,113,232)(63,205,114,221)(64,194,115,240)(65,183,116,229)(66,202,117,218)(67,191,118,237)(68,210,119,226)(69,199,120,215)(70,188,91,234)(71,207,92,223)(72,196,93,212)(73,185,94,231)(74,204,95,220)(75,193,96,239)(76,182,97,228)(77,201,98,217)(78,190,99,236)(79,209,100,225)(80,198,101,214)(81,187,102,233)(82,206,103,222)(83,195,104,211)(84,184,105,230)(85,203,106,219)(86,192,107,238)(87,181,108,227)(88,200,109,216)(89,189,110,235)(90,208,111,224), (1,149)(2,130)(3,141)(4,122)(5,133)(6,144)(7,125)(8,136)(9,147)(10,128)(11,139)(12,150)(13,131)(14,142)(15,123)(16,134)(17,145)(18,126)(19,137)(20,148)(21,129)(22,140)(23,121)(24,132)(25,143)(26,124)(27,135)(28,146)(29,127)(30,138)(31,169)(32,180)(33,161)(34,172)(35,153)(36,164)(37,175)(38,156)(39,167)(40,178)(41,159)(42,170)(43,151)(44,162)(45,173)(46,154)(47,165)(48,176)(49,157)(50,168)(51,179)(52,160)(53,171)(54,152)(55,163)(56,174)(57,155)(58,166)(59,177)(60,158)(61,208)(62,189)(63,200)(64,181)(65,192)(66,203)(67,184)(68,195)(69,206)(70,187)(71,198)(72,209)(73,190)(74,201)(75,182)(76,193)(77,204)(78,185)(79,196)(80,207)(81,188)(82,199)(83,210)(84,191)(85,202)(86,183)(87,194)(88,205)(89,186)(90,197)(91,233)(92,214)(93,225)(94,236)(95,217)(96,228)(97,239)(98,220)(99,231)(100,212)(101,223)(102,234)(103,215)(104,226)(105,237)(106,218)(107,229)(108,240)(109,221)(110,232)(111,213)(112,224)(113,235)(114,216)(115,227)(116,238)(117,219)(118,230)(119,211)(120,222)>;
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), (1,104,16,119)(2,103,17,118)(3,102,18,117)(4,101,19,116)(5,100,20,115)(6,99,21,114)(7,98,22,113)(8,97,23,112)(9,96,24,111)(10,95,25,110)(11,94,26,109)(12,93,27,108)(13,92,28,107)(14,91,29,106)(15,120,30,105)(31,75,46,90)(32,74,47,89)(33,73,48,88)(34,72,49,87)(35,71,50,86)(36,70,51,85)(37,69,52,84)(38,68,53,83)(39,67,54,82)(40,66,55,81)(41,65,56,80)(42,64,57,79)(43,63,58,78)(44,62,59,77)(45,61,60,76)(121,224,136,239)(122,223,137,238)(123,222,138,237)(124,221,139,236)(125,220,140,235)(126,219,141,234)(127,218,142,233)(128,217,143,232)(129,216,144,231)(130,215,145,230)(131,214,146,229)(132,213,147,228)(133,212,148,227)(134,211,149,226)(135,240,150,225)(151,200,166,185)(152,199,167,184)(153,198,168,183)(154,197,169,182)(155,196,170,181)(156,195,171,210)(157,194,172,209)(158,193,173,208)(159,192,174,207)(160,191,175,206)(161,190,176,205)(162,189,177,204)(163,188,178,203)(164,187,179,202)(165,186,180,201), (1,134,53,156)(2,123,54,175)(3,142,55,164)(4,131,56,153)(5,150,57,172)(6,139,58,161)(7,128,59,180)(8,147,60,169)(9,136,31,158)(10,125,32,177)(11,144,33,166)(12,133,34,155)(13,122,35,174)(14,141,36,163)(15,130,37,152)(16,149,38,171)(17,138,39,160)(18,127,40,179)(19,146,41,168)(20,135,42,157)(21,124,43,176)(22,143,44,165)(23,132,45,154)(24,121,46,173)(25,140,47,162)(26,129,48,151)(27,148,49,170)(28,137,50,159)(29,126,51,178)(30,145,52,167)(61,197,112,213)(62,186,113,232)(63,205,114,221)(64,194,115,240)(65,183,116,229)(66,202,117,218)(67,191,118,237)(68,210,119,226)(69,199,120,215)(70,188,91,234)(71,207,92,223)(72,196,93,212)(73,185,94,231)(74,204,95,220)(75,193,96,239)(76,182,97,228)(77,201,98,217)(78,190,99,236)(79,209,100,225)(80,198,101,214)(81,187,102,233)(82,206,103,222)(83,195,104,211)(84,184,105,230)(85,203,106,219)(86,192,107,238)(87,181,108,227)(88,200,109,216)(89,189,110,235)(90,208,111,224), (1,149)(2,130)(3,141)(4,122)(5,133)(6,144)(7,125)(8,136)(9,147)(10,128)(11,139)(12,150)(13,131)(14,142)(15,123)(16,134)(17,145)(18,126)(19,137)(20,148)(21,129)(22,140)(23,121)(24,132)(25,143)(26,124)(27,135)(28,146)(29,127)(30,138)(31,169)(32,180)(33,161)(34,172)(35,153)(36,164)(37,175)(38,156)(39,167)(40,178)(41,159)(42,170)(43,151)(44,162)(45,173)(46,154)(47,165)(48,176)(49,157)(50,168)(51,179)(52,160)(53,171)(54,152)(55,163)(56,174)(57,155)(58,166)(59,177)(60,158)(61,208)(62,189)(63,200)(64,181)(65,192)(66,203)(67,184)(68,195)(69,206)(70,187)(71,198)(72,209)(73,190)(74,201)(75,182)(76,193)(77,204)(78,185)(79,196)(80,207)(81,188)(82,199)(83,210)(84,191)(85,202)(86,183)(87,194)(88,205)(89,186)(90,197)(91,233)(92,214)(93,225)(94,236)(95,217)(96,228)(97,239)(98,220)(99,231)(100,212)(101,223)(102,234)(103,215)(104,226)(105,237)(106,218)(107,229)(108,240)(109,221)(110,232)(111,213)(112,224)(113,235)(114,216)(115,227)(116,238)(117,219)(118,230)(119,211)(120,222) );
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)], [(1,104,16,119),(2,103,17,118),(3,102,18,117),(4,101,19,116),(5,100,20,115),(6,99,21,114),(7,98,22,113),(8,97,23,112),(9,96,24,111),(10,95,25,110),(11,94,26,109),(12,93,27,108),(13,92,28,107),(14,91,29,106),(15,120,30,105),(31,75,46,90),(32,74,47,89),(33,73,48,88),(34,72,49,87),(35,71,50,86),(36,70,51,85),(37,69,52,84),(38,68,53,83),(39,67,54,82),(40,66,55,81),(41,65,56,80),(42,64,57,79),(43,63,58,78),(44,62,59,77),(45,61,60,76),(121,224,136,239),(122,223,137,238),(123,222,138,237),(124,221,139,236),(125,220,140,235),(126,219,141,234),(127,218,142,233),(128,217,143,232),(129,216,144,231),(130,215,145,230),(131,214,146,229),(132,213,147,228),(133,212,148,227),(134,211,149,226),(135,240,150,225),(151,200,166,185),(152,199,167,184),(153,198,168,183),(154,197,169,182),(155,196,170,181),(156,195,171,210),(157,194,172,209),(158,193,173,208),(159,192,174,207),(160,191,175,206),(161,190,176,205),(162,189,177,204),(163,188,178,203),(164,187,179,202),(165,186,180,201)], [(1,134,53,156),(2,123,54,175),(3,142,55,164),(4,131,56,153),(5,150,57,172),(6,139,58,161),(7,128,59,180),(8,147,60,169),(9,136,31,158),(10,125,32,177),(11,144,33,166),(12,133,34,155),(13,122,35,174),(14,141,36,163),(15,130,37,152),(16,149,38,171),(17,138,39,160),(18,127,40,179),(19,146,41,168),(20,135,42,157),(21,124,43,176),(22,143,44,165),(23,132,45,154),(24,121,46,173),(25,140,47,162),(26,129,48,151),(27,148,49,170),(28,137,50,159),(29,126,51,178),(30,145,52,167),(61,197,112,213),(62,186,113,232),(63,205,114,221),(64,194,115,240),(65,183,116,229),(66,202,117,218),(67,191,118,237),(68,210,119,226),(69,199,120,215),(70,188,91,234),(71,207,92,223),(72,196,93,212),(73,185,94,231),(74,204,95,220),(75,193,96,239),(76,182,97,228),(77,201,98,217),(78,190,99,236),(79,209,100,225),(80,198,101,214),(81,187,102,233),(82,206,103,222),(83,195,104,211),(84,184,105,230),(85,203,106,219),(86,192,107,238),(87,181,108,227),(88,200,109,216),(89,189,110,235),(90,208,111,224)], [(1,149),(2,130),(3,141),(4,122),(5,133),(6,144),(7,125),(8,136),(9,147),(10,128),(11,139),(12,150),(13,131),(14,142),(15,123),(16,134),(17,145),(18,126),(19,137),(20,148),(21,129),(22,140),(23,121),(24,132),(25,143),(26,124),(27,135),(28,146),(29,127),(30,138),(31,169),(32,180),(33,161),(34,172),(35,153),(36,164),(37,175),(38,156),(39,167),(40,178),(41,159),(42,170),(43,151),(44,162),(45,173),(46,154),(47,165),(48,176),(49,157),(50,168),(51,179),(52,160),(53,171),(54,152),(55,163),(56,174),(57,155),(58,166),(59,177),(60,158),(61,208),(62,189),(63,200),(64,181),(65,192),(66,203),(67,184),(68,195),(69,206),(70,187),(71,198),(72,209),(73,190),(74,201),(75,182),(76,193),(77,204),(78,185),(79,196),(80,207),(81,188),(82,199),(83,210),(84,191),(85,202),(86,183),(87,194),(88,205),(89,186),(90,197),(91,233),(92,214),(93,225),(94,236),(95,217),(96,228),(97,239),(98,220),(99,231),(100,212),(101,223),(102,234),(103,215),(104,226),(105,237),(106,218),(107,229),(108,240),(109,221),(110,232),(111,213),(112,224),(113,235),(114,216),(115,227),(116,238),(117,219),(118,230),(119,211),(120,222)]])
66 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 | 6B | 6C | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 12A | 12B | 12C | 12D | 12E | 12F | 15A | 15B | 20A | 20B | 20C | 20D | 20E | 20F | 20G | 20H | 30A | ··· | 30F | 60A | ··· | 60H |
| 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 | 6 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 6 | 6 | 30 | 30 | 2 | 2 | 2 | 6 | 6 | 10 | 10 | 10 | 10 | 15 | 15 | 15 | 15 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 12 | 12 | 12 | 12 | 4 | 4 | 20 | 20 | 20 | 20 | 4 | 4 | 4 | 4 | 4 | 4 | 12 | 12 | 12 | 12 | 4 | ··· | 4 | 4 | ··· | 4 |
66 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 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 | D10 | C4×S3 | C4×D5 | S3×D4 | Q8⋊3S3 | S3×D5 | D4×D5 | D4⋊2D5 | C2×S3×D5 | D12⋊D5 | C4×S3×D5 | D10⋊D6 |
| kernel | Dic15⋊14D4 | Dic3×Dic5 | D30⋊4C4 | C3×C10.D4 | C5×D6⋊C4 | C2×S3×Dic5 | C2×C5⋊D12 | C2×C4×D15 | C5⋊D12 | C10.D4 | Dic15 | D6⋊C4 | C2×Dic5 | C2×C20 | C30 | C2×Dic3 | C2×C12 | C22×S3 | Dic5 | D6 | C10 | C10 | C2×C4 | C6 | C6 | C22 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
Matrix representation of Dic15⋊14D4 ►in GL6(𝔽61)
| 1 | 60 | 0 | 0 | 0 | 0 |
| 19 | 43 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 41 | 0 | 0 |
| 0 | 0 | 52 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 15 | 50 | 0 | 0 | 0 | 0 |
| 15 | 46 | 0 | 0 | 0 | 0 |
| 0 | 0 | 50 | 37 | 0 | 0 |
| 0 | 0 | 0 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 18 | 60 | 0 | 0 | 0 | 0 |
| 18 | 43 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 58 |
| 0 | 0 | 0 | 0 | 42 | 53 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 41 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 53 | 3 |
| 0 | 0 | 0 | 0 | 40 | 8 |
G:=sub<GL(6,GF(61))| [1,19,0,0,0,0,60,43,0,0,0,0,0,0,2,52,0,0,0,0,41,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[15,15,0,0,0,0,50,46,0,0,0,0,0,0,50,0,0,0,0,0,37,11,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[18,18,0,0,0,0,60,43,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,8,42,0,0,0,0,58,53],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,41,60,0,0,0,0,0,0,53,40,0,0,0,0,3,8] >;
Dic15⋊14D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{15}\rtimes_{14}D_4 % in TeX
G:=Group("Dic15:14D4"); // GroupNames label
G:=SmallGroup(480,482);
// by ID
G=gap.SmallGroup(480,482);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,135,100,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^30=c^4=d^2=1,b^2=a^15,b*a*b^-1=a^-1,c*a*c^-1=a^19,d*a*d=a^11,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations