G = C15⋊17(C4×D4) order 480 = 25·3·5
13rd semidirect product of C15 and C4×D4 acting via C4×D4/C2×C4=C22
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D6⋊6(C4×D5), C15⋊17(C4×D4), D10⋊5(C4×S3), C15⋊D4⋊4C4, D6⋊Dic5⋊13C2, (C5×Dic3)⋊11D4, C10.133(S3×D4), C30.142(C2×D4), (C2×C20).266D6, D10⋊C4⋊21S3, Dic15⋊10(C2×C4), C6.57(C4○D20), C30.77(C4○D4), (C2×C12).196D10, C5⋊6(Dic3⋊4D4), Dic3⋊6(C5⋊D4), C30.60(C22×C4), C30.4Q8⋊32C2, (C22×D5).55D6, (Dic3×Dic5)⋊20C2, C2.5(D20⋊5S3), (C2×C60).410C22, (C2×C30).131C23, (C2×Dic5).115D6, (C22×S3).70D10, C10.31(D4⋊2S3), (C2×Dic3).183D10, (C6×Dic5).81C22, (C2×Dic15).103C22, (C10×Dic3).184C22, (S3×C2×C4)⋊9D5, C3⋊3(C4×C5⋊D4), C6.28(C2×C4×D5), C2.30(C4×S3×D5), (S3×C2×C20)⋊18C2, (C6×D5)⋊5(C2×C4), C10.61(S3×C2×C4), C2.2(S3×C5⋊D4), (C2×D5×Dic3)⋊10C2, (C2×C4).78(S3×D5), C6.34(C2×C5⋊D4), (S3×C10)⋊19(C2×C4), C22.63(C2×S3×D5), (C2×C15⋊D4).3C2, (D5×C2×C6).25C22, (S3×C2×C10).85C22, (C3×D10⋊C4)⋊32C2, (C2×C6).143(C22×D5), (C2×C10).143(C22×S3), SmallGroup(480,517)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C15⋊17(C4×D4)
G = < a,b,c,d | a15=b4=c4=d2=1, bab-1=dad=a11, cac-1=a-1, bc=cb, bd=db, dcd=c-1 >
Subgroups: 844 in 188 conjugacy classes, 62 normal (44 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, S3, C6, C6, C2×C4, C2×C4, D4, C23, D5, C10, C10, Dic3, Dic3, C12, D6, D6, C2×C6, C2×C6, C15, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5, C20, D10, D10, C2×C10, C2×C10, C4×S3, C2×Dic3, C2×Dic3, C3⋊D4, C2×C12, C2×C12, C22×S3, C22×C6, C5×S3, C3×D5, C30, C4×D4, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×C10, C4×Dic3, Dic3⋊C4, D6⋊C4, C3×C22⋊C4, S3×C2×C4, C22×Dic3, C2×C3⋊D4, C5×Dic3, C3×Dic5, Dic15, Dic15, C60, C6×D5, C6×D5, S3×C10, S3×C10, C2×C30, C4×Dic5, C10.D4, D10⋊C4, C23.D5, C2×C4×D5, C2×C5⋊D4, C22×C20, Dic3⋊4D4, D5×Dic3, C15⋊D4, C6×Dic5, S3×C20, C10×Dic3, C2×Dic15, C2×C60, D5×C2×C6, S3×C2×C10, C4×C5⋊D4, Dic3×Dic5, D6⋊Dic5, C3×D10⋊C4, C30.4Q8, C2×D5×Dic3, C2×C15⋊D4, S3×C2×C20, C15⋊17(C4×D4)
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, C5⋊D4, C22×D5, S3×C2×C4, S3×D4, D4⋊2S3, S3×D5, C2×C4×D5, C4○D20, C2×C5⋊D4, Dic3⋊4D4, C2×S3×D5, C4×C5⋊D4, D20⋊5S3, C4×S3×D5, S3×C5⋊D4, C15⋊17(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)
(1 218 39 189)(2 214 40 185)(3 225 41 181)(4 221 42 192)(5 217 43 188)(6 213 44 184)(7 224 45 195)(8 220 31 191)(9 216 32 187)(10 212 33 183)(11 223 34 194)(12 219 35 190)(13 215 36 186)(14 211 37 182)(15 222 38 193)(16 235 50 210)(17 231 51 206)(18 227 52 202)(19 238 53 198)(20 234 54 209)(21 230 55 205)(22 226 56 201)(23 237 57 197)(24 233 58 208)(25 229 59 204)(26 240 60 200)(27 236 46 196)(28 232 47 207)(29 228 48 203)(30 239 49 199)(61 134 99 154)(62 130 100 165)(63 126 101 161)(64 122 102 157)(65 133 103 153)(66 129 104 164)(67 125 105 160)(68 121 91 156)(69 132 92 152)(70 128 93 163)(71 124 94 159)(72 135 95 155)(73 131 96 151)(74 127 97 162)(75 123 98 158)(76 139 118 180)(77 150 119 176)(78 146 120 172)(79 142 106 168)(80 138 107 179)(81 149 108 175)(82 145 109 171)(83 141 110 167)(84 137 111 178)(85 148 112 174)(86 144 113 170)(87 140 114 166)(88 136 115 177)(89 147 116 173)(90 143 117 169)
(1 179 20 152)(2 178 21 151)(3 177 22 165)(4 176 23 164)(5 175 24 163)(6 174 25 162)(7 173 26 161)(8 172 27 160)(9 171 28 159)(10 170 29 158)(11 169 30 157)(12 168 16 156)(13 167 17 155)(14 166 18 154)(15 180 19 153)(31 146 46 125)(32 145 47 124)(33 144 48 123)(34 143 49 122)(35 142 50 121)(36 141 51 135)(37 140 52 134)(38 139 53 133)(39 138 54 132)(40 137 55 131)(41 136 56 130)(42 150 57 129)(43 149 58 128)(44 148 59 127)(45 147 60 126)(61 211 87 227)(62 225 88 226)(63 224 89 240)(64 223 90 239)(65 222 76 238)(66 221 77 237)(67 220 78 236)(68 219 79 235)(69 218 80 234)(70 217 81 233)(71 216 82 232)(72 215 83 231)(73 214 84 230)(74 213 85 229)(75 212 86 228)(91 190 106 210)(92 189 107 209)(93 188 108 208)(94 187 109 207)(95 186 110 206)(96 185 111 205)(97 184 112 204)(98 183 113 203)(99 182 114 202)(100 181 115 201)(101 195 116 200)(102 194 117 199)(103 193 118 198)(104 192 119 197)(105 191 120 196)
(1 132)(2 128)(3 124)(4 135)(5 131)(6 127)(7 123)(8 134)(9 130)(10 126)(11 122)(12 133)(13 129)(14 125)(15 121)(16 139)(17 150)(18 146)(19 142)(20 138)(21 149)(22 145)(23 141)(24 137)(25 148)(26 144)(27 140)(28 136)(29 147)(30 143)(31 154)(32 165)(33 161)(34 157)(35 153)(36 164)(37 160)(38 156)(39 152)(40 163)(41 159)(42 155)(43 151)(44 162)(45 158)(46 166)(47 177)(48 173)(49 169)(50 180)(51 176)(52 172)(53 168)(54 179)(55 175)(56 171)(57 167)(58 178)(59 174)(60 170)(61 191)(62 187)(63 183)(64 194)(65 190)(66 186)(67 182)(68 193)(69 189)(70 185)(71 181)(72 192)(73 188)(74 184)(75 195)(76 210)(77 206)(78 202)(79 198)(80 209)(81 205)(82 201)(83 197)(84 208)(85 204)(86 200)(87 196)(88 207)(89 203)(90 199)(91 222)(92 218)(93 214)(94 225)(95 221)(96 217)(97 213)(98 224)(99 220)(100 216)(101 212)(102 223)(103 219)(104 215)(105 211)(106 238)(107 234)(108 230)(109 226)(110 237)(111 233)(112 229)(113 240)(114 236)(115 232)(116 228)(117 239)(118 235)(119 231)(120 227)
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), (1,218,39,189)(2,214,40,185)(3,225,41,181)(4,221,42,192)(5,217,43,188)(6,213,44,184)(7,224,45,195)(8,220,31,191)(9,216,32,187)(10,212,33,183)(11,223,34,194)(12,219,35,190)(13,215,36,186)(14,211,37,182)(15,222,38,193)(16,235,50,210)(17,231,51,206)(18,227,52,202)(19,238,53,198)(20,234,54,209)(21,230,55,205)(22,226,56,201)(23,237,57,197)(24,233,58,208)(25,229,59,204)(26,240,60,200)(27,236,46,196)(28,232,47,207)(29,228,48,203)(30,239,49,199)(61,134,99,154)(62,130,100,165)(63,126,101,161)(64,122,102,157)(65,133,103,153)(66,129,104,164)(67,125,105,160)(68,121,91,156)(69,132,92,152)(70,128,93,163)(71,124,94,159)(72,135,95,155)(73,131,96,151)(74,127,97,162)(75,123,98,158)(76,139,118,180)(77,150,119,176)(78,146,120,172)(79,142,106,168)(80,138,107,179)(81,149,108,175)(82,145,109,171)(83,141,110,167)(84,137,111,178)(85,148,112,174)(86,144,113,170)(87,140,114,166)(88,136,115,177)(89,147,116,173)(90,143,117,169), (1,179,20,152)(2,178,21,151)(3,177,22,165)(4,176,23,164)(5,175,24,163)(6,174,25,162)(7,173,26,161)(8,172,27,160)(9,171,28,159)(10,170,29,158)(11,169,30,157)(12,168,16,156)(13,167,17,155)(14,166,18,154)(15,180,19,153)(31,146,46,125)(32,145,47,124)(33,144,48,123)(34,143,49,122)(35,142,50,121)(36,141,51,135)(37,140,52,134)(38,139,53,133)(39,138,54,132)(40,137,55,131)(41,136,56,130)(42,150,57,129)(43,149,58,128)(44,148,59,127)(45,147,60,126)(61,211,87,227)(62,225,88,226)(63,224,89,240)(64,223,90,239)(65,222,76,238)(66,221,77,237)(67,220,78,236)(68,219,79,235)(69,218,80,234)(70,217,81,233)(71,216,82,232)(72,215,83,231)(73,214,84,230)(74,213,85,229)(75,212,86,228)(91,190,106,210)(92,189,107,209)(93,188,108,208)(94,187,109,207)(95,186,110,206)(96,185,111,205)(97,184,112,204)(98,183,113,203)(99,182,114,202)(100,181,115,201)(101,195,116,200)(102,194,117,199)(103,193,118,198)(104,192,119,197)(105,191,120,196), (1,132)(2,128)(3,124)(4,135)(5,131)(6,127)(7,123)(8,134)(9,130)(10,126)(11,122)(12,133)(13,129)(14,125)(15,121)(16,139)(17,150)(18,146)(19,142)(20,138)(21,149)(22,145)(23,141)(24,137)(25,148)(26,144)(27,140)(28,136)(29,147)(30,143)(31,154)(32,165)(33,161)(34,157)(35,153)(36,164)(37,160)(38,156)(39,152)(40,163)(41,159)(42,155)(43,151)(44,162)(45,158)(46,166)(47,177)(48,173)(49,169)(50,180)(51,176)(52,172)(53,168)(54,179)(55,175)(56,171)(57,167)(58,178)(59,174)(60,170)(61,191)(62,187)(63,183)(64,194)(65,190)(66,186)(67,182)(68,193)(69,189)(70,185)(71,181)(72,192)(73,188)(74,184)(75,195)(76,210)(77,206)(78,202)(79,198)(80,209)(81,205)(82,201)(83,197)(84,208)(85,204)(86,200)(87,196)(88,207)(89,203)(90,199)(91,222)(92,218)(93,214)(94,225)(95,221)(96,217)(97,213)(98,224)(99,220)(100,216)(101,212)(102,223)(103,219)(104,215)(105,211)(106,238)(107,234)(108,230)(109,226)(110,237)(111,233)(112,229)(113,240)(114,236)(115,232)(116,228)(117,239)(118,235)(119,231)(120,227)>;
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), (1,218,39,189)(2,214,40,185)(3,225,41,181)(4,221,42,192)(5,217,43,188)(6,213,44,184)(7,224,45,195)(8,220,31,191)(9,216,32,187)(10,212,33,183)(11,223,34,194)(12,219,35,190)(13,215,36,186)(14,211,37,182)(15,222,38,193)(16,235,50,210)(17,231,51,206)(18,227,52,202)(19,238,53,198)(20,234,54,209)(21,230,55,205)(22,226,56,201)(23,237,57,197)(24,233,58,208)(25,229,59,204)(26,240,60,200)(27,236,46,196)(28,232,47,207)(29,228,48,203)(30,239,49,199)(61,134,99,154)(62,130,100,165)(63,126,101,161)(64,122,102,157)(65,133,103,153)(66,129,104,164)(67,125,105,160)(68,121,91,156)(69,132,92,152)(70,128,93,163)(71,124,94,159)(72,135,95,155)(73,131,96,151)(74,127,97,162)(75,123,98,158)(76,139,118,180)(77,150,119,176)(78,146,120,172)(79,142,106,168)(80,138,107,179)(81,149,108,175)(82,145,109,171)(83,141,110,167)(84,137,111,178)(85,148,112,174)(86,144,113,170)(87,140,114,166)(88,136,115,177)(89,147,116,173)(90,143,117,169), (1,179,20,152)(2,178,21,151)(3,177,22,165)(4,176,23,164)(5,175,24,163)(6,174,25,162)(7,173,26,161)(8,172,27,160)(9,171,28,159)(10,170,29,158)(11,169,30,157)(12,168,16,156)(13,167,17,155)(14,166,18,154)(15,180,19,153)(31,146,46,125)(32,145,47,124)(33,144,48,123)(34,143,49,122)(35,142,50,121)(36,141,51,135)(37,140,52,134)(38,139,53,133)(39,138,54,132)(40,137,55,131)(41,136,56,130)(42,150,57,129)(43,149,58,128)(44,148,59,127)(45,147,60,126)(61,211,87,227)(62,225,88,226)(63,224,89,240)(64,223,90,239)(65,222,76,238)(66,221,77,237)(67,220,78,236)(68,219,79,235)(69,218,80,234)(70,217,81,233)(71,216,82,232)(72,215,83,231)(73,214,84,230)(74,213,85,229)(75,212,86,228)(91,190,106,210)(92,189,107,209)(93,188,108,208)(94,187,109,207)(95,186,110,206)(96,185,111,205)(97,184,112,204)(98,183,113,203)(99,182,114,202)(100,181,115,201)(101,195,116,200)(102,194,117,199)(103,193,118,198)(104,192,119,197)(105,191,120,196), (1,132)(2,128)(3,124)(4,135)(5,131)(6,127)(7,123)(8,134)(9,130)(10,126)(11,122)(12,133)(13,129)(14,125)(15,121)(16,139)(17,150)(18,146)(19,142)(20,138)(21,149)(22,145)(23,141)(24,137)(25,148)(26,144)(27,140)(28,136)(29,147)(30,143)(31,154)(32,165)(33,161)(34,157)(35,153)(36,164)(37,160)(38,156)(39,152)(40,163)(41,159)(42,155)(43,151)(44,162)(45,158)(46,166)(47,177)(48,173)(49,169)(50,180)(51,176)(52,172)(53,168)(54,179)(55,175)(56,171)(57,167)(58,178)(59,174)(60,170)(61,191)(62,187)(63,183)(64,194)(65,190)(66,186)(67,182)(68,193)(69,189)(70,185)(71,181)(72,192)(73,188)(74,184)(75,195)(76,210)(77,206)(78,202)(79,198)(80,209)(81,205)(82,201)(83,197)(84,208)(85,204)(86,200)(87,196)(88,207)(89,203)(90,199)(91,222)(92,218)(93,214)(94,225)(95,221)(96,217)(97,213)(98,224)(99,220)(100,216)(101,212)(102,223)(103,219)(104,215)(105,211)(106,238)(107,234)(108,230)(109,226)(110,237)(111,233)(112,229)(113,240)(114,236)(115,232)(116,228)(117,239)(118,235)(119,231)(120,227) );
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)], [(1,218,39,189),(2,214,40,185),(3,225,41,181),(4,221,42,192),(5,217,43,188),(6,213,44,184),(7,224,45,195),(8,220,31,191),(9,216,32,187),(10,212,33,183),(11,223,34,194),(12,219,35,190),(13,215,36,186),(14,211,37,182),(15,222,38,193),(16,235,50,210),(17,231,51,206),(18,227,52,202),(19,238,53,198),(20,234,54,209),(21,230,55,205),(22,226,56,201),(23,237,57,197),(24,233,58,208),(25,229,59,204),(26,240,60,200),(27,236,46,196),(28,232,47,207),(29,228,48,203),(30,239,49,199),(61,134,99,154),(62,130,100,165),(63,126,101,161),(64,122,102,157),(65,133,103,153),(66,129,104,164),(67,125,105,160),(68,121,91,156),(69,132,92,152),(70,128,93,163),(71,124,94,159),(72,135,95,155),(73,131,96,151),(74,127,97,162),(75,123,98,158),(76,139,118,180),(77,150,119,176),(78,146,120,172),(79,142,106,168),(80,138,107,179),(81,149,108,175),(82,145,109,171),(83,141,110,167),(84,137,111,178),(85,148,112,174),(86,144,113,170),(87,140,114,166),(88,136,115,177),(89,147,116,173),(90,143,117,169)], [(1,179,20,152),(2,178,21,151),(3,177,22,165),(4,176,23,164),(5,175,24,163),(6,174,25,162),(7,173,26,161),(8,172,27,160),(9,171,28,159),(10,170,29,158),(11,169,30,157),(12,168,16,156),(13,167,17,155),(14,166,18,154),(15,180,19,153),(31,146,46,125),(32,145,47,124),(33,144,48,123),(34,143,49,122),(35,142,50,121),(36,141,51,135),(37,140,52,134),(38,139,53,133),(39,138,54,132),(40,137,55,131),(41,136,56,130),(42,150,57,129),(43,149,58,128),(44,148,59,127),(45,147,60,126),(61,211,87,227),(62,225,88,226),(63,224,89,240),(64,223,90,239),(65,222,76,238),(66,221,77,237),(67,220,78,236),(68,219,79,235),(69,218,80,234),(70,217,81,233),(71,216,82,232),(72,215,83,231),(73,214,84,230),(74,213,85,229),(75,212,86,228),(91,190,106,210),(92,189,107,209),(93,188,108,208),(94,187,109,207),(95,186,110,206),(96,185,111,205),(97,184,112,204),(98,183,113,203),(99,182,114,202),(100,181,115,201),(101,195,116,200),(102,194,117,199),(103,193,118,198),(104,192,119,197),(105,191,120,196)], [(1,132),(2,128),(3,124),(4,135),(5,131),(6,127),(7,123),(8,134),(9,130),(10,126),(11,122),(12,133),(13,129),(14,125),(15,121),(16,139),(17,150),(18,146),(19,142),(20,138),(21,149),(22,145),(23,141),(24,137),(25,148),(26,144),(27,140),(28,136),(29,147),(30,143),(31,154),(32,165),(33,161),(34,157),(35,153),(36,164),(37,160),(38,156),(39,152),(40,163),(41,159),(42,155),(43,151),(44,162),(45,158),(46,166),(47,177),(48,173),(49,169),(50,180),(51,176),(52,172),(53,168),(54,179),(55,175),(56,171),(57,167),(58,178),(59,174),(60,170),(61,191),(62,187),(63,183),(64,194),(65,190),(66,186),(67,182),(68,193),(69,189),(70,185),(71,181),(72,192),(73,188),(74,184),(75,195),(76,210),(77,206),(78,202),(79,198),(80,209),(81,205),(82,201),(83,197),(84,208),(85,204),(86,200),(87,196),(88,207),(89,203),(90,199),(91,222),(92,218),(93,214),(94,225),(95,221),(96,217),(97,213),(98,224),(99,220),(100,216),(101,212),(102,223),(103,219),(104,215),(105,211),(106,238),(107,234),(108,230),(109,226),(110,237),(111,233),(112,229),(113,240),(114,236),(115,232),(116,228),(117,239),(118,235),(119,231),(120,227)]])
78 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 | 6D | 6E | 10A | ··· | 10F | 10G | ··· | 10N | 12A | 12B | 12C | 12D | 15A | 15B | 20A | ··· | 20H | 20I | ··· | 20P | 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 | 6 | 6 | 10 | ··· | 10 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 6 | 6 | 10 | 10 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 10 | 10 | 30 | 30 | 30 | 30 | 2 | 2 | 2 | 2 | 2 | 20 | 20 | 2 | ··· | 2 | 6 | ··· | 6 | 4 | 4 | 20 | 20 | 4 | 4 | 2 | ··· | 2 | 6 | ··· | 6 | 4 | ··· | 4 | 4 | ··· | 4 |
78 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 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 | D6 | C4○D4 | D10 | D10 | D10 | C4×S3 | C5⋊D4 | C4×D5 | C4○D20 | S3×D4 | D4⋊2S3 | S3×D5 | C2×S3×D5 | D20⋊5S3 | C4×S3×D5 | S3×C5⋊D4 |
| kernel | C15⋊17(C4×D4) | Dic3×Dic5 | D6⋊Dic5 | C3×D10⋊C4 | C30.4Q8 | C2×D5×Dic3 | C2×C15⋊D4 | S3×C2×C20 | C15⋊D4 | D10⋊C4 | C5×Dic3 | S3×C2×C4 | C2×Dic5 | C2×C20 | C22×D5 | C30 | C2×Dic3 | C2×C12 | C22×S3 | D10 | Dic3 | D6 | C6 | C10 | C10 | C2×C4 | C22 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 8 | 1 | 1 | 2 | 2 | 4 | 4 | 4 |
Matrix representation of C15⋊17(C4×D4) ►in GL4(𝔽61) generated by
| 60 | 43 | 0 | 0 |
| 18 | 18 | 0 | 0 |
| 0 | 0 | 60 | 1 |
| 0 | 0 | 60 | 0 |
| 60 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 23 | 59 |
| 0 | 0 | 21 | 38 |
| 30 | 44 | 0 | 0 |
| 53 | 31 | 0 | 0 |
| 0 | 0 | 9 | 39 |
| 0 | 0 | 48 | 52 |
| 30 | 44 | 0 | 0 |
| 17 | 31 | 0 | 0 |
| 0 | 0 | 52 | 22 |
| 0 | 0 | 13 | 9 |
G:=sub<GL(4,GF(61))| [60,18,0,0,43,18,0,0,0,0,60,60,0,0,1,0],[60,0,0,0,0,60,0,0,0,0,23,21,0,0,59,38],[30,53,0,0,44,31,0,0,0,0,9,48,0,0,39,52],[30,17,0,0,44,31,0,0,0,0,52,13,0,0,22,9] >;
C15⋊17(C4×D4) in GAP, Magma, Sage, TeX
C_{15}\rtimes_{17}(C_4\times D_4) % in TeX
G:=Group("C15:17(C4xD4)"); // GroupNames label
G:=SmallGroup(480,517);
// by ID
G=gap.SmallGroup(480,517);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,422,58,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^15=b^4=c^4=d^2=1,b*a*b^-1=d*a*d=a^11,c*a*c^-1=a^-1,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations