G = C15⋊22(C4×D4) order 480 = 25·3·5
18th semidirect product of C15 and C4×D4 acting via C4×D4/C2×C4=C22
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D6⋊8(C4×D5), C15⋊22(C4×D4), C5⋊D12⋊5C4, D30⋊13(C2×C4), Dic5⋊4(C4×S3), C5⋊5(Dic3⋊5D4), D6⋊Dic5⋊14C2, (C5×Dic3)⋊12D4, (C2×C20).267D6, C10.134(S3×D4), C30.146(C2×D4), D30⋊3C4⋊32C2, C6.13(C4○D20), C30.81(C4○D4), (C2×C12).198D10, C10.D4⋊21S3, Dic3⋊7(C5⋊D4), C30.65(C22×C4), (Dic3×Dic5)⋊22C2, C2.5(D60⋊C2), (C2×C30).136C23, (C2×C60).411C22, (C2×Dic5).117D6, (C22×S3).72D10, C10.18(Q8⋊3S3), (C2×Dic3).184D10, (C6×Dic5).83C22, (C22×D15).45C22, (C10×Dic3).187C22, (C2×Dic15).105C22, C3⋊2(C4×C5⋊D4), (S3×C2×C4)⋊11D5, C6.33(C2×C4×D5), C2.35(C4×S3×D5), (S3×C2×C20)⋊19C2, C10.66(S3×C2×C4), C2.3(S3×C5⋊D4), (C2×C4).79(S3×D5), C6.35(C2×C5⋊D4), (S3×C10)⋊21(C2×C4), C22.68(C2×S3×D5), (C3×Dic5)⋊4(C2×C4), (C2×C5⋊D12).9C2, (C2×D30.C2)⋊10C2, (S3×C2×C10).87C22, (C3×C10.D4)⋊33C2, (C2×C6).148(C22×D5), (C2×C10).148(C22×S3), SmallGroup(480,522)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C15⋊22(C4×D4)
G = < a,b,c,d | a15=b4=c4=d2=1, bab-1=dad=a11, cac-1=a4, bc=cb, bd=db, dcd=c-1 >
Subgroups: 940 in 188 conjugacy classes, 62 normal (44 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, S3, C6, C2×C4, C2×C4, D4, C23, D5, C10, C10, Dic3, 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, C3×C4⋊C4, S3×C2×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, C23.D5, C2×C4×D5, C2×C5⋊D4, C22×C20, Dic3⋊5D4, D30.C2, C5⋊D12, C6×Dic5, S3×C20, C10×Dic3, C2×Dic15, C2×C60, S3×C2×C10, C22×D15, C4×C5⋊D4, Dic3×Dic5, D6⋊Dic5, C3×C10.D4, D30⋊3C4, C2×D30.C2, C2×C5⋊D12, S3×C2×C20, C15⋊22(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, Q8⋊3S3, S3×D5, C2×C4×D5, C4○D20, C2×C5⋊D4, Dic3⋊5D4, C2×S3×D5, C4×C5⋊D4, D60⋊C2, C4×S3×D5, S3×C5⋊D4, C15⋊22(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)
(1 217 43 186)(2 213 44 182)(3 224 45 193)(4 220 31 189)(5 216 32 185)(6 212 33 181)(7 223 34 192)(8 219 35 188)(9 215 36 184)(10 211 37 195)(11 222 38 191)(12 218 39 187)(13 214 40 183)(14 225 41 194)(15 221 42 190)(16 240 58 208)(17 236 59 204)(18 232 60 200)(19 228 46 196)(20 239 47 207)(21 235 48 203)(22 231 49 199)(23 227 50 210)(24 238 51 206)(25 234 52 202)(26 230 53 198)(27 226 54 209)(28 237 55 205)(29 233 56 201)(30 229 57 197)(61 128 102 157)(62 124 103 153)(63 135 104 164)(64 131 105 160)(65 127 91 156)(66 123 92 152)(67 134 93 163)(68 130 94 159)(69 126 95 155)(70 122 96 151)(71 133 97 162)(72 129 98 158)(73 125 99 154)(74 121 100 165)(75 132 101 161)(76 148 117 168)(77 144 118 179)(78 140 119 175)(79 136 120 171)(80 147 106 167)(81 143 107 178)(82 139 108 174)(83 150 109 170)(84 146 110 166)(85 142 111 177)(86 138 112 173)(87 149 113 169)(88 145 114 180)(89 141 115 176)(90 137 116 172)
(1 126 20 144)(2 130 21 148)(3 134 22 137)(4 123 23 141)(5 127 24 145)(6 131 25 149)(7 135 26 138)(8 124 27 142)(9 128 28 146)(10 132 29 150)(11 121 30 139)(12 125 16 143)(13 129 17 147)(14 133 18 136)(15 122 19 140)(31 152 50 176)(32 156 51 180)(33 160 52 169)(34 164 53 173)(35 153 54 177)(36 157 55 166)(37 161 56 170)(38 165 57 174)(39 154 58 178)(40 158 59 167)(41 162 60 171)(42 151 46 175)(43 155 47 179)(44 159 48 168)(45 163 49 172)(61 205 84 184)(62 209 85 188)(63 198 86 192)(64 202 87 181)(65 206 88 185)(66 210 89 189)(67 199 90 193)(68 203 76 182)(69 207 77 186)(70 196 78 190)(71 200 79 194)(72 204 80 183)(73 208 81 187)(74 197 82 191)(75 201 83 195)(91 238 114 216)(92 227 115 220)(93 231 116 224)(94 235 117 213)(95 239 118 217)(96 228 119 221)(97 232 120 225)(98 236 106 214)(99 240 107 218)(100 229 108 222)(101 233 109 211)(102 237 110 215)(103 226 111 219)(104 230 112 223)(105 234 113 212)
(1 155)(2 151)(3 162)(4 158)(5 154)(6 165)(7 161)(8 157)(9 153)(10 164)(11 160)(12 156)(13 152)(14 163)(15 159)(16 180)(17 176)(18 172)(19 168)(20 179)(21 175)(22 171)(23 167)(24 178)(25 174)(26 170)(27 166)(28 177)(29 173)(30 169)(31 129)(32 125)(33 121)(34 132)(35 128)(36 124)(37 135)(38 131)(39 127)(40 123)(41 134)(42 130)(43 126)(44 122)(45 133)(46 148)(47 144)(48 140)(49 136)(50 147)(51 143)(52 139)(53 150)(54 146)(55 142)(56 138)(57 149)(58 145)(59 141)(60 137)(61 219)(62 215)(63 211)(64 222)(65 218)(66 214)(67 225)(68 221)(69 217)(70 213)(71 224)(72 220)(73 216)(74 212)(75 223)(76 228)(77 239)(78 235)(79 231)(80 227)(81 238)(82 234)(83 230)(84 226)(85 237)(86 233)(87 229)(88 240)(89 236)(90 232)(91 187)(92 183)(93 194)(94 190)(95 186)(96 182)(97 193)(98 189)(99 185)(100 181)(101 192)(102 188)(103 184)(104 195)(105 191)(106 210)(107 206)(108 202)(109 198)(110 209)(111 205)(112 201)(113 197)(114 208)(115 204)(116 200)(117 196)(118 207)(119 203)(120 199)
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), (1,217,43,186)(2,213,44,182)(3,224,45,193)(4,220,31,189)(5,216,32,185)(6,212,33,181)(7,223,34,192)(8,219,35,188)(9,215,36,184)(10,211,37,195)(11,222,38,191)(12,218,39,187)(13,214,40,183)(14,225,41,194)(15,221,42,190)(16,240,58,208)(17,236,59,204)(18,232,60,200)(19,228,46,196)(20,239,47,207)(21,235,48,203)(22,231,49,199)(23,227,50,210)(24,238,51,206)(25,234,52,202)(26,230,53,198)(27,226,54,209)(28,237,55,205)(29,233,56,201)(30,229,57,197)(61,128,102,157)(62,124,103,153)(63,135,104,164)(64,131,105,160)(65,127,91,156)(66,123,92,152)(67,134,93,163)(68,130,94,159)(69,126,95,155)(70,122,96,151)(71,133,97,162)(72,129,98,158)(73,125,99,154)(74,121,100,165)(75,132,101,161)(76,148,117,168)(77,144,118,179)(78,140,119,175)(79,136,120,171)(80,147,106,167)(81,143,107,178)(82,139,108,174)(83,150,109,170)(84,146,110,166)(85,142,111,177)(86,138,112,173)(87,149,113,169)(88,145,114,180)(89,141,115,176)(90,137,116,172), (1,126,20,144)(2,130,21,148)(3,134,22,137)(4,123,23,141)(5,127,24,145)(6,131,25,149)(7,135,26,138)(8,124,27,142)(9,128,28,146)(10,132,29,150)(11,121,30,139)(12,125,16,143)(13,129,17,147)(14,133,18,136)(15,122,19,140)(31,152,50,176)(32,156,51,180)(33,160,52,169)(34,164,53,173)(35,153,54,177)(36,157,55,166)(37,161,56,170)(38,165,57,174)(39,154,58,178)(40,158,59,167)(41,162,60,171)(42,151,46,175)(43,155,47,179)(44,159,48,168)(45,163,49,172)(61,205,84,184)(62,209,85,188)(63,198,86,192)(64,202,87,181)(65,206,88,185)(66,210,89,189)(67,199,90,193)(68,203,76,182)(69,207,77,186)(70,196,78,190)(71,200,79,194)(72,204,80,183)(73,208,81,187)(74,197,82,191)(75,201,83,195)(91,238,114,216)(92,227,115,220)(93,231,116,224)(94,235,117,213)(95,239,118,217)(96,228,119,221)(97,232,120,225)(98,236,106,214)(99,240,107,218)(100,229,108,222)(101,233,109,211)(102,237,110,215)(103,226,111,219)(104,230,112,223)(105,234,113,212), (1,155)(2,151)(3,162)(4,158)(5,154)(6,165)(7,161)(8,157)(9,153)(10,164)(11,160)(12,156)(13,152)(14,163)(15,159)(16,180)(17,176)(18,172)(19,168)(20,179)(21,175)(22,171)(23,167)(24,178)(25,174)(26,170)(27,166)(28,177)(29,173)(30,169)(31,129)(32,125)(33,121)(34,132)(35,128)(36,124)(37,135)(38,131)(39,127)(40,123)(41,134)(42,130)(43,126)(44,122)(45,133)(46,148)(47,144)(48,140)(49,136)(50,147)(51,143)(52,139)(53,150)(54,146)(55,142)(56,138)(57,149)(58,145)(59,141)(60,137)(61,219)(62,215)(63,211)(64,222)(65,218)(66,214)(67,225)(68,221)(69,217)(70,213)(71,224)(72,220)(73,216)(74,212)(75,223)(76,228)(77,239)(78,235)(79,231)(80,227)(81,238)(82,234)(83,230)(84,226)(85,237)(86,233)(87,229)(88,240)(89,236)(90,232)(91,187)(92,183)(93,194)(94,190)(95,186)(96,182)(97,193)(98,189)(99,185)(100,181)(101,192)(102,188)(103,184)(104,195)(105,191)(106,210)(107,206)(108,202)(109,198)(110,209)(111,205)(112,201)(113,197)(114,208)(115,204)(116,200)(117,196)(118,207)(119,203)(120,199)>;
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), (1,217,43,186)(2,213,44,182)(3,224,45,193)(4,220,31,189)(5,216,32,185)(6,212,33,181)(7,223,34,192)(8,219,35,188)(9,215,36,184)(10,211,37,195)(11,222,38,191)(12,218,39,187)(13,214,40,183)(14,225,41,194)(15,221,42,190)(16,240,58,208)(17,236,59,204)(18,232,60,200)(19,228,46,196)(20,239,47,207)(21,235,48,203)(22,231,49,199)(23,227,50,210)(24,238,51,206)(25,234,52,202)(26,230,53,198)(27,226,54,209)(28,237,55,205)(29,233,56,201)(30,229,57,197)(61,128,102,157)(62,124,103,153)(63,135,104,164)(64,131,105,160)(65,127,91,156)(66,123,92,152)(67,134,93,163)(68,130,94,159)(69,126,95,155)(70,122,96,151)(71,133,97,162)(72,129,98,158)(73,125,99,154)(74,121,100,165)(75,132,101,161)(76,148,117,168)(77,144,118,179)(78,140,119,175)(79,136,120,171)(80,147,106,167)(81,143,107,178)(82,139,108,174)(83,150,109,170)(84,146,110,166)(85,142,111,177)(86,138,112,173)(87,149,113,169)(88,145,114,180)(89,141,115,176)(90,137,116,172), (1,126,20,144)(2,130,21,148)(3,134,22,137)(4,123,23,141)(5,127,24,145)(6,131,25,149)(7,135,26,138)(8,124,27,142)(9,128,28,146)(10,132,29,150)(11,121,30,139)(12,125,16,143)(13,129,17,147)(14,133,18,136)(15,122,19,140)(31,152,50,176)(32,156,51,180)(33,160,52,169)(34,164,53,173)(35,153,54,177)(36,157,55,166)(37,161,56,170)(38,165,57,174)(39,154,58,178)(40,158,59,167)(41,162,60,171)(42,151,46,175)(43,155,47,179)(44,159,48,168)(45,163,49,172)(61,205,84,184)(62,209,85,188)(63,198,86,192)(64,202,87,181)(65,206,88,185)(66,210,89,189)(67,199,90,193)(68,203,76,182)(69,207,77,186)(70,196,78,190)(71,200,79,194)(72,204,80,183)(73,208,81,187)(74,197,82,191)(75,201,83,195)(91,238,114,216)(92,227,115,220)(93,231,116,224)(94,235,117,213)(95,239,118,217)(96,228,119,221)(97,232,120,225)(98,236,106,214)(99,240,107,218)(100,229,108,222)(101,233,109,211)(102,237,110,215)(103,226,111,219)(104,230,112,223)(105,234,113,212), (1,155)(2,151)(3,162)(4,158)(5,154)(6,165)(7,161)(8,157)(9,153)(10,164)(11,160)(12,156)(13,152)(14,163)(15,159)(16,180)(17,176)(18,172)(19,168)(20,179)(21,175)(22,171)(23,167)(24,178)(25,174)(26,170)(27,166)(28,177)(29,173)(30,169)(31,129)(32,125)(33,121)(34,132)(35,128)(36,124)(37,135)(38,131)(39,127)(40,123)(41,134)(42,130)(43,126)(44,122)(45,133)(46,148)(47,144)(48,140)(49,136)(50,147)(51,143)(52,139)(53,150)(54,146)(55,142)(56,138)(57,149)(58,145)(59,141)(60,137)(61,219)(62,215)(63,211)(64,222)(65,218)(66,214)(67,225)(68,221)(69,217)(70,213)(71,224)(72,220)(73,216)(74,212)(75,223)(76,228)(77,239)(78,235)(79,231)(80,227)(81,238)(82,234)(83,230)(84,226)(85,237)(86,233)(87,229)(88,240)(89,236)(90,232)(91,187)(92,183)(93,194)(94,190)(95,186)(96,182)(97,193)(98,189)(99,185)(100,181)(101,192)(102,188)(103,184)(104,195)(105,191)(106,210)(107,206)(108,202)(109,198)(110,209)(111,205)(112,201)(113,197)(114,208)(115,204)(116,200)(117,196)(118,207)(119,203)(120,199) );
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)], [(1,217,43,186),(2,213,44,182),(3,224,45,193),(4,220,31,189),(5,216,32,185),(6,212,33,181),(7,223,34,192),(8,219,35,188),(9,215,36,184),(10,211,37,195),(11,222,38,191),(12,218,39,187),(13,214,40,183),(14,225,41,194),(15,221,42,190),(16,240,58,208),(17,236,59,204),(18,232,60,200),(19,228,46,196),(20,239,47,207),(21,235,48,203),(22,231,49,199),(23,227,50,210),(24,238,51,206),(25,234,52,202),(26,230,53,198),(27,226,54,209),(28,237,55,205),(29,233,56,201),(30,229,57,197),(61,128,102,157),(62,124,103,153),(63,135,104,164),(64,131,105,160),(65,127,91,156),(66,123,92,152),(67,134,93,163),(68,130,94,159),(69,126,95,155),(70,122,96,151),(71,133,97,162),(72,129,98,158),(73,125,99,154),(74,121,100,165),(75,132,101,161),(76,148,117,168),(77,144,118,179),(78,140,119,175),(79,136,120,171),(80,147,106,167),(81,143,107,178),(82,139,108,174),(83,150,109,170),(84,146,110,166),(85,142,111,177),(86,138,112,173),(87,149,113,169),(88,145,114,180),(89,141,115,176),(90,137,116,172)], [(1,126,20,144),(2,130,21,148),(3,134,22,137),(4,123,23,141),(5,127,24,145),(6,131,25,149),(7,135,26,138),(8,124,27,142),(9,128,28,146),(10,132,29,150),(11,121,30,139),(12,125,16,143),(13,129,17,147),(14,133,18,136),(15,122,19,140),(31,152,50,176),(32,156,51,180),(33,160,52,169),(34,164,53,173),(35,153,54,177),(36,157,55,166),(37,161,56,170),(38,165,57,174),(39,154,58,178),(40,158,59,167),(41,162,60,171),(42,151,46,175),(43,155,47,179),(44,159,48,168),(45,163,49,172),(61,205,84,184),(62,209,85,188),(63,198,86,192),(64,202,87,181),(65,206,88,185),(66,210,89,189),(67,199,90,193),(68,203,76,182),(69,207,77,186),(70,196,78,190),(71,200,79,194),(72,204,80,183),(73,208,81,187),(74,197,82,191),(75,201,83,195),(91,238,114,216),(92,227,115,220),(93,231,116,224),(94,235,117,213),(95,239,118,217),(96,228,119,221),(97,232,120,225),(98,236,106,214),(99,240,107,218),(100,229,108,222),(101,233,109,211),(102,237,110,215),(103,226,111,219),(104,230,112,223),(105,234,113,212)], [(1,155),(2,151),(3,162),(4,158),(5,154),(6,165),(7,161),(8,157),(9,153),(10,164),(11,160),(12,156),(13,152),(14,163),(15,159),(16,180),(17,176),(18,172),(19,168),(20,179),(21,175),(22,171),(23,167),(24,178),(25,174),(26,170),(27,166),(28,177),(29,173),(30,169),(31,129),(32,125),(33,121),(34,132),(35,128),(36,124),(37,135),(38,131),(39,127),(40,123),(41,134),(42,130),(43,126),(44,122),(45,133),(46,148),(47,144),(48,140),(49,136),(50,147),(51,143),(52,139),(53,150),(54,146),(55,142),(56,138),(57,149),(58,145),(59,141),(60,137),(61,219),(62,215),(63,211),(64,222),(65,218),(66,214),(67,225),(68,221),(69,217),(70,213),(71,224),(72,220),(73,216),(74,212),(75,223),(76,228),(77,239),(78,235),(79,231),(80,227),(81,238),(82,234),(83,230),(84,226),(85,237),(86,233),(87,229),(88,240),(89,236),(90,232),(91,187),(92,183),(93,194),(94,190),(95,186),(96,182),(97,193),(98,189),(99,185),(100,181),(101,192),(102,188),(103,184),(104,195),(105,191),(106,210),(107,206),(108,202),(109,198),(110,209),(111,205),(112,201),(113,197),(114,208),(115,204),(116,200),(117,196),(118,207),(119,203),(120,199)]])
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 | 10A | ··· | 10F | 10G | ··· | 10N | 12A | 12B | 12C | 12D | 12E | 12F | 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 | 10 | ··· | 10 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 6 | 6 | 30 | 30 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 10 | 10 | 10 | 10 | 30 | 30 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 6 | ··· | 6 | 4 | 4 | 20 | 20 | 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 | 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 | C5⋊D4 | C4×D5 | C4○D20 | S3×D4 | Q8⋊3S3 | S3×D5 | C2×S3×D5 | D60⋊C2 | C4×S3×D5 | S3×C5⋊D4 |
| kernel | C15⋊22(C4×D4) | Dic3×Dic5 | D6⋊Dic5 | C3×C10.D4 | D30⋊3C4 | C2×D30.C2 | C2×C5⋊D12 | S3×C2×C20 | C5⋊D12 | C10.D4 | C5×Dic3 | S3×C2×C4 | C2×Dic5 | C2×C20 | C30 | C2×Dic3 | C2×C12 | C22×S3 | Dic5 | Dic3 | D6 | C6 | C10 | C10 | C2×C4 | 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 | 8 | 8 | 1 | 1 | 2 | 2 | 4 | 4 | 4 |
Matrix representation of C15⋊22(C4×D4) ►in GL4(𝔽61) generated by
| 0 | 1 | 0 | 0 |
| 60 | 60 | 0 | 0 |
| 0 | 0 | 43 | 17 |
| 0 | 0 | 43 | 0 |
| 11 | 0 | 0 | 0 |
| 50 | 50 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 53 | 47 |
| 0 | 0 | 9 | 8 |
| 60 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 30 | 45 |
| 0 | 0 | 60 | 31 |
G:=sub<GL(4,GF(61))| [0,60,0,0,1,60,0,0,0,0,43,43,0,0,17,0],[11,50,0,0,0,50,0,0,0,0,60,0,0,0,0,60],[1,0,0,0,0,1,0,0,0,0,53,9,0,0,47,8],[60,1,0,0,0,1,0,0,0,0,30,60,0,0,45,31] >;
C15⋊22(C4×D4) in GAP, Magma, Sage, TeX
C_{15}\rtimes_{22}(C_4\times D_4) % in TeX
G:=Group("C15:22(C4xD4)"); // GroupNames label
G:=SmallGroup(480,522);
// by ID
G=gap.SmallGroup(480,522);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,253,422,58,1356,18822]);
// 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^4,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations