direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4×C15⋊7D4, C60⋊30D4, C23.27D30, C15⋊40(C4×D4), D30⋊21(C2×C4), (C2×C4).67D30, C22⋊3(C4×D15), (C22×C4)⋊4D15, (C22×C12)⋊9D5, C12⋊14(C5⋊D4), C20⋊14(C3⋊D4), (C22×C60)⋊13C2, (C22×C20)⋊13S3, (C2×C20).418D6, C30.376(C2×D4), D30⋊3C4⋊40C2, (C4×Dic15)⋊22C2, Dic15⋊14(C2×C4), (C2×C12).383D10, C30.4Q8⋊40C2, C30.177(C4○D4), C6.105(C4○D20), C30.38D4⋊30C2, (C2×C60).465C22, (C2×C30).302C23, C30.171(C22×C4), (C22×C10).137D6, (C22×C6).119D10, C10.105(C4○D12), C2.5(D60⋊11C2), C22.24(C22×D15), (C22×C30).142C22, (C22×D15).86C22, (C2×Dic15).170C22, C3⋊7(C4×C5⋊D4), C5⋊8(C4×C3⋊D4), C6.76(C2×C4×D5), (C2×C4×D15)⋊20C2, (C2×C6)⋊11(C4×D5), C2.20(C2×C4×D15), (C2×C30)⋊33(C2×C4), (C2×C10)⋊20(C4×S3), C10.108(S3×C2×C4), C2.3(C2×C15⋊7D4), C6.100(C2×C5⋊D4), (C2×C15⋊7D4).14C2, C10.100(C2×C3⋊D4), (C2×C6).298(C22×D5), (C2×C10).297(C22×S3), SmallGroup(480,893)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4×C15⋊7D4
G = < a,b,c,d | a4=b15=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
Subgroups: 948 in 188 conjugacy classes, 71 normal (47 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C22, C5, S3, C6, C6, C2×C4, C2×C4, D4, C23, C23, D5, C10, C10, Dic3, C12, C12, D6, C2×C6, C2×C6, C2×C6, C15, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, Dic5, C20, C20, D10, C2×C10, C2×C10, C2×C10, C4×S3, C2×Dic3, C3⋊D4, C2×C12, C2×C12, C22×S3, C22×C6, D15, C30, C30, C4×D4, C4×D5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×C10, C4×Dic3, Dic3⋊C4, D6⋊C4, C6.D4, S3×C2×C4, C2×C3⋊D4, C22×C12, Dic15, Dic15, C60, C60, D30, D30, C2×C30, C2×C30, C2×C30, C4×Dic5, C10.D4, D10⋊C4, C23.D5, C2×C4×D5, C2×C5⋊D4, C22×C20, C4×C3⋊D4, C4×D15, C2×Dic15, C15⋊7D4, C2×C60, C2×C60, C22×D15, C22×C30, C4×C5⋊D4, C4×Dic15, C30.4Q8, D30⋊3C4, C30.38D4, C2×C4×D15, C2×C15⋊7D4, C22×C60, C4×C15⋊7D4
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, D15, C4×D4, C4×D5, C5⋊D4, C22×D5, S3×C2×C4, C4○D12, C2×C3⋊D4, D30, C2×C4×D5, C4○D20, C2×C5⋊D4, C4×C3⋊D4, C4×D15, C15⋊7D4, C22×D15, C4×C5⋊D4, C2×C4×D15, D60⋊11C2, C2×C15⋊7D4, C4×C15⋊7D4
►On 240 points
Generators in S240
(1 94 36 72)(2 95 37 73)(3 96 38 74)(4 97 39 75)(5 98 40 61)(6 99 41 62)(7 100 42 63)(8 101 43 64)(9 102 44 65)(10 103 45 66)(11 104 31 67)(12 105 32 68)(13 91 33 69)(14 92 34 70)(15 93 35 71)(16 119 55 82)(17 120 56 83)(18 106 57 84)(19 107 58 85)(20 108 59 86)(21 109 60 87)(22 110 46 88)(23 111 47 89)(24 112 48 90)(25 113 49 76)(26 114 50 77)(27 115 51 78)(28 116 52 79)(29 117 53 80)(30 118 54 81)(121 218 156 194)(122 219 157 195)(123 220 158 181)(124 221 159 182)(125 222 160 183)(126 223 161 184)(127 224 162 185)(128 225 163 186)(129 211 164 187)(130 212 165 188)(131 213 151 189)(132 214 152 190)(133 215 153 191)(134 216 154 192)(135 217 155 193)(136 229 180 207)(137 230 166 208)(138 231 167 209)(139 232 168 210)(140 233 169 196)(141 234 170 197)(142 235 171 198)(143 236 172 199)(144 237 173 200)(145 238 174 201)(146 239 175 202)(147 240 176 203)(148 226 177 204)(149 227 178 205)(150 228 179 206)
(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)
(1 151 26 179)(2 165 27 178)(3 164 28 177)(4 163 29 176)(5 162 30 175)(6 161 16 174)(7 160 17 173)(8 159 18 172)(9 158 19 171)(10 157 20 170)(11 156 21 169)(12 155 22 168)(13 154 23 167)(14 153 24 166)(15 152 25 180)(31 121 60 140)(32 135 46 139)(33 134 47 138)(34 133 48 137)(35 132 49 136)(36 131 50 150)(37 130 51 149)(38 129 52 148)(39 128 53 147)(40 127 54 146)(41 126 55 145)(42 125 56 144)(43 124 57 143)(44 123 58 142)(45 122 59 141)(61 224 81 239)(62 223 82 238)(63 222 83 237)(64 221 84 236)(65 220 85 235)(66 219 86 234)(67 218 87 233)(68 217 88 232)(69 216 89 231)(70 215 90 230)(71 214 76 229)(72 213 77 228)(73 212 78 227)(74 211 79 226)(75 225 80 240)(91 192 111 209)(92 191 112 208)(93 190 113 207)(94 189 114 206)(95 188 115 205)(96 187 116 204)(97 186 117 203)(98 185 118 202)(99 184 119 201)(100 183 120 200)(101 182 106 199)(102 181 107 198)(103 195 108 197)(104 194 109 196)(105 193 110 210)
(1 36)(2 35)(3 34)(4 33)(5 32)(6 31)(7 45)(8 44)(9 43)(10 42)(11 41)(12 40)(13 39)(14 38)(15 37)(16 60)(17 59)(18 58)(19 57)(20 56)(21 55)(22 54)(23 53)(24 52)(25 51)(26 50)(27 49)(28 48)(29 47)(30 46)(61 105)(62 104)(63 103)(64 102)(65 101)(66 100)(67 99)(68 98)(69 97)(70 96)(71 95)(72 94)(73 93)(74 92)(75 91)(76 115)(77 114)(78 113)(79 112)(80 111)(81 110)(82 109)(83 108)(84 107)(85 106)(86 120)(87 119)(88 118)(89 117)(90 116)(121 174)(122 173)(123 172)(124 171)(125 170)(126 169)(127 168)(128 167)(129 166)(130 180)(131 179)(132 178)(133 177)(134 176)(135 175)(136 165)(137 164)(138 163)(139 162)(140 161)(141 160)(142 159)(143 158)(144 157)(145 156)(146 155)(147 154)(148 153)(149 152)(150 151)(181 236)(182 235)(183 234)(184 233)(185 232)(186 231)(187 230)(188 229)(189 228)(190 227)(191 226)(192 240)(193 239)(194 238)(195 237)(196 223)(197 222)(198 221)(199 220)(200 219)(201 218)(202 217)(203 216)(204 215)(205 214)(206 213)(207 212)(208 211)(209 225)(210 224)
G:=sub<Sym(240)| (1,94,36,72)(2,95,37,73)(3,96,38,74)(4,97,39,75)(5,98,40,61)(6,99,41,62)(7,100,42,63)(8,101,43,64)(9,102,44,65)(10,103,45,66)(11,104,31,67)(12,105,32,68)(13,91,33,69)(14,92,34,70)(15,93,35,71)(16,119,55,82)(17,120,56,83)(18,106,57,84)(19,107,58,85)(20,108,59,86)(21,109,60,87)(22,110,46,88)(23,111,47,89)(24,112,48,90)(25,113,49,76)(26,114,50,77)(27,115,51,78)(28,116,52,79)(29,117,53,80)(30,118,54,81)(121,218,156,194)(122,219,157,195)(123,220,158,181)(124,221,159,182)(125,222,160,183)(126,223,161,184)(127,224,162,185)(128,225,163,186)(129,211,164,187)(130,212,165,188)(131,213,151,189)(132,214,152,190)(133,215,153,191)(134,216,154,192)(135,217,155,193)(136,229,180,207)(137,230,166,208)(138,231,167,209)(139,232,168,210)(140,233,169,196)(141,234,170,197)(142,235,171,198)(143,236,172,199)(144,237,173,200)(145,238,174,201)(146,239,175,202)(147,240,176,203)(148,226,177,204)(149,227,178,205)(150,228,179,206), (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), (1,151,26,179)(2,165,27,178)(3,164,28,177)(4,163,29,176)(5,162,30,175)(6,161,16,174)(7,160,17,173)(8,159,18,172)(9,158,19,171)(10,157,20,170)(11,156,21,169)(12,155,22,168)(13,154,23,167)(14,153,24,166)(15,152,25,180)(31,121,60,140)(32,135,46,139)(33,134,47,138)(34,133,48,137)(35,132,49,136)(36,131,50,150)(37,130,51,149)(38,129,52,148)(39,128,53,147)(40,127,54,146)(41,126,55,145)(42,125,56,144)(43,124,57,143)(44,123,58,142)(45,122,59,141)(61,224,81,239)(62,223,82,238)(63,222,83,237)(64,221,84,236)(65,220,85,235)(66,219,86,234)(67,218,87,233)(68,217,88,232)(69,216,89,231)(70,215,90,230)(71,214,76,229)(72,213,77,228)(73,212,78,227)(74,211,79,226)(75,225,80,240)(91,192,111,209)(92,191,112,208)(93,190,113,207)(94,189,114,206)(95,188,115,205)(96,187,116,204)(97,186,117,203)(98,185,118,202)(99,184,119,201)(100,183,120,200)(101,182,106,199)(102,181,107,198)(103,195,108,197)(104,194,109,196)(105,193,110,210), (1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,45)(8,44)(9,43)(10,42)(11,41)(12,40)(13,39)(14,38)(15,37)(16,60)(17,59)(18,58)(19,57)(20,56)(21,55)(22,54)(23,53)(24,52)(25,51)(26,50)(27,49)(28,48)(29,47)(30,46)(61,105)(62,104)(63,103)(64,102)(65,101)(66,100)(67,99)(68,98)(69,97)(70,96)(71,95)(72,94)(73,93)(74,92)(75,91)(76,115)(77,114)(78,113)(79,112)(80,111)(81,110)(82,109)(83,108)(84,107)(85,106)(86,120)(87,119)(88,118)(89,117)(90,116)(121,174)(122,173)(123,172)(124,171)(125,170)(126,169)(127,168)(128,167)(129,166)(130,180)(131,179)(132,178)(133,177)(134,176)(135,175)(136,165)(137,164)(138,163)(139,162)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(181,236)(182,235)(183,234)(184,233)(185,232)(186,231)(187,230)(188,229)(189,228)(190,227)(191,226)(192,240)(193,239)(194,238)(195,237)(196,223)(197,222)(198,221)(199,220)(200,219)(201,218)(202,217)(203,216)(204,215)(205,214)(206,213)(207,212)(208,211)(209,225)(210,224)>;
G:=Group( (1,94,36,72)(2,95,37,73)(3,96,38,74)(4,97,39,75)(5,98,40,61)(6,99,41,62)(7,100,42,63)(8,101,43,64)(9,102,44,65)(10,103,45,66)(11,104,31,67)(12,105,32,68)(13,91,33,69)(14,92,34,70)(15,93,35,71)(16,119,55,82)(17,120,56,83)(18,106,57,84)(19,107,58,85)(20,108,59,86)(21,109,60,87)(22,110,46,88)(23,111,47,89)(24,112,48,90)(25,113,49,76)(26,114,50,77)(27,115,51,78)(28,116,52,79)(29,117,53,80)(30,118,54,81)(121,218,156,194)(122,219,157,195)(123,220,158,181)(124,221,159,182)(125,222,160,183)(126,223,161,184)(127,224,162,185)(128,225,163,186)(129,211,164,187)(130,212,165,188)(131,213,151,189)(132,214,152,190)(133,215,153,191)(134,216,154,192)(135,217,155,193)(136,229,180,207)(137,230,166,208)(138,231,167,209)(139,232,168,210)(140,233,169,196)(141,234,170,197)(142,235,171,198)(143,236,172,199)(144,237,173,200)(145,238,174,201)(146,239,175,202)(147,240,176,203)(148,226,177,204)(149,227,178,205)(150,228,179,206), (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), (1,151,26,179)(2,165,27,178)(3,164,28,177)(4,163,29,176)(5,162,30,175)(6,161,16,174)(7,160,17,173)(8,159,18,172)(9,158,19,171)(10,157,20,170)(11,156,21,169)(12,155,22,168)(13,154,23,167)(14,153,24,166)(15,152,25,180)(31,121,60,140)(32,135,46,139)(33,134,47,138)(34,133,48,137)(35,132,49,136)(36,131,50,150)(37,130,51,149)(38,129,52,148)(39,128,53,147)(40,127,54,146)(41,126,55,145)(42,125,56,144)(43,124,57,143)(44,123,58,142)(45,122,59,141)(61,224,81,239)(62,223,82,238)(63,222,83,237)(64,221,84,236)(65,220,85,235)(66,219,86,234)(67,218,87,233)(68,217,88,232)(69,216,89,231)(70,215,90,230)(71,214,76,229)(72,213,77,228)(73,212,78,227)(74,211,79,226)(75,225,80,240)(91,192,111,209)(92,191,112,208)(93,190,113,207)(94,189,114,206)(95,188,115,205)(96,187,116,204)(97,186,117,203)(98,185,118,202)(99,184,119,201)(100,183,120,200)(101,182,106,199)(102,181,107,198)(103,195,108,197)(104,194,109,196)(105,193,110,210), (1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,45)(8,44)(9,43)(10,42)(11,41)(12,40)(13,39)(14,38)(15,37)(16,60)(17,59)(18,58)(19,57)(20,56)(21,55)(22,54)(23,53)(24,52)(25,51)(26,50)(27,49)(28,48)(29,47)(30,46)(61,105)(62,104)(63,103)(64,102)(65,101)(66,100)(67,99)(68,98)(69,97)(70,96)(71,95)(72,94)(73,93)(74,92)(75,91)(76,115)(77,114)(78,113)(79,112)(80,111)(81,110)(82,109)(83,108)(84,107)(85,106)(86,120)(87,119)(88,118)(89,117)(90,116)(121,174)(122,173)(123,172)(124,171)(125,170)(126,169)(127,168)(128,167)(129,166)(130,180)(131,179)(132,178)(133,177)(134,176)(135,175)(136,165)(137,164)(138,163)(139,162)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(181,236)(182,235)(183,234)(184,233)(185,232)(186,231)(187,230)(188,229)(189,228)(190,227)(191,226)(192,240)(193,239)(194,238)(195,237)(196,223)(197,222)(198,221)(199,220)(200,219)(201,218)(202,217)(203,216)(204,215)(205,214)(206,213)(207,212)(208,211)(209,225)(210,224) );
G=PermutationGroup([[(1,94,36,72),(2,95,37,73),(3,96,38,74),(4,97,39,75),(5,98,40,61),(6,99,41,62),(7,100,42,63),(8,101,43,64),(9,102,44,65),(10,103,45,66),(11,104,31,67),(12,105,32,68),(13,91,33,69),(14,92,34,70),(15,93,35,71),(16,119,55,82),(17,120,56,83),(18,106,57,84),(19,107,58,85),(20,108,59,86),(21,109,60,87),(22,110,46,88),(23,111,47,89),(24,112,48,90),(25,113,49,76),(26,114,50,77),(27,115,51,78),(28,116,52,79),(29,117,53,80),(30,118,54,81),(121,218,156,194),(122,219,157,195),(123,220,158,181),(124,221,159,182),(125,222,160,183),(126,223,161,184),(127,224,162,185),(128,225,163,186),(129,211,164,187),(130,212,165,188),(131,213,151,189),(132,214,152,190),(133,215,153,191),(134,216,154,192),(135,217,155,193),(136,229,180,207),(137,230,166,208),(138,231,167,209),(139,232,168,210),(140,233,169,196),(141,234,170,197),(142,235,171,198),(143,236,172,199),(144,237,173,200),(145,238,174,201),(146,239,175,202),(147,240,176,203),(148,226,177,204),(149,227,178,205),(150,228,179,206)], [(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)], [(1,151,26,179),(2,165,27,178),(3,164,28,177),(4,163,29,176),(5,162,30,175),(6,161,16,174),(7,160,17,173),(8,159,18,172),(9,158,19,171),(10,157,20,170),(11,156,21,169),(12,155,22,168),(13,154,23,167),(14,153,24,166),(15,152,25,180),(31,121,60,140),(32,135,46,139),(33,134,47,138),(34,133,48,137),(35,132,49,136),(36,131,50,150),(37,130,51,149),(38,129,52,148),(39,128,53,147),(40,127,54,146),(41,126,55,145),(42,125,56,144),(43,124,57,143),(44,123,58,142),(45,122,59,141),(61,224,81,239),(62,223,82,238),(63,222,83,237),(64,221,84,236),(65,220,85,235),(66,219,86,234),(67,218,87,233),(68,217,88,232),(69,216,89,231),(70,215,90,230),(71,214,76,229),(72,213,77,228),(73,212,78,227),(74,211,79,226),(75,225,80,240),(91,192,111,209),(92,191,112,208),(93,190,113,207),(94,189,114,206),(95,188,115,205),(96,187,116,204),(97,186,117,203),(98,185,118,202),(99,184,119,201),(100,183,120,200),(101,182,106,199),(102,181,107,198),(103,195,108,197),(104,194,109,196),(105,193,110,210)], [(1,36),(2,35),(3,34),(4,33),(5,32),(6,31),(7,45),(8,44),(9,43),(10,42),(11,41),(12,40),(13,39),(14,38),(15,37),(16,60),(17,59),(18,58),(19,57),(20,56),(21,55),(22,54),(23,53),(24,52),(25,51),(26,50),(27,49),(28,48),(29,47),(30,46),(61,105),(62,104),(63,103),(64,102),(65,101),(66,100),(67,99),(68,98),(69,97),(70,96),(71,95),(72,94),(73,93),(74,92),(75,91),(76,115),(77,114),(78,113),(79,112),(80,111),(81,110),(82,109),(83,108),(84,107),(85,106),(86,120),(87,119),(88,118),(89,117),(90,116),(121,174),(122,173),(123,172),(124,171),(125,170),(126,169),(127,168),(128,167),(129,166),(130,180),(131,179),(132,178),(133,177),(134,176),(135,175),(136,165),(137,164),(138,163),(139,162),(140,161),(141,160),(142,159),(143,158),(144,157),(145,156),(146,155),(147,154),(148,153),(149,152),(150,151),(181,236),(182,235),(183,234),(184,233),(185,232),(186,231),(187,230),(188,229),(189,228),(190,227),(191,226),(192,240),(193,239),(194,238),(195,237),(196,223),(197,222),(198,221),(199,220),(200,219),(201,218),(202,217),(203,216),(204,215),(205,214),(206,213),(207,212),(208,211),(209,225),(210,224)]])
132 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | ··· | 4L | 5A | 5B | 6A | ··· | 6G | 10A | ··· | 10N | 12A | ··· | 12H | 15A | 15B | 15C | 15D | 20A | ··· | 20P | 30A | ··· | 30AB | 60A | ··· | 60AF |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 30 | 30 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 30 | ··· | 30 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
132 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 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | S3 | D4 | D5 | D6 | D6 | C4○D4 | D10 | D10 | C3⋊D4 | C4×S3 | D15 | C5⋊D4 | C4×D5 | C4○D12 | D30 | D30 | C4○D20 | C15⋊7D4 | C4×D15 | D60⋊11C2 |
| kernel | C4×C15⋊7D4 | C4×Dic15 | C30.4Q8 | D30⋊3C4 | C30.38D4 | C2×C4×D15 | C2×C15⋊7D4 | C22×C60 | C15⋊7D4 | C22×C20 | C60 | C22×C12 | C2×C20 | C22×C10 | C30 | C2×C12 | C22×C6 | C20 | C2×C10 | C22×C4 | C12 | C2×C6 | C10 | C2×C4 | C23 | C6 | C4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 2 | 2 | 2 | 1 | 2 | 4 | 2 | 4 | 4 | 4 | 8 | 8 | 4 | 8 | 4 | 8 | 16 | 16 | 16 |
Matrix representation of C4×C15⋊7D4 ►in GL4(𝔽61) generated by
| 50 | 0 | 0 | 0 |
| 0 | 50 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 23 | 39 | 0 | 0 |
| 14 | 45 | 0 | 0 |
| 0 | 0 | 0 | 44 |
| 0 | 0 | 18 | 43 |
| 43 | 43 | 0 | 0 |
| 1 | 18 | 0 | 0 |
| 0 | 0 | 8 | 14 |
| 0 | 0 | 52 | 53 |
| 18 | 18 | 0 | 0 |
| 60 | 43 | 0 | 0 |
| 0 | 0 | 43 | 1 |
| 0 | 0 | 43 | 18 |
G:=sub<GL(4,GF(61))| [50,0,0,0,0,50,0,0,0,0,60,0,0,0,0,60],[23,14,0,0,39,45,0,0,0,0,0,18,0,0,44,43],[43,1,0,0,43,18,0,0,0,0,8,52,0,0,14,53],[18,60,0,0,18,43,0,0,0,0,43,43,0,0,1,18] >;
C4×C15⋊7D4 in GAP, Magma, Sage, TeX
C_4\times C_{15}\rtimes_7D_4 % in TeX
G:=Group("C4xC15:7D4"); // GroupNames label
G:=SmallGroup(480,893);
// by ID
G=gap.SmallGroup(480,893);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,58,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^15=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations