direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C15×C42⋊2C2, C42⋊5C30, C4⋊C4⋊5C30, (C4×C60)⋊5C2, (C4×C20)⋊9C6, (C4×C12)⋊3C10, C22⋊C4.2C30, C23.4(C2×C30), C30.282(C4○D4), (C2×C60).438C22, (C2×C30).461C23, (C22×C30).4C22, C22.16(C22×C30), (C5×C4⋊C4)⋊14C6, (C15×C4⋊C4)⋊32C2, (C3×C4⋊C4)⋊14C10, C6.46(C5×C4○D4), C2.9(C15×C4○D4), (C2×C20).84(C2×C6), (C2×C4).15(C2×C30), C10.46(C3×C4○D4), (C5×C22⋊C4).5C6, (C2×C12).84(C2×C10), (C3×C22⋊C4).5C10, (C22×C6).3(C2×C10), (C22×C10).8(C2×C6), (C15×C22⋊C4).11C2, (C2×C10).81(C22×C6), (C2×C6).81(C22×C10), SmallGroup(480,931)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C15×C42⋊2C2
G = < a,b,c,d | a15=b4=c4=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=bc2, dcd=b2c-1 >
Subgroups: 168 in 120 conjugacy classes, 80 normal (20 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, C6, C6, C2×C4, C23, C10, C10, C12, C2×C6, C2×C6, C15, C42, C22⋊C4, C4⋊C4, C20, C2×C10, C2×C10, C2×C12, C22×C6, C30, C30, C42⋊2C2, C2×C20, C22×C10, C4×C12, C3×C22⋊C4, C3×C4⋊C4, C60, C2×C30, C2×C30, C4×C20, C5×C22⋊C4, C5×C4⋊C4, C3×C42⋊2C2, C2×C60, C22×C30, C5×C42⋊2C2, C4×C60, C15×C22⋊C4, C15×C4⋊C4, C15×C42⋊2C2
Quotients: C1, C2, C3, C22, C5, C6, C23, C10, C2×C6, C15, C4○D4, C2×C10, C22×C6, C30, C42⋊2C2, C22×C10, C3×C4○D4, C2×C30, C5×C4○D4, C3×C42⋊2C2, C22×C30, C5×C42⋊2C2, C15×C4○D4, C15×C42⋊2C2
►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)
(1 139 230 120)(2 140 231 106)(3 141 232 107)(4 142 233 108)(5 143 234 109)(6 144 235 110)(7 145 236 111)(8 146 237 112)(9 147 238 113)(10 148 239 114)(11 149 240 115)(12 150 226 116)(13 136 227 117)(14 137 228 118)(15 138 229 119)(16 158 69 122)(17 159 70 123)(18 160 71 124)(19 161 72 125)(20 162 73 126)(21 163 74 127)(22 164 75 128)(23 165 61 129)(24 151 62 130)(25 152 63 131)(26 153 64 132)(27 154 65 133)(28 155 66 134)(29 156 67 135)(30 157 68 121)(31 199 175 223)(32 200 176 224)(33 201 177 225)(34 202 178 211)(35 203 179 212)(36 204 180 213)(37 205 166 214)(38 206 167 215)(39 207 168 216)(40 208 169 217)(41 209 170 218)(42 210 171 219)(43 196 172 220)(44 197 173 221)(45 198 174 222)(46 99 186 83)(47 100 187 84)(48 101 188 85)(49 102 189 86)(50 103 190 87)(51 104 191 88)(52 105 192 89)(53 91 193 90)(54 92 194 76)(55 93 195 77)(56 94 181 78)(57 95 182 79)(58 96 183 80)(59 97 184 81)(60 98 185 82)
(1 38 100 133)(2 39 101 134)(3 40 102 135)(4 41 103 121)(5 42 104 122)(6 43 105 123)(7 44 91 124)(8 45 92 125)(9 31 93 126)(10 32 94 127)(11 33 95 128)(12 34 96 129)(13 35 97 130)(14 36 98 131)(15 37 99 132)(16 143 210 191)(17 144 196 192)(18 145 197 193)(19 146 198 194)(20 147 199 195)(21 148 200 181)(22 149 201 182)(23 150 202 183)(24 136 203 184)(25 137 204 185)(26 138 205 186)(27 139 206 187)(28 140 207 188)(29 141 208 189)(30 142 209 190)(46 64 119 214)(47 65 120 215)(48 66 106 216)(49 67 107 217)(50 68 108 218)(51 69 109 219)(52 70 110 220)(53 71 111 221)(54 72 112 222)(55 73 113 223)(56 74 114 224)(57 75 115 225)(58 61 116 211)(59 62 117 212)(60 63 118 213)(76 161 237 174)(77 162 238 175)(78 163 239 176)(79 164 240 177)(80 165 226 178)(81 151 227 179)(82 152 228 180)(83 153 229 166)(84 154 230 167)(85 155 231 168)(86 156 232 169)(87 157 233 170)(88 158 234 171)(89 159 235 172)(90 160 236 173)
(16 69)(17 70)(18 71)(19 72)(20 73)(21 74)(22 75)(23 61)(24 62)(25 63)(26 64)(27 65)(28 66)(29 67)(30 68)(31 162)(32 163)(33 164)(34 165)(35 151)(36 152)(37 153)(38 154)(39 155)(40 156)(41 157)(42 158)(43 159)(44 160)(45 161)(46 119)(47 120)(48 106)(49 107)(50 108)(51 109)(52 110)(53 111)(54 112)(55 113)(56 114)(57 115)(58 116)(59 117)(60 118)(121 170)(122 171)(123 172)(124 173)(125 174)(126 175)(127 176)(128 177)(129 178)(130 179)(131 180)(132 166)(133 167)(134 168)(135 169)(136 184)(137 185)(138 186)(139 187)(140 188)(141 189)(142 190)(143 191)(144 192)(145 193)(146 194)(147 195)(148 181)(149 182)(150 183)(196 220)(197 221)(198 222)(199 223)(200 224)(201 225)(202 211)(203 212)(204 213)(205 214)(206 215)(207 216)(208 217)(209 218)(210 219)
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), (1,139,230,120)(2,140,231,106)(3,141,232,107)(4,142,233,108)(5,143,234,109)(6,144,235,110)(7,145,236,111)(8,146,237,112)(9,147,238,113)(10,148,239,114)(11,149,240,115)(12,150,226,116)(13,136,227,117)(14,137,228,118)(15,138,229,119)(16,158,69,122)(17,159,70,123)(18,160,71,124)(19,161,72,125)(20,162,73,126)(21,163,74,127)(22,164,75,128)(23,165,61,129)(24,151,62,130)(25,152,63,131)(26,153,64,132)(27,154,65,133)(28,155,66,134)(29,156,67,135)(30,157,68,121)(31,199,175,223)(32,200,176,224)(33,201,177,225)(34,202,178,211)(35,203,179,212)(36,204,180,213)(37,205,166,214)(38,206,167,215)(39,207,168,216)(40,208,169,217)(41,209,170,218)(42,210,171,219)(43,196,172,220)(44,197,173,221)(45,198,174,222)(46,99,186,83)(47,100,187,84)(48,101,188,85)(49,102,189,86)(50,103,190,87)(51,104,191,88)(52,105,192,89)(53,91,193,90)(54,92,194,76)(55,93,195,77)(56,94,181,78)(57,95,182,79)(58,96,183,80)(59,97,184,81)(60,98,185,82), (1,38,100,133)(2,39,101,134)(3,40,102,135)(4,41,103,121)(5,42,104,122)(6,43,105,123)(7,44,91,124)(8,45,92,125)(9,31,93,126)(10,32,94,127)(11,33,95,128)(12,34,96,129)(13,35,97,130)(14,36,98,131)(15,37,99,132)(16,143,210,191)(17,144,196,192)(18,145,197,193)(19,146,198,194)(20,147,199,195)(21,148,200,181)(22,149,201,182)(23,150,202,183)(24,136,203,184)(25,137,204,185)(26,138,205,186)(27,139,206,187)(28,140,207,188)(29,141,208,189)(30,142,209,190)(46,64,119,214)(47,65,120,215)(48,66,106,216)(49,67,107,217)(50,68,108,218)(51,69,109,219)(52,70,110,220)(53,71,111,221)(54,72,112,222)(55,73,113,223)(56,74,114,224)(57,75,115,225)(58,61,116,211)(59,62,117,212)(60,63,118,213)(76,161,237,174)(77,162,238,175)(78,163,239,176)(79,164,240,177)(80,165,226,178)(81,151,227,179)(82,152,228,180)(83,153,229,166)(84,154,230,167)(85,155,231,168)(86,156,232,169)(87,157,233,170)(88,158,234,171)(89,159,235,172)(90,160,236,173), (16,69)(17,70)(18,71)(19,72)(20,73)(21,74)(22,75)(23,61)(24,62)(25,63)(26,64)(27,65)(28,66)(29,67)(30,68)(31,162)(32,163)(33,164)(34,165)(35,151)(36,152)(37,153)(38,154)(39,155)(40,156)(41,157)(42,158)(43,159)(44,160)(45,161)(46,119)(47,120)(48,106)(49,107)(50,108)(51,109)(52,110)(53,111)(54,112)(55,113)(56,114)(57,115)(58,116)(59,117)(60,118)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,166)(133,167)(134,168)(135,169)(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194)(147,195)(148,181)(149,182)(150,183)(196,220)(197,221)(198,222)(199,223)(200,224)(201,225)(202,211)(203,212)(204,213)(205,214)(206,215)(207,216)(208,217)(209,218)(210,219)>;
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), (1,139,230,120)(2,140,231,106)(3,141,232,107)(4,142,233,108)(5,143,234,109)(6,144,235,110)(7,145,236,111)(8,146,237,112)(9,147,238,113)(10,148,239,114)(11,149,240,115)(12,150,226,116)(13,136,227,117)(14,137,228,118)(15,138,229,119)(16,158,69,122)(17,159,70,123)(18,160,71,124)(19,161,72,125)(20,162,73,126)(21,163,74,127)(22,164,75,128)(23,165,61,129)(24,151,62,130)(25,152,63,131)(26,153,64,132)(27,154,65,133)(28,155,66,134)(29,156,67,135)(30,157,68,121)(31,199,175,223)(32,200,176,224)(33,201,177,225)(34,202,178,211)(35,203,179,212)(36,204,180,213)(37,205,166,214)(38,206,167,215)(39,207,168,216)(40,208,169,217)(41,209,170,218)(42,210,171,219)(43,196,172,220)(44,197,173,221)(45,198,174,222)(46,99,186,83)(47,100,187,84)(48,101,188,85)(49,102,189,86)(50,103,190,87)(51,104,191,88)(52,105,192,89)(53,91,193,90)(54,92,194,76)(55,93,195,77)(56,94,181,78)(57,95,182,79)(58,96,183,80)(59,97,184,81)(60,98,185,82), (1,38,100,133)(2,39,101,134)(3,40,102,135)(4,41,103,121)(5,42,104,122)(6,43,105,123)(7,44,91,124)(8,45,92,125)(9,31,93,126)(10,32,94,127)(11,33,95,128)(12,34,96,129)(13,35,97,130)(14,36,98,131)(15,37,99,132)(16,143,210,191)(17,144,196,192)(18,145,197,193)(19,146,198,194)(20,147,199,195)(21,148,200,181)(22,149,201,182)(23,150,202,183)(24,136,203,184)(25,137,204,185)(26,138,205,186)(27,139,206,187)(28,140,207,188)(29,141,208,189)(30,142,209,190)(46,64,119,214)(47,65,120,215)(48,66,106,216)(49,67,107,217)(50,68,108,218)(51,69,109,219)(52,70,110,220)(53,71,111,221)(54,72,112,222)(55,73,113,223)(56,74,114,224)(57,75,115,225)(58,61,116,211)(59,62,117,212)(60,63,118,213)(76,161,237,174)(77,162,238,175)(78,163,239,176)(79,164,240,177)(80,165,226,178)(81,151,227,179)(82,152,228,180)(83,153,229,166)(84,154,230,167)(85,155,231,168)(86,156,232,169)(87,157,233,170)(88,158,234,171)(89,159,235,172)(90,160,236,173), (16,69)(17,70)(18,71)(19,72)(20,73)(21,74)(22,75)(23,61)(24,62)(25,63)(26,64)(27,65)(28,66)(29,67)(30,68)(31,162)(32,163)(33,164)(34,165)(35,151)(36,152)(37,153)(38,154)(39,155)(40,156)(41,157)(42,158)(43,159)(44,160)(45,161)(46,119)(47,120)(48,106)(49,107)(50,108)(51,109)(52,110)(53,111)(54,112)(55,113)(56,114)(57,115)(58,116)(59,117)(60,118)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,166)(133,167)(134,168)(135,169)(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194)(147,195)(148,181)(149,182)(150,183)(196,220)(197,221)(198,222)(199,223)(200,224)(201,225)(202,211)(203,212)(204,213)(205,214)(206,215)(207,216)(208,217)(209,218)(210,219) );
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)], [(1,139,230,120),(2,140,231,106),(3,141,232,107),(4,142,233,108),(5,143,234,109),(6,144,235,110),(7,145,236,111),(8,146,237,112),(9,147,238,113),(10,148,239,114),(11,149,240,115),(12,150,226,116),(13,136,227,117),(14,137,228,118),(15,138,229,119),(16,158,69,122),(17,159,70,123),(18,160,71,124),(19,161,72,125),(20,162,73,126),(21,163,74,127),(22,164,75,128),(23,165,61,129),(24,151,62,130),(25,152,63,131),(26,153,64,132),(27,154,65,133),(28,155,66,134),(29,156,67,135),(30,157,68,121),(31,199,175,223),(32,200,176,224),(33,201,177,225),(34,202,178,211),(35,203,179,212),(36,204,180,213),(37,205,166,214),(38,206,167,215),(39,207,168,216),(40,208,169,217),(41,209,170,218),(42,210,171,219),(43,196,172,220),(44,197,173,221),(45,198,174,222),(46,99,186,83),(47,100,187,84),(48,101,188,85),(49,102,189,86),(50,103,190,87),(51,104,191,88),(52,105,192,89),(53,91,193,90),(54,92,194,76),(55,93,195,77),(56,94,181,78),(57,95,182,79),(58,96,183,80),(59,97,184,81),(60,98,185,82)], [(1,38,100,133),(2,39,101,134),(3,40,102,135),(4,41,103,121),(5,42,104,122),(6,43,105,123),(7,44,91,124),(8,45,92,125),(9,31,93,126),(10,32,94,127),(11,33,95,128),(12,34,96,129),(13,35,97,130),(14,36,98,131),(15,37,99,132),(16,143,210,191),(17,144,196,192),(18,145,197,193),(19,146,198,194),(20,147,199,195),(21,148,200,181),(22,149,201,182),(23,150,202,183),(24,136,203,184),(25,137,204,185),(26,138,205,186),(27,139,206,187),(28,140,207,188),(29,141,208,189),(30,142,209,190),(46,64,119,214),(47,65,120,215),(48,66,106,216),(49,67,107,217),(50,68,108,218),(51,69,109,219),(52,70,110,220),(53,71,111,221),(54,72,112,222),(55,73,113,223),(56,74,114,224),(57,75,115,225),(58,61,116,211),(59,62,117,212),(60,63,118,213),(76,161,237,174),(77,162,238,175),(78,163,239,176),(79,164,240,177),(80,165,226,178),(81,151,227,179),(82,152,228,180),(83,153,229,166),(84,154,230,167),(85,155,231,168),(86,156,232,169),(87,157,233,170),(88,158,234,171),(89,159,235,172),(90,160,236,173)], [(16,69),(17,70),(18,71),(19,72),(20,73),(21,74),(22,75),(23,61),(24,62),(25,63),(26,64),(27,65),(28,66),(29,67),(30,68),(31,162),(32,163),(33,164),(34,165),(35,151),(36,152),(37,153),(38,154),(39,155),(40,156),(41,157),(42,158),(43,159),(44,160),(45,161),(46,119),(47,120),(48,106),(49,107),(50,108),(51,109),(52,110),(53,111),(54,112),(55,113),(56,114),(57,115),(58,116),(59,117),(60,118),(121,170),(122,171),(123,172),(124,173),(125,174),(126,175),(127,176),(128,177),(129,178),(130,179),(131,180),(132,166),(133,167),(134,168),(135,169),(136,184),(137,185),(138,186),(139,187),(140,188),(141,189),(142,190),(143,191),(144,192),(145,193),(146,194),(147,195),(148,181),(149,182),(150,183),(196,220),(197,221),(198,222),(199,223),(200,224),(201,225),(202,211),(203,212),(204,213),(205,214),(206,215),(207,216),(208,217),(209,218),(210,219)]])
210 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3A | 3B | 4A | ··· | 4F | 4G | 4H | 4I | 5A | 5B | 5C | 5D | 6A | ··· | 6F | 6G | 6H | 10A | ··· | 10L | 10M | 10N | 10O | 10P | 12A | ··· | 12L | 12M | ··· | 12R | 15A | ··· | 15H | 20A | ··· | 20X | 20Y | ··· | 20AJ | 30A | ··· | 30X | 30Y | ··· | 30AF | 60A | ··· | 60AV | 60AW | ··· | 60BT |
| order | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | ··· | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | ··· | 6 | 6 | 6 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 12 | ··· | 12 | 12 | ··· | 12 | 15 | ··· | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 30 | ··· | 30 | 60 | ··· | 60 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 4 | 4 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
210 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | ||||||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C5 | C6 | C6 | C6 | C10 | C10 | C10 | C15 | C30 | C30 | C30 | C4○D4 | C3×C4○D4 | C5×C4○D4 | C15×C4○D4 |
| kernel | C15×C42⋊2C2 | C4×C60 | C15×C22⋊C4 | C15×C4⋊C4 | C5×C42⋊2C2 | C3×C42⋊2C2 | C4×C20 | C5×C22⋊C4 | C5×C4⋊C4 | C4×C12 | C3×C22⋊C4 | C3×C4⋊C4 | C42⋊2C2 | C42 | C22⋊C4 | C4⋊C4 | C30 | C10 | C6 | C2 |
| # reps | 1 | 1 | 3 | 3 | 2 | 4 | 2 | 6 | 6 | 4 | 12 | 12 | 8 | 8 | 24 | 24 | 6 | 12 | 24 | 48 |
Matrix representation of C15×C42⋊2C2 ►in GL4(𝔽61) generated by
| 42 | 0 | 0 | 0 |
| 0 | 42 | 0 | 0 |
| 0 | 0 | 47 | 0 |
| 0 | 0 | 0 | 47 |
| 11 | 0 | 0 | 0 |
| 2 | 50 | 0 | 0 |
| 0 | 0 | 50 | 0 |
| 0 | 0 | 0 | 50 |
| 11 | 0 | 0 | 0 |
| 0 | 11 | 0 | 0 |
| 0 | 0 | 45 | 50 |
| 0 | 0 | 1 | 16 |
| 1 | 50 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 1 | 32 |
| 0 | 0 | 0 | 60 |
G:=sub<GL(4,GF(61))| [42,0,0,0,0,42,0,0,0,0,47,0,0,0,0,47],[11,2,0,0,0,50,0,0,0,0,50,0,0,0,0,50],[11,0,0,0,0,11,0,0,0,0,45,1,0,0,50,16],[1,0,0,0,50,60,0,0,0,0,1,0,0,0,32,60] >;
C15×C42⋊2C2 in GAP, Magma, Sage, TeX
C_{15}\times C_4^2\rtimes_2C_2 % in TeX
G:=Group("C15xC4^2:2C2"); // GroupNames label
G:=SmallGroup(480,931);
// by ID
G=gap.SmallGroup(480,931);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-5,-2,-2,1709,2528,5126,646]);
// Polycyclic
G:=Group<a,b,c,d|a^15=b^4=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b*c^2,d*c*d=b^2*c^-1>;
// generators/relations