direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×C5⋊SD32, D40.2C6, C30.48D8, C15⋊14SD32, C24.50D10, C60.115D4, C120.43C22, C5⋊2C16⋊3C6, C8.6(C6×D5), C5⋊3(C3×SD32), C40.4(C2×C6), Q16⋊1(C3×D5), (C5×Q16)⋊1C6, (C3×Q16)⋊5D5, C20.5(C3×D4), (C15×Q16)⋊5C2, (C3×D40).4C2, C10.10(C3×D8), C6.26(D4⋊D5), C12.71(C5⋊D4), C2.6(C3×D4⋊D5), (C3×C5⋊2C16)⋊6C2, C4.3(C3×C5⋊D4), SmallGroup(480,106)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C5⋊SD32
G = < a,b,c,d | a3=b5=c16=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c7 >
Smallest permutation representation of C3×C5⋊SD32
►On 240 points
Generators in S240
(1 218 62)(2 219 63)(3 220 64)(4 221 49)(5 222 50)(6 223 51)(7 224 52)(8 209 53)(9 210 54)(10 211 55)(11 212 56)(12 213 57)(13 214 58)(14 215 59)(15 216 60)(16 217 61)(17 158 126)(18 159 127)(19 160 128)(20 145 113)(21 146 114)(22 147 115)(23 148 116)(24 149 117)(25 150 118)(26 151 119)(27 152 120)(28 153 121)(29 154 122)(30 155 123)(31 156 124)(32 157 125)(33 81 169)(34 82 170)(35 83 171)(36 84 172)(37 85 173)(38 86 174)(39 87 175)(40 88 176)(41 89 161)(42 90 162)(43 91 163)(44 92 164)(45 93 165)(46 94 166)(47 95 167)(48 96 168)(65 184 110)(66 185 111)(67 186 112)(68 187 97)(69 188 98)(70 189 99)(71 190 100)(72 191 101)(73 192 102)(74 177 103)(75 178 104)(76 179 105)(77 180 106)(78 181 107)(79 182 108)(80 183 109)(129 198 235)(130 199 236)(131 200 237)(132 201 238)(133 202 239)(134 203 240)(135 204 225)(136 205 226)(137 206 227)(138 207 228)(139 208 229)(140 193 230)(141 194 231)(142 195 232)(143 196 233)(144 197 234)
(1 179 132 152 87)(2 88 153 133 180)(3 181 134 154 89)(4 90 155 135 182)(5 183 136 156 91)(6 92 157 137 184)(7 185 138 158 93)(8 94 159 139 186)(9 187 140 160 95)(10 96 145 141 188)(11 189 142 146 81)(12 82 147 143 190)(13 191 144 148 83)(14 84 149 129 192)(15 177 130 150 85)(16 86 151 131 178)(17 45 52 66 228)(18 229 67 53 46)(19 47 54 68 230)(20 231 69 55 48)(21 33 56 70 232)(22 233 71 57 34)(23 35 58 72 234)(24 235 73 59 36)(25 37 60 74 236)(26 237 75 61 38)(27 39 62 76 238)(28 239 77 63 40)(29 41 64 78 240)(30 225 79 49 42)(31 43 50 80 226)(32 227 65 51 44)(97 193 128 167 210)(98 211 168 113 194)(99 195 114 169 212)(100 213 170 115 196)(101 197 116 171 214)(102 215 172 117 198)(103 199 118 173 216)(104 217 174 119 200)(105 201 120 175 218)(106 219 176 121 202)(107 203 122 161 220)(108 221 162 123 204)(109 205 124 163 222)(110 223 164 125 206)(111 207 126 165 224)(112 209 166 127 208)
(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)
(2 8)(3 15)(4 6)(5 13)(7 11)(10 16)(12 14)(17 232)(18 239)(19 230)(20 237)(21 228)(22 235)(23 226)(24 233)(25 240)(26 231)(27 238)(28 229)(29 236)(30 227)(31 234)(32 225)(33 66)(34 73)(35 80)(36 71)(37 78)(38 69)(39 76)(40 67)(41 74)(42 65)(43 72)(44 79)(45 70)(46 77)(47 68)(48 75)(49 51)(50 58)(52 56)(53 63)(55 61)(57 59)(60 64)(81 185)(82 192)(83 183)(84 190)(85 181)(86 188)(87 179)(88 186)(89 177)(90 184)(91 191)(92 182)(93 189)(94 180)(95 187)(96 178)(97 167)(98 174)(99 165)(100 172)(101 163)(102 170)(103 161)(104 168)(105 175)(106 166)(107 173)(108 164)(109 171)(110 162)(111 169)(112 176)(113 200)(114 207)(115 198)(116 205)(117 196)(118 203)(119 194)(120 201)(121 208)(122 199)(123 206)(124 197)(125 204)(126 195)(127 202)(128 193)(129 147)(130 154)(131 145)(132 152)(133 159)(134 150)(135 157)(136 148)(137 155)(138 146)(139 153)(140 160)(141 151)(142 158)(143 149)(144 156)(209 219)(211 217)(212 224)(213 215)(214 222)(216 220)(221 223)
G:=sub<Sym(240)| (1,218,62)(2,219,63)(3,220,64)(4,221,49)(5,222,50)(6,223,51)(7,224,52)(8,209,53)(9,210,54)(10,211,55)(11,212,56)(12,213,57)(13,214,58)(14,215,59)(15,216,60)(16,217,61)(17,158,126)(18,159,127)(19,160,128)(20,145,113)(21,146,114)(22,147,115)(23,148,116)(24,149,117)(25,150,118)(26,151,119)(27,152,120)(28,153,121)(29,154,122)(30,155,123)(31,156,124)(32,157,125)(33,81,169)(34,82,170)(35,83,171)(36,84,172)(37,85,173)(38,86,174)(39,87,175)(40,88,176)(41,89,161)(42,90,162)(43,91,163)(44,92,164)(45,93,165)(46,94,166)(47,95,167)(48,96,168)(65,184,110)(66,185,111)(67,186,112)(68,187,97)(69,188,98)(70,189,99)(71,190,100)(72,191,101)(73,192,102)(74,177,103)(75,178,104)(76,179,105)(77,180,106)(78,181,107)(79,182,108)(80,183,109)(129,198,235)(130,199,236)(131,200,237)(132,201,238)(133,202,239)(134,203,240)(135,204,225)(136,205,226)(137,206,227)(138,207,228)(139,208,229)(140,193,230)(141,194,231)(142,195,232)(143,196,233)(144,197,234), (1,179,132,152,87)(2,88,153,133,180)(3,181,134,154,89)(4,90,155,135,182)(5,183,136,156,91)(6,92,157,137,184)(7,185,138,158,93)(8,94,159,139,186)(9,187,140,160,95)(10,96,145,141,188)(11,189,142,146,81)(12,82,147,143,190)(13,191,144,148,83)(14,84,149,129,192)(15,177,130,150,85)(16,86,151,131,178)(17,45,52,66,228)(18,229,67,53,46)(19,47,54,68,230)(20,231,69,55,48)(21,33,56,70,232)(22,233,71,57,34)(23,35,58,72,234)(24,235,73,59,36)(25,37,60,74,236)(26,237,75,61,38)(27,39,62,76,238)(28,239,77,63,40)(29,41,64,78,240)(30,225,79,49,42)(31,43,50,80,226)(32,227,65,51,44)(97,193,128,167,210)(98,211,168,113,194)(99,195,114,169,212)(100,213,170,115,196)(101,197,116,171,214)(102,215,172,117,198)(103,199,118,173,216)(104,217,174,119,200)(105,201,120,175,218)(106,219,176,121,202)(107,203,122,161,220)(108,221,162,123,204)(109,205,124,163,222)(110,223,164,125,206)(111,207,126,165,224)(112,209,166,127,208), (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), (2,8)(3,15)(4,6)(5,13)(7,11)(10,16)(12,14)(17,232)(18,239)(19,230)(20,237)(21,228)(22,235)(23,226)(24,233)(25,240)(26,231)(27,238)(28,229)(29,236)(30,227)(31,234)(32,225)(33,66)(34,73)(35,80)(36,71)(37,78)(38,69)(39,76)(40,67)(41,74)(42,65)(43,72)(44,79)(45,70)(46,77)(47,68)(48,75)(49,51)(50,58)(52,56)(53,63)(55,61)(57,59)(60,64)(81,185)(82,192)(83,183)(84,190)(85,181)(86,188)(87,179)(88,186)(89,177)(90,184)(91,191)(92,182)(93,189)(94,180)(95,187)(96,178)(97,167)(98,174)(99,165)(100,172)(101,163)(102,170)(103,161)(104,168)(105,175)(106,166)(107,173)(108,164)(109,171)(110,162)(111,169)(112,176)(113,200)(114,207)(115,198)(116,205)(117,196)(118,203)(119,194)(120,201)(121,208)(122,199)(123,206)(124,197)(125,204)(126,195)(127,202)(128,193)(129,147)(130,154)(131,145)(132,152)(133,159)(134,150)(135,157)(136,148)(137,155)(138,146)(139,153)(140,160)(141,151)(142,158)(143,149)(144,156)(209,219)(211,217)(212,224)(213,215)(214,222)(216,220)(221,223)>;
G:=Group( (1,218,62)(2,219,63)(3,220,64)(4,221,49)(5,222,50)(6,223,51)(7,224,52)(8,209,53)(9,210,54)(10,211,55)(11,212,56)(12,213,57)(13,214,58)(14,215,59)(15,216,60)(16,217,61)(17,158,126)(18,159,127)(19,160,128)(20,145,113)(21,146,114)(22,147,115)(23,148,116)(24,149,117)(25,150,118)(26,151,119)(27,152,120)(28,153,121)(29,154,122)(30,155,123)(31,156,124)(32,157,125)(33,81,169)(34,82,170)(35,83,171)(36,84,172)(37,85,173)(38,86,174)(39,87,175)(40,88,176)(41,89,161)(42,90,162)(43,91,163)(44,92,164)(45,93,165)(46,94,166)(47,95,167)(48,96,168)(65,184,110)(66,185,111)(67,186,112)(68,187,97)(69,188,98)(70,189,99)(71,190,100)(72,191,101)(73,192,102)(74,177,103)(75,178,104)(76,179,105)(77,180,106)(78,181,107)(79,182,108)(80,183,109)(129,198,235)(130,199,236)(131,200,237)(132,201,238)(133,202,239)(134,203,240)(135,204,225)(136,205,226)(137,206,227)(138,207,228)(139,208,229)(140,193,230)(141,194,231)(142,195,232)(143,196,233)(144,197,234), (1,179,132,152,87)(2,88,153,133,180)(3,181,134,154,89)(4,90,155,135,182)(5,183,136,156,91)(6,92,157,137,184)(7,185,138,158,93)(8,94,159,139,186)(9,187,140,160,95)(10,96,145,141,188)(11,189,142,146,81)(12,82,147,143,190)(13,191,144,148,83)(14,84,149,129,192)(15,177,130,150,85)(16,86,151,131,178)(17,45,52,66,228)(18,229,67,53,46)(19,47,54,68,230)(20,231,69,55,48)(21,33,56,70,232)(22,233,71,57,34)(23,35,58,72,234)(24,235,73,59,36)(25,37,60,74,236)(26,237,75,61,38)(27,39,62,76,238)(28,239,77,63,40)(29,41,64,78,240)(30,225,79,49,42)(31,43,50,80,226)(32,227,65,51,44)(97,193,128,167,210)(98,211,168,113,194)(99,195,114,169,212)(100,213,170,115,196)(101,197,116,171,214)(102,215,172,117,198)(103,199,118,173,216)(104,217,174,119,200)(105,201,120,175,218)(106,219,176,121,202)(107,203,122,161,220)(108,221,162,123,204)(109,205,124,163,222)(110,223,164,125,206)(111,207,126,165,224)(112,209,166,127,208), (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), (2,8)(3,15)(4,6)(5,13)(7,11)(10,16)(12,14)(17,232)(18,239)(19,230)(20,237)(21,228)(22,235)(23,226)(24,233)(25,240)(26,231)(27,238)(28,229)(29,236)(30,227)(31,234)(32,225)(33,66)(34,73)(35,80)(36,71)(37,78)(38,69)(39,76)(40,67)(41,74)(42,65)(43,72)(44,79)(45,70)(46,77)(47,68)(48,75)(49,51)(50,58)(52,56)(53,63)(55,61)(57,59)(60,64)(81,185)(82,192)(83,183)(84,190)(85,181)(86,188)(87,179)(88,186)(89,177)(90,184)(91,191)(92,182)(93,189)(94,180)(95,187)(96,178)(97,167)(98,174)(99,165)(100,172)(101,163)(102,170)(103,161)(104,168)(105,175)(106,166)(107,173)(108,164)(109,171)(110,162)(111,169)(112,176)(113,200)(114,207)(115,198)(116,205)(117,196)(118,203)(119,194)(120,201)(121,208)(122,199)(123,206)(124,197)(125,204)(126,195)(127,202)(128,193)(129,147)(130,154)(131,145)(132,152)(133,159)(134,150)(135,157)(136,148)(137,155)(138,146)(139,153)(140,160)(141,151)(142,158)(143,149)(144,156)(209,219)(211,217)(212,224)(213,215)(214,222)(216,220)(221,223) );
G=PermutationGroup([[(1,218,62),(2,219,63),(3,220,64),(4,221,49),(5,222,50),(6,223,51),(7,224,52),(8,209,53),(9,210,54),(10,211,55),(11,212,56),(12,213,57),(13,214,58),(14,215,59),(15,216,60),(16,217,61),(17,158,126),(18,159,127),(19,160,128),(20,145,113),(21,146,114),(22,147,115),(23,148,116),(24,149,117),(25,150,118),(26,151,119),(27,152,120),(28,153,121),(29,154,122),(30,155,123),(31,156,124),(32,157,125),(33,81,169),(34,82,170),(35,83,171),(36,84,172),(37,85,173),(38,86,174),(39,87,175),(40,88,176),(41,89,161),(42,90,162),(43,91,163),(44,92,164),(45,93,165),(46,94,166),(47,95,167),(48,96,168),(65,184,110),(66,185,111),(67,186,112),(68,187,97),(69,188,98),(70,189,99),(71,190,100),(72,191,101),(73,192,102),(74,177,103),(75,178,104),(76,179,105),(77,180,106),(78,181,107),(79,182,108),(80,183,109),(129,198,235),(130,199,236),(131,200,237),(132,201,238),(133,202,239),(134,203,240),(135,204,225),(136,205,226),(137,206,227),(138,207,228),(139,208,229),(140,193,230),(141,194,231),(142,195,232),(143,196,233),(144,197,234)], [(1,179,132,152,87),(2,88,153,133,180),(3,181,134,154,89),(4,90,155,135,182),(5,183,136,156,91),(6,92,157,137,184),(7,185,138,158,93),(8,94,159,139,186),(9,187,140,160,95),(10,96,145,141,188),(11,189,142,146,81),(12,82,147,143,190),(13,191,144,148,83),(14,84,149,129,192),(15,177,130,150,85),(16,86,151,131,178),(17,45,52,66,228),(18,229,67,53,46),(19,47,54,68,230),(20,231,69,55,48),(21,33,56,70,232),(22,233,71,57,34),(23,35,58,72,234),(24,235,73,59,36),(25,37,60,74,236),(26,237,75,61,38),(27,39,62,76,238),(28,239,77,63,40),(29,41,64,78,240),(30,225,79,49,42),(31,43,50,80,226),(32,227,65,51,44),(97,193,128,167,210),(98,211,168,113,194),(99,195,114,169,212),(100,213,170,115,196),(101,197,116,171,214),(102,215,172,117,198),(103,199,118,173,216),(104,217,174,119,200),(105,201,120,175,218),(106,219,176,121,202),(107,203,122,161,220),(108,221,162,123,204),(109,205,124,163,222),(110,223,164,125,206),(111,207,126,165,224),(112,209,166,127,208)], [(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)], [(2,8),(3,15),(4,6),(5,13),(7,11),(10,16),(12,14),(17,232),(18,239),(19,230),(20,237),(21,228),(22,235),(23,226),(24,233),(25,240),(26,231),(27,238),(28,229),(29,236),(30,227),(31,234),(32,225),(33,66),(34,73),(35,80),(36,71),(37,78),(38,69),(39,76),(40,67),(41,74),(42,65),(43,72),(44,79),(45,70),(46,77),(47,68),(48,75),(49,51),(50,58),(52,56),(53,63),(55,61),(57,59),(60,64),(81,185),(82,192),(83,183),(84,190),(85,181),(86,188),(87,179),(88,186),(89,177),(90,184),(91,191),(92,182),(93,189),(94,180),(95,187),(96,178),(97,167),(98,174),(99,165),(100,172),(101,163),(102,170),(103,161),(104,168),(105,175),(106,166),(107,173),(108,164),(109,171),(110,162),(111,169),(112,176),(113,200),(114,207),(115,198),(116,205),(117,196),(118,203),(119,194),(120,201),(121,208),(122,199),(123,206),(124,197),(125,204),(126,195),(127,202),(128,193),(129,147),(130,154),(131,145),(132,152),(133,159),(134,150),(135,157),(136,148),(137,155),(138,146),(139,153),(140,160),(141,151),(142,158),(143,149),(144,156),(209,219),(211,217),(212,224),(213,215),(214,222),(216,220),(221,223)]])
75 conjugacy classes
| class | 1 | 2A | 2B | 3A | 3B | 4A | 4B | 5A | 5B | 6A | 6B | 6C | 6D | 8A | 8B | 10A | 10B | 12A | 12B | 12C | 12D | 15A | 15B | 15C | 15D | 16A | 16B | 16C | 16D | 20A | 20B | 20C | 20D | 20E | 20F | 24A | 24B | 24C | 24D | 30A | 30B | 30C | 30D | 40A | 40B | 40C | 40D | 48A | ··· | 48H | 60A | 60B | 60C | 60D | 60E | ··· | 60L | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 8 | 8 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 30 | 30 | 30 | 30 | 40 | 40 | 40 | 40 | 48 | ··· | 48 | 60 | 60 | 60 | 60 | 60 | ··· | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 40 | 1 | 1 | 2 | 8 | 2 | 2 | 1 | 1 | 40 | 40 | 2 | 2 | 2 | 2 | 2 | 2 | 8 | 8 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 4 | 4 | 8 | 8 | 8 | 8 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
75 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | ||||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | D4 | D5 | D8 | D10 | C3×D4 | C3×D5 | SD32 | C5⋊D4 | C3×D8 | C6×D5 | C3×SD32 | C3×C5⋊D4 | D4⋊D5 | C5⋊SD32 | C3×D4⋊D5 | C3×C5⋊SD32 |
| kernel | C3×C5⋊SD32 | C3×C5⋊2C16 | C3×D40 | C15×Q16 | C5⋊SD32 | C5⋊2C16 | D40 | C5×Q16 | C60 | C3×Q16 | C30 | C24 | C20 | Q16 | C15 | C12 | C10 | C8 | C5 | C4 | C6 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 2 | 4 | 4 | 8 |
Matrix representation of C3×C5⋊SD32 ►in GL4(𝔽241) generated by
| 225 | 0 | 0 | 0 |
| 0 | 225 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 240 | 188 | 0 | 0 |
| 1 | 52 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 145 | 42 | 0 | 0 |
| 165 | 96 | 0 | 0 |
| 0 | 0 | 179 | 160 |
| 0 | 0 | 223 | 97 |
| 189 | 189 | 0 | 0 |
| 1 | 52 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 123 | 240 |
G:=sub<GL(4,GF(241))| [225,0,0,0,0,225,0,0,0,0,1,0,0,0,0,1],[240,1,0,0,188,52,0,0,0,0,1,0,0,0,0,1],[145,165,0,0,42,96,0,0,0,0,179,223,0,0,160,97],[189,1,0,0,189,52,0,0,0,0,1,123,0,0,0,240] >;
C3×C5⋊SD32 in GAP, Magma, Sage, TeX
C_3\times C_5\rtimes {\rm SD}_{32} % in TeX
G:=Group("C3xC5:SD32"); // GroupNames label
G:=SmallGroup(480,106);
// by ID
G=gap.SmallGroup(480,106);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,197,344,1011,514,192,2524,1271,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^5=c^16=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^7>;
// generators/relations
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