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G = C5×C3⋊D16order 480 = 25·3·5

Direct product of C5 and C3⋊D16

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C5×C3⋊D16, C159D16, D243C10, C40.56D6, C30.53D8, C60.136D4, C120.63C22, C32(C5×D16), C3⋊C161C10, (C5×D8)⋊5S3, D81(C5×S3), C6.8(C5×D8), (C15×D8)⋊8C2, (C3×D8)⋊1C10, C8.4(S3×C10), C12.3(C5×D4), (C5×D24)⋊11C2, C24.2(C2×C10), C10.24(D4⋊S3), C20.66(C3⋊D4), (C5×C3⋊C16)⋊8C2, C2.4(C5×D4⋊S3), C4.1(C5×C3⋊D4), SmallGroup(480,145)

Series: Derived Chief Lower central Upper central

C1C24 — C5×C3⋊D16
C1C3C6C12C24C120C5×D24 — C5×C3⋊D16
C3C6C12C24 — C5×C3⋊D16
C1C10C20C40C5×D8

Generators and relations for C5×C3⋊D16
 G = < a,b,c,d | a5=b3=c16=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >

8C2
24C2
4C22
12C22
8C6
8S3
8C10
24C10
2D4
6D4
4D6
4C2×C6
4C2×C10
12C2×C10
8C30
8C5×S3
3D8
3C16
2C3×D4
2D12
2C5×D4
6C5×D4
4C2×C30
4S3×C10
3D16
3C5×D8
3C80
2D4×C15
2C5×D12
3C5×D16

Smallest permutation representation of C5×C3⋊D16
On 240 points
Generators in S240
(1 103 174 193 63)(2 104 175 194 64)(3 105 176 195 49)(4 106 161 196 50)(5 107 162 197 51)(6 108 163 198 52)(7 109 164 199 53)(8 110 165 200 54)(9 111 166 201 55)(10 112 167 202 56)(11 97 168 203 57)(12 98 169 204 58)(13 99 170 205 59)(14 100 171 206 60)(15 101 172 207 61)(16 102 173 208 62)(17 153 184 85 233)(18 154 185 86 234)(19 155 186 87 235)(20 156 187 88 236)(21 157 188 89 237)(22 158 189 90 238)(23 159 190 91 239)(24 160 191 92 240)(25 145 192 93 225)(26 146 177 94 226)(27 147 178 95 227)(28 148 179 96 228)(29 149 180 81 229)(30 150 181 82 230)(31 151 182 83 231)(32 152 183 84 232)(33 210 127 71 136)(34 211 128 72 137)(35 212 113 73 138)(36 213 114 74 139)(37 214 115 75 140)(38 215 116 76 141)(39 216 117 77 142)(40 217 118 78 143)(41 218 119 79 144)(42 219 120 80 129)(43 220 121 65 130)(44 221 122 66 131)(45 222 123 67 132)(46 223 124 68 133)(47 224 125 69 134)(48 209 126 70 135)
(1 33 190)(2 191 34)(3 35 192)(4 177 36)(5 37 178)(6 179 38)(7 39 180)(8 181 40)(9 41 182)(10 183 42)(11 43 184)(12 185 44)(13 45 186)(14 187 46)(15 47 188)(16 189 48)(17 203 65)(18 66 204)(19 205 67)(20 68 206)(21 207 69)(22 70 208)(23 193 71)(24 72 194)(25 195 73)(26 74 196)(27 197 75)(28 76 198)(29 199 77)(30 78 200)(31 201 79)(32 80 202)(49 138 145)(50 146 139)(51 140 147)(52 148 141)(53 142 149)(54 150 143)(55 144 151)(56 152 129)(57 130 153)(58 154 131)(59 132 155)(60 156 133)(61 134 157)(62 158 135)(63 136 159)(64 160 137)(81 109 216)(82 217 110)(83 111 218)(84 219 112)(85 97 220)(86 221 98)(87 99 222)(88 223 100)(89 101 224)(90 209 102)(91 103 210)(92 211 104)(93 105 212)(94 213 106)(95 107 214)(96 215 108)(113 225 176)(114 161 226)(115 227 162)(116 163 228)(117 229 164)(118 165 230)(119 231 166)(120 167 232)(121 233 168)(122 169 234)(123 235 170)(124 171 236)(125 237 172)(126 173 238)(127 239 174)(128 175 240)
(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)
(2 16)(3 15)(4 14)(5 13)(6 12)(7 11)(8 10)(17 77)(18 76)(19 75)(20 74)(21 73)(22 72)(23 71)(24 70)(25 69)(26 68)(27 67)(28 66)(29 65)(30 80)(31 79)(32 78)(33 190)(34 189)(35 188)(36 187)(37 186)(38 185)(39 184)(40 183)(41 182)(42 181)(43 180)(44 179)(45 178)(46 177)(47 192)(48 191)(49 61)(50 60)(51 59)(52 58)(53 57)(54 56)(62 64)(81 220)(82 219)(83 218)(84 217)(85 216)(86 215)(87 214)(88 213)(89 212)(90 211)(91 210)(92 209)(93 224)(94 223)(95 222)(96 221)(97 109)(98 108)(99 107)(100 106)(101 105)(102 104)(110 112)(113 237)(114 236)(115 235)(116 234)(117 233)(118 232)(119 231)(120 230)(121 229)(122 228)(123 227)(124 226)(125 225)(126 240)(127 239)(128 238)(129 150)(130 149)(131 148)(132 147)(133 146)(134 145)(135 160)(136 159)(137 158)(138 157)(139 156)(140 155)(141 154)(142 153)(143 152)(144 151)(161 171)(162 170)(163 169)(164 168)(165 167)(172 176)(173 175)(194 208)(195 207)(196 206)(197 205)(198 204)(199 203)(200 202)

G:=sub<Sym(240)| (1,103,174,193,63)(2,104,175,194,64)(3,105,176,195,49)(4,106,161,196,50)(5,107,162,197,51)(6,108,163,198,52)(7,109,164,199,53)(8,110,165,200,54)(9,111,166,201,55)(10,112,167,202,56)(11,97,168,203,57)(12,98,169,204,58)(13,99,170,205,59)(14,100,171,206,60)(15,101,172,207,61)(16,102,173,208,62)(17,153,184,85,233)(18,154,185,86,234)(19,155,186,87,235)(20,156,187,88,236)(21,157,188,89,237)(22,158,189,90,238)(23,159,190,91,239)(24,160,191,92,240)(25,145,192,93,225)(26,146,177,94,226)(27,147,178,95,227)(28,148,179,96,228)(29,149,180,81,229)(30,150,181,82,230)(31,151,182,83,231)(32,152,183,84,232)(33,210,127,71,136)(34,211,128,72,137)(35,212,113,73,138)(36,213,114,74,139)(37,214,115,75,140)(38,215,116,76,141)(39,216,117,77,142)(40,217,118,78,143)(41,218,119,79,144)(42,219,120,80,129)(43,220,121,65,130)(44,221,122,66,131)(45,222,123,67,132)(46,223,124,68,133)(47,224,125,69,134)(48,209,126,70,135), (1,33,190)(2,191,34)(3,35,192)(4,177,36)(5,37,178)(6,179,38)(7,39,180)(8,181,40)(9,41,182)(10,183,42)(11,43,184)(12,185,44)(13,45,186)(14,187,46)(15,47,188)(16,189,48)(17,203,65)(18,66,204)(19,205,67)(20,68,206)(21,207,69)(22,70,208)(23,193,71)(24,72,194)(25,195,73)(26,74,196)(27,197,75)(28,76,198)(29,199,77)(30,78,200)(31,201,79)(32,80,202)(49,138,145)(50,146,139)(51,140,147)(52,148,141)(53,142,149)(54,150,143)(55,144,151)(56,152,129)(57,130,153)(58,154,131)(59,132,155)(60,156,133)(61,134,157)(62,158,135)(63,136,159)(64,160,137)(81,109,216)(82,217,110)(83,111,218)(84,219,112)(85,97,220)(86,221,98)(87,99,222)(88,223,100)(89,101,224)(90,209,102)(91,103,210)(92,211,104)(93,105,212)(94,213,106)(95,107,214)(96,215,108)(113,225,176)(114,161,226)(115,227,162)(116,163,228)(117,229,164)(118,165,230)(119,231,166)(120,167,232)(121,233,168)(122,169,234)(123,235,170)(124,171,236)(125,237,172)(126,173,238)(127,239,174)(128,175,240), (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), (2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(17,77)(18,76)(19,75)(20,74)(21,73)(22,72)(23,71)(24,70)(25,69)(26,68)(27,67)(28,66)(29,65)(30,80)(31,79)(32,78)(33,190)(34,189)(35,188)(36,187)(37,186)(38,185)(39,184)(40,183)(41,182)(42,181)(43,180)(44,179)(45,178)(46,177)(47,192)(48,191)(49,61)(50,60)(51,59)(52,58)(53,57)(54,56)(62,64)(81,220)(82,219)(83,218)(84,217)(85,216)(86,215)(87,214)(88,213)(89,212)(90,211)(91,210)(92,209)(93,224)(94,223)(95,222)(96,221)(97,109)(98,108)(99,107)(100,106)(101,105)(102,104)(110,112)(113,237)(114,236)(115,235)(116,234)(117,233)(118,232)(119,231)(120,230)(121,229)(122,228)(123,227)(124,226)(125,225)(126,240)(127,239)(128,238)(129,150)(130,149)(131,148)(132,147)(133,146)(134,145)(135,160)(136,159)(137,158)(138,157)(139,156)(140,155)(141,154)(142,153)(143,152)(144,151)(161,171)(162,170)(163,169)(164,168)(165,167)(172,176)(173,175)(194,208)(195,207)(196,206)(197,205)(198,204)(199,203)(200,202)>;

G:=Group( (1,103,174,193,63)(2,104,175,194,64)(3,105,176,195,49)(4,106,161,196,50)(5,107,162,197,51)(6,108,163,198,52)(7,109,164,199,53)(8,110,165,200,54)(9,111,166,201,55)(10,112,167,202,56)(11,97,168,203,57)(12,98,169,204,58)(13,99,170,205,59)(14,100,171,206,60)(15,101,172,207,61)(16,102,173,208,62)(17,153,184,85,233)(18,154,185,86,234)(19,155,186,87,235)(20,156,187,88,236)(21,157,188,89,237)(22,158,189,90,238)(23,159,190,91,239)(24,160,191,92,240)(25,145,192,93,225)(26,146,177,94,226)(27,147,178,95,227)(28,148,179,96,228)(29,149,180,81,229)(30,150,181,82,230)(31,151,182,83,231)(32,152,183,84,232)(33,210,127,71,136)(34,211,128,72,137)(35,212,113,73,138)(36,213,114,74,139)(37,214,115,75,140)(38,215,116,76,141)(39,216,117,77,142)(40,217,118,78,143)(41,218,119,79,144)(42,219,120,80,129)(43,220,121,65,130)(44,221,122,66,131)(45,222,123,67,132)(46,223,124,68,133)(47,224,125,69,134)(48,209,126,70,135), (1,33,190)(2,191,34)(3,35,192)(4,177,36)(5,37,178)(6,179,38)(7,39,180)(8,181,40)(9,41,182)(10,183,42)(11,43,184)(12,185,44)(13,45,186)(14,187,46)(15,47,188)(16,189,48)(17,203,65)(18,66,204)(19,205,67)(20,68,206)(21,207,69)(22,70,208)(23,193,71)(24,72,194)(25,195,73)(26,74,196)(27,197,75)(28,76,198)(29,199,77)(30,78,200)(31,201,79)(32,80,202)(49,138,145)(50,146,139)(51,140,147)(52,148,141)(53,142,149)(54,150,143)(55,144,151)(56,152,129)(57,130,153)(58,154,131)(59,132,155)(60,156,133)(61,134,157)(62,158,135)(63,136,159)(64,160,137)(81,109,216)(82,217,110)(83,111,218)(84,219,112)(85,97,220)(86,221,98)(87,99,222)(88,223,100)(89,101,224)(90,209,102)(91,103,210)(92,211,104)(93,105,212)(94,213,106)(95,107,214)(96,215,108)(113,225,176)(114,161,226)(115,227,162)(116,163,228)(117,229,164)(118,165,230)(119,231,166)(120,167,232)(121,233,168)(122,169,234)(123,235,170)(124,171,236)(125,237,172)(126,173,238)(127,239,174)(128,175,240), (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), (2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(17,77)(18,76)(19,75)(20,74)(21,73)(22,72)(23,71)(24,70)(25,69)(26,68)(27,67)(28,66)(29,65)(30,80)(31,79)(32,78)(33,190)(34,189)(35,188)(36,187)(37,186)(38,185)(39,184)(40,183)(41,182)(42,181)(43,180)(44,179)(45,178)(46,177)(47,192)(48,191)(49,61)(50,60)(51,59)(52,58)(53,57)(54,56)(62,64)(81,220)(82,219)(83,218)(84,217)(85,216)(86,215)(87,214)(88,213)(89,212)(90,211)(91,210)(92,209)(93,224)(94,223)(95,222)(96,221)(97,109)(98,108)(99,107)(100,106)(101,105)(102,104)(110,112)(113,237)(114,236)(115,235)(116,234)(117,233)(118,232)(119,231)(120,230)(121,229)(122,228)(123,227)(124,226)(125,225)(126,240)(127,239)(128,238)(129,150)(130,149)(131,148)(132,147)(133,146)(134,145)(135,160)(136,159)(137,158)(138,157)(139,156)(140,155)(141,154)(142,153)(143,152)(144,151)(161,171)(162,170)(163,169)(164,168)(165,167)(172,176)(173,175)(194,208)(195,207)(196,206)(197,205)(198,204)(199,203)(200,202) );

G=PermutationGroup([(1,103,174,193,63),(2,104,175,194,64),(3,105,176,195,49),(4,106,161,196,50),(5,107,162,197,51),(6,108,163,198,52),(7,109,164,199,53),(8,110,165,200,54),(9,111,166,201,55),(10,112,167,202,56),(11,97,168,203,57),(12,98,169,204,58),(13,99,170,205,59),(14,100,171,206,60),(15,101,172,207,61),(16,102,173,208,62),(17,153,184,85,233),(18,154,185,86,234),(19,155,186,87,235),(20,156,187,88,236),(21,157,188,89,237),(22,158,189,90,238),(23,159,190,91,239),(24,160,191,92,240),(25,145,192,93,225),(26,146,177,94,226),(27,147,178,95,227),(28,148,179,96,228),(29,149,180,81,229),(30,150,181,82,230),(31,151,182,83,231),(32,152,183,84,232),(33,210,127,71,136),(34,211,128,72,137),(35,212,113,73,138),(36,213,114,74,139),(37,214,115,75,140),(38,215,116,76,141),(39,216,117,77,142),(40,217,118,78,143),(41,218,119,79,144),(42,219,120,80,129),(43,220,121,65,130),(44,221,122,66,131),(45,222,123,67,132),(46,223,124,68,133),(47,224,125,69,134),(48,209,126,70,135)], [(1,33,190),(2,191,34),(3,35,192),(4,177,36),(5,37,178),(6,179,38),(7,39,180),(8,181,40),(9,41,182),(10,183,42),(11,43,184),(12,185,44),(13,45,186),(14,187,46),(15,47,188),(16,189,48),(17,203,65),(18,66,204),(19,205,67),(20,68,206),(21,207,69),(22,70,208),(23,193,71),(24,72,194),(25,195,73),(26,74,196),(27,197,75),(28,76,198),(29,199,77),(30,78,200),(31,201,79),(32,80,202),(49,138,145),(50,146,139),(51,140,147),(52,148,141),(53,142,149),(54,150,143),(55,144,151),(56,152,129),(57,130,153),(58,154,131),(59,132,155),(60,156,133),(61,134,157),(62,158,135),(63,136,159),(64,160,137),(81,109,216),(82,217,110),(83,111,218),(84,219,112),(85,97,220),(86,221,98),(87,99,222),(88,223,100),(89,101,224),(90,209,102),(91,103,210),(92,211,104),(93,105,212),(94,213,106),(95,107,214),(96,215,108),(113,225,176),(114,161,226),(115,227,162),(116,163,228),(117,229,164),(118,165,230),(119,231,166),(120,167,232),(121,233,168),(122,169,234),(123,235,170),(124,171,236),(125,237,172),(126,173,238),(127,239,174),(128,175,240)], [(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)], [(2,16),(3,15),(4,14),(5,13),(6,12),(7,11),(8,10),(17,77),(18,76),(19,75),(20,74),(21,73),(22,72),(23,71),(24,70),(25,69),(26,68),(27,67),(28,66),(29,65),(30,80),(31,79),(32,78),(33,190),(34,189),(35,188),(36,187),(37,186),(38,185),(39,184),(40,183),(41,182),(42,181),(43,180),(44,179),(45,178),(46,177),(47,192),(48,191),(49,61),(50,60),(51,59),(52,58),(53,57),(54,56),(62,64),(81,220),(82,219),(83,218),(84,217),(85,216),(86,215),(87,214),(88,213),(89,212),(90,211),(91,210),(92,209),(93,224),(94,223),(95,222),(96,221),(97,109),(98,108),(99,107),(100,106),(101,105),(102,104),(110,112),(113,237),(114,236),(115,235),(116,234),(117,233),(118,232),(119,231),(120,230),(121,229),(122,228),(123,227),(124,226),(125,225),(126,240),(127,239),(128,238),(129,150),(130,149),(131,148),(132,147),(133,146),(134,145),(135,160),(136,159),(137,158),(138,157),(139,156),(140,155),(141,154),(142,153),(143,152),(144,151),(161,171),(162,170),(163,169),(164,168),(165,167),(172,176),(173,175),(194,208),(195,207),(196,206),(197,205),(198,204),(199,203),(200,202)])

90 conjugacy classes

class 1 2A2B2C 3  4 5A5B5C5D6A6B6C8A8B10A10B10C10D10E10F10G10H10I10J10K10L 12 15A15B15C15D16A16B16C16D20A20B20C20D24A24B30A30B30C30D30E···30L40A···40H60A60B60C60D80A···80P120A···120H
order1222345555666881010101010101010101010101215151515161616162020202024243030303030···3040···406060606080···80120···120
size1182422111128822111188882424242442222666622224422228···82···244446···64···4

90 irreducible representations

dim111111112222222222224444
type+++++++++++
imageC1C2C2C2C5C10C10C10S3D4D6D8C3⋊D4C5×S3D16C5×D4S3×C10C5×D8C5×C3⋊D4C5×D16D4⋊S3C3⋊D16C5×D4⋊S3C5×C3⋊D16
kernelC5×C3⋊D16C5×C3⋊C16C5×D24C15×D8C3⋊D16C3⋊C16D24C3×D8C5×D8C60C40C30C20D8C15C12C8C6C4C3C10C5C2C1
# reps1111444411122444488161248

Matrix representation of C5×C3⋊D16 in GL4(𝔽241) generated by

205000
020500
0010
0001
,
24024000
1000
0010
0001
,
240000
1100
0058137
00227129
,
1000
24024000
0010
00238240
G:=sub<GL(4,GF(241))| [205,0,0,0,0,205,0,0,0,0,1,0,0,0,0,1],[240,1,0,0,240,0,0,0,0,0,1,0,0,0,0,1],[240,1,0,0,0,1,0,0,0,0,58,227,0,0,137,129],[1,240,0,0,0,240,0,0,0,0,1,238,0,0,0,240] >;

C5×C3⋊D16 in GAP, Magma, Sage, TeX

C_5\times C_3\rtimes D_{16}
% in TeX

G:=Group("C5xC3:D16");
// GroupNames label

G:=SmallGroup(480,145);
// by ID

G=gap.SmallGroup(480,145);
# by ID

G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,309,1683,850,192,4204,2111,102,15686]);
// Polycyclic

G:=Group<a,b,c,d|a^5=b^3=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^-1>;
// generators/relations

Export

Subgroup lattice of C5×C3⋊D16 in TeX

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