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G = D5×C3⋊C16order 480 = 25·3·5

Direct product of D5 and C3⋊C16

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

Aliases: D5×C3⋊C16, C40.48D6, C24.55D10, C120.51C22, C33(D5×C16), C155(C2×C16), (C3×D5)⋊1C16, (C6×D5).1C8, C6.11(C8×D5), C8.34(S3×D5), C153C169C2, C30.19(C2×C8), D10.4(C3⋊C8), (D5×C12).2C4, (C8×D5).11S3, (D5×C24).3C2, C12.73(C4×D5), C60.135(C2×C4), Dic5.4(C3⋊C8), (C4×D5).9Dic3, (C3×Dic5).1C8, C4.16(D5×Dic3), C52C8.7Dic3, C20.42(C2×Dic3), C53(C2×C3⋊C16), (C5×C3⋊C16)⋊4C2, C2.1(D5×C3⋊C8), C10.10(C2×C3⋊C8), (C3×C52C8).2C4, SmallGroup(480,7)

Series: Derived Chief Lower central Upper central

C1C15 — D5×C3⋊C16
C1C5C15C30C60C120D5×C24 — D5×C3⋊C16
C15 — D5×C3⋊C16
C1C8

Generators and relations for D5×C3⋊C16
 G = < a,b,c,d | a5=b2=c3=d16=1, bab=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >

5C2
5C2
5C4
5C22
5C6
5C6
5C8
5C2×C4
5C12
5C2×C6
3C16
5C2×C8
15C16
5C24
5C2×C12
15C2×C16
5C3⋊C16
5C2×C24
3C80
3C52C16
5C2×C3⋊C16
3D5×C16

Smallest permutation representation of D5×C3⋊C16
On 240 points
Generators in S240
(1 192 170 214 207)(2 177 171 215 208)(3 178 172 216 193)(4 179 173 217 194)(5 180 174 218 195)(6 181 175 219 196)(7 182 176 220 197)(8 183 161 221 198)(9 184 162 222 199)(10 185 163 223 200)(11 186 164 224 201)(12 187 165 209 202)(13 188 166 210 203)(14 189 167 211 204)(15 190 168 212 205)(16 191 169 213 206)(17 110 227 123 65)(18 111 228 124 66)(19 112 229 125 67)(20 97 230 126 68)(21 98 231 127 69)(22 99 232 128 70)(23 100 233 113 71)(24 101 234 114 72)(25 102 235 115 73)(26 103 236 116 74)(27 104 237 117 75)(28 105 238 118 76)(29 106 239 119 77)(30 107 240 120 78)(31 108 225 121 79)(32 109 226 122 80)(33 138 153 84 49)(34 139 154 85 50)(35 140 155 86 51)(36 141 156 87 52)(37 142 157 88 53)(38 143 158 89 54)(39 144 159 90 55)(40 129 160 91 56)(41 130 145 92 57)(42 131 146 93 58)(43 132 147 94 59)(44 133 148 95 60)(45 134 149 96 61)(46 135 150 81 62)(47 136 151 82 63)(48 137 152 83 64)
(1 199)(2 200)(3 201)(4 202)(5 203)(6 204)(7 205)(8 206)(9 207)(10 208)(11 193)(12 194)(13 195)(14 196)(15 197)(16 198)(17 115)(18 116)(19 117)(20 118)(21 119)(22 120)(23 121)(24 122)(25 123)(26 124)(27 125)(28 126)(29 127)(30 128)(31 113)(32 114)(33 145)(34 146)(35 147)(36 148)(37 149)(38 150)(39 151)(40 152)(41 153)(42 154)(43 155)(44 156)(45 157)(46 158)(47 159)(48 160)(49 92)(50 93)(51 94)(52 95)(53 96)(54 81)(55 82)(56 83)(57 84)(58 85)(59 86)(60 87)(61 88)(62 89)(63 90)(64 91)(65 73)(66 74)(67 75)(68 76)(69 77)(70 78)(71 79)(72 80)(97 238)(98 239)(99 240)(100 225)(101 226)(102 227)(103 228)(104 229)(105 230)(106 231)(107 232)(108 233)(109 234)(110 235)(111 236)(112 237)(129 137)(130 138)(131 139)(132 140)(133 141)(134 142)(135 143)(136 144)(161 169)(162 170)(163 171)(164 172)(165 173)(166 174)(167 175)(168 176)(177 223)(178 224)(179 209)(180 210)(181 211)(182 212)(183 213)(184 214)(185 215)(186 216)(187 217)(188 218)(189 219)(190 220)(191 221)(192 222)
(1 52 235)(2 236 53)(3 54 237)(4 238 55)(5 56 239)(6 240 57)(7 58 225)(8 226 59)(9 60 227)(10 228 61)(11 62 229)(12 230 63)(13 64 231)(14 232 49)(15 50 233)(16 234 51)(17 222 148)(18 149 223)(19 224 150)(20 151 209)(21 210 152)(22 153 211)(23 212 154)(24 155 213)(25 214 156)(26 157 215)(27 216 158)(28 159 217)(29 218 160)(30 145 219)(31 220 146)(32 147 221)(33 189 128)(34 113 190)(35 191 114)(36 115 192)(37 177 116)(38 117 178)(39 179 118)(40 119 180)(41 181 120)(42 121 182)(43 183 122)(44 123 184)(45 185 124)(46 125 186)(47 187 126)(48 127 188)(65 162 133)(66 134 163)(67 164 135)(68 136 165)(69 166 137)(70 138 167)(71 168 139)(72 140 169)(73 170 141)(74 142 171)(75 172 143)(76 144 173)(77 174 129)(78 130 175)(79 176 131)(80 132 161)(81 112 201)(82 202 97)(83 98 203)(84 204 99)(85 100 205)(86 206 101)(87 102 207)(88 208 103)(89 104 193)(90 194 105)(91 106 195)(92 196 107)(93 108 197)(94 198 109)(95 110 199)(96 200 111)
(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)

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

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

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

96 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D5A5B6A6B6C8A8B8C8D8E8F8G8H10A10B12A12B12C12D15A15B16A···16H16I···16P20A20B20C20D24A24B24C24D24E24F24G24H30A30B40A···40H60A60B60C60D80A···80P120A···120H
order1222344445566688888888101012121212151516···1616···16202020202424242424242424303040···406060606080···80120···120
size11552115522210101111555522221010443···315···152222222210101010442···244446···64···4

96 irreducible representations

dim1111111112222222222224444
type++++++-+-++-
imageC1C2C2C2C4C4C8C8C16S3D5Dic3D6Dic3D10C3⋊C8C3⋊C8C4×D5C3⋊C16C8×D5D5×C16S3×D5D5×Dic3D5×C3⋊C8D5×C3⋊C16
kernelD5×C3⋊C16C5×C3⋊C16C153C16D5×C24C3×C52C8D5×C12C3×Dic5C6×D5C3×D5C8×D5C3⋊C16C52C8C40C4×D5C24Dic5D10C12D5C6C3C8C4C2C1
# reps111122441612111222488162248

Matrix representation of D5×C3⋊C16 in GL4(𝔽241) generated by

240100
1885200
0010
0001
,
1000
5324000
0010
0001
,
1000
0100
00149
00177239
,
130000
013000
006815
00222173
G:=sub<GL(4,GF(241))| [240,188,0,0,1,52,0,0,0,0,1,0,0,0,0,1],[1,53,0,0,0,240,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,1,177,0,0,49,239],[130,0,0,0,0,130,0,0,0,0,68,222,0,0,15,173] >;

D5×C3⋊C16 in GAP, Magma, Sage, TeX

D_5\times C_3\rtimes C_{16}
% in TeX

G:=Group("D5xC3:C16");
// GroupNames label

G:=SmallGroup(480,7);
// by ID

G=gap.SmallGroup(480,7);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,36,58,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^5=b^2=c^3=d^16=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

Export

Subgroup lattice of D5×C3⋊C16 in TeX

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