metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C40.5C8, Dic5⋊2C16, C20.21C42, C5⋊C16⋊9C4, C5⋊3(C4×C16), C8.6(C5⋊C8), C10.9(C4×C8), C4.17(C4×F5), (C2×C8).23F5, C20.47(C2×C8), (C2×C40).20C4, C10.3(C2×C16), C2.2(D5⋊C16), (C2×Dic5).8C8, C22.7(D5⋊C8), (C8×Dic5).25C2, (C4×Dic5).40C4, C2.3(C4×C5⋊C8), C4.14(C2×C5⋊C8), (C2×C5⋊C16).6C2, (C2×C10).3(C2×C8), C5⋊2C8.36(C2×C4), (C2×C4).153(C2×F5), (C2×C20).159(C2×C4), (C2×C5⋊2C8).343C22, SmallGroup(320,223)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — Dic5⋊C16 |
Generators and relations for Dic5⋊C16
G = < a,b,c | a10=c16=1, b2=a5, bab-1=a-1, cac-1=a3, bc=cb >
Smallest permutation representation of Dic5⋊C16
►Regular action on 320 points
Generators in S320
(1 88 219 151 65 242 193 177 232 33)(2 152 194 34 220 243 233 89 66 178)(3 35 234 179 195 244 67 153 221 90)(4 180 68 91 235 245 222 36 196 154)(5 92 223 155 69 246 197 181 236 37)(6 156 198 38 224 247 237 93 70 182)(7 39 238 183 199 248 71 157 209 94)(8 184 72 95 239 249 210 40 200 158)(9 96 211 159 73 250 201 185 240 41)(10 160 202 42 212 251 225 81 74 186)(11 43 226 187 203 252 75 145 213 82)(12 188 76 83 227 253 214 44 204 146)(13 84 215 147 77 254 205 189 228 45)(14 148 206 46 216 255 229 85 78 190)(15 47 230 191 207 256 79 149 217 86)(16 192 80 87 231 241 218 48 208 150)(17 110 130 314 173 277 61 120 262 298)(18 315 62 299 131 278 263 111 174 121)(19 300 264 122 63 279 175 316 132 112)(20 123 176 97 265 280 133 301 64 317)(21 98 134 318 161 281 49 124 266 302)(22 319 50 303 135 282 267 99 162 125)(23 304 268 126 51 283 163 320 136 100)(24 127 164 101 269 284 137 289 52 305)(25 102 138 306 165 285 53 128 270 290)(26 307 54 291 139 286 271 103 166 113)(27 292 272 114 55 287 167 308 140 104)(28 115 168 105 257 288 141 293 56 309)(29 106 142 310 169 273 57 116 258 294)(30 311 58 295 143 274 259 107 170 117)(31 296 260 118 59 275 171 312 144 108)(32 119 172 109 261 276 129 297 60 313)
(1 121 242 131)(2 122 243 132)(3 123 244 133)(4 124 245 134)(5 125 246 135)(6 126 247 136)(7 127 248 137)(8 128 249 138)(9 113 250 139)(10 114 251 140)(11 115 252 141)(12 116 253 142)(13 117 254 143)(14 118 255 144)(15 119 256 129)(16 120 241 130)(17 80 277 48)(18 65 278 33)(19 66 279 34)(20 67 280 35)(21 68 281 36)(22 69 282 37)(23 70 283 38)(24 71 284 39)(25 72 285 40)(26 73 286 41)(27 74 287 42)(28 75 288 43)(29 76 273 44)(30 77 274 45)(31 78 275 46)(32 79 276 47)(49 222 98 180)(50 223 99 181)(51 224 100 182)(52 209 101 183)(53 210 102 184)(54 211 103 185)(55 212 104 186)(56 213 105 187)(57 214 106 188)(58 215 107 189)(59 216 108 190)(60 217 109 191)(61 218 110 192)(62 219 111 177)(63 220 112 178)(64 221 97 179)(81 167 202 292)(82 168 203 293)(83 169 204 294)(84 170 205 295)(85 171 206 296)(86 172 207 297)(87 173 208 298)(88 174 193 299)(89 175 194 300)(90 176 195 301)(91 161 196 302)(92 162 197 303)(93 163 198 304)(94 164 199 289)(95 165 200 290)(96 166 201 291)(145 257 226 309)(146 258 227 310)(147 259 228 311)(148 260 229 312)(149 261 230 313)(150 262 231 314)(151 263 232 315)(152 264 233 316)(153 265 234 317)(154 266 235 318)(155 267 236 319)(156 268 237 320)(157 269 238 305)(158 270 239 306)(159 271 240 307)(160 272 225 308)
(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)(241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256)(257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272)(273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288)(289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304)(305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320)
G:=sub<Sym(320)| (1,88,219,151,65,242,193,177,232,33)(2,152,194,34,220,243,233,89,66,178)(3,35,234,179,195,244,67,153,221,90)(4,180,68,91,235,245,222,36,196,154)(5,92,223,155,69,246,197,181,236,37)(6,156,198,38,224,247,237,93,70,182)(7,39,238,183,199,248,71,157,209,94)(8,184,72,95,239,249,210,40,200,158)(9,96,211,159,73,250,201,185,240,41)(10,160,202,42,212,251,225,81,74,186)(11,43,226,187,203,252,75,145,213,82)(12,188,76,83,227,253,214,44,204,146)(13,84,215,147,77,254,205,189,228,45)(14,148,206,46,216,255,229,85,78,190)(15,47,230,191,207,256,79,149,217,86)(16,192,80,87,231,241,218,48,208,150)(17,110,130,314,173,277,61,120,262,298)(18,315,62,299,131,278,263,111,174,121)(19,300,264,122,63,279,175,316,132,112)(20,123,176,97,265,280,133,301,64,317)(21,98,134,318,161,281,49,124,266,302)(22,319,50,303,135,282,267,99,162,125)(23,304,268,126,51,283,163,320,136,100)(24,127,164,101,269,284,137,289,52,305)(25,102,138,306,165,285,53,128,270,290)(26,307,54,291,139,286,271,103,166,113)(27,292,272,114,55,287,167,308,140,104)(28,115,168,105,257,288,141,293,56,309)(29,106,142,310,169,273,57,116,258,294)(30,311,58,295,143,274,259,107,170,117)(31,296,260,118,59,275,171,312,144,108)(32,119,172,109,261,276,129,297,60,313), (1,121,242,131)(2,122,243,132)(3,123,244,133)(4,124,245,134)(5,125,246,135)(6,126,247,136)(7,127,248,137)(8,128,249,138)(9,113,250,139)(10,114,251,140)(11,115,252,141)(12,116,253,142)(13,117,254,143)(14,118,255,144)(15,119,256,129)(16,120,241,130)(17,80,277,48)(18,65,278,33)(19,66,279,34)(20,67,280,35)(21,68,281,36)(22,69,282,37)(23,70,283,38)(24,71,284,39)(25,72,285,40)(26,73,286,41)(27,74,287,42)(28,75,288,43)(29,76,273,44)(30,77,274,45)(31,78,275,46)(32,79,276,47)(49,222,98,180)(50,223,99,181)(51,224,100,182)(52,209,101,183)(53,210,102,184)(54,211,103,185)(55,212,104,186)(56,213,105,187)(57,214,106,188)(58,215,107,189)(59,216,108,190)(60,217,109,191)(61,218,110,192)(62,219,111,177)(63,220,112,178)(64,221,97,179)(81,167,202,292)(82,168,203,293)(83,169,204,294)(84,170,205,295)(85,171,206,296)(86,172,207,297)(87,173,208,298)(88,174,193,299)(89,175,194,300)(90,176,195,301)(91,161,196,302)(92,162,197,303)(93,163,198,304)(94,164,199,289)(95,165,200,290)(96,166,201,291)(145,257,226,309)(146,258,227,310)(147,259,228,311)(148,260,229,312)(149,261,230,313)(150,262,231,314)(151,263,232,315)(152,264,233,316)(153,265,234,317)(154,266,235,318)(155,267,236,319)(156,268,237,320)(157,269,238,305)(158,270,239,306)(159,271,240,307)(160,272,225,308), (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)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304)(305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320)>;
G:=Group( (1,88,219,151,65,242,193,177,232,33)(2,152,194,34,220,243,233,89,66,178)(3,35,234,179,195,244,67,153,221,90)(4,180,68,91,235,245,222,36,196,154)(5,92,223,155,69,246,197,181,236,37)(6,156,198,38,224,247,237,93,70,182)(7,39,238,183,199,248,71,157,209,94)(8,184,72,95,239,249,210,40,200,158)(9,96,211,159,73,250,201,185,240,41)(10,160,202,42,212,251,225,81,74,186)(11,43,226,187,203,252,75,145,213,82)(12,188,76,83,227,253,214,44,204,146)(13,84,215,147,77,254,205,189,228,45)(14,148,206,46,216,255,229,85,78,190)(15,47,230,191,207,256,79,149,217,86)(16,192,80,87,231,241,218,48,208,150)(17,110,130,314,173,277,61,120,262,298)(18,315,62,299,131,278,263,111,174,121)(19,300,264,122,63,279,175,316,132,112)(20,123,176,97,265,280,133,301,64,317)(21,98,134,318,161,281,49,124,266,302)(22,319,50,303,135,282,267,99,162,125)(23,304,268,126,51,283,163,320,136,100)(24,127,164,101,269,284,137,289,52,305)(25,102,138,306,165,285,53,128,270,290)(26,307,54,291,139,286,271,103,166,113)(27,292,272,114,55,287,167,308,140,104)(28,115,168,105,257,288,141,293,56,309)(29,106,142,310,169,273,57,116,258,294)(30,311,58,295,143,274,259,107,170,117)(31,296,260,118,59,275,171,312,144,108)(32,119,172,109,261,276,129,297,60,313), (1,121,242,131)(2,122,243,132)(3,123,244,133)(4,124,245,134)(5,125,246,135)(6,126,247,136)(7,127,248,137)(8,128,249,138)(9,113,250,139)(10,114,251,140)(11,115,252,141)(12,116,253,142)(13,117,254,143)(14,118,255,144)(15,119,256,129)(16,120,241,130)(17,80,277,48)(18,65,278,33)(19,66,279,34)(20,67,280,35)(21,68,281,36)(22,69,282,37)(23,70,283,38)(24,71,284,39)(25,72,285,40)(26,73,286,41)(27,74,287,42)(28,75,288,43)(29,76,273,44)(30,77,274,45)(31,78,275,46)(32,79,276,47)(49,222,98,180)(50,223,99,181)(51,224,100,182)(52,209,101,183)(53,210,102,184)(54,211,103,185)(55,212,104,186)(56,213,105,187)(57,214,106,188)(58,215,107,189)(59,216,108,190)(60,217,109,191)(61,218,110,192)(62,219,111,177)(63,220,112,178)(64,221,97,179)(81,167,202,292)(82,168,203,293)(83,169,204,294)(84,170,205,295)(85,171,206,296)(86,172,207,297)(87,173,208,298)(88,174,193,299)(89,175,194,300)(90,176,195,301)(91,161,196,302)(92,162,197,303)(93,163,198,304)(94,164,199,289)(95,165,200,290)(96,166,201,291)(145,257,226,309)(146,258,227,310)(147,259,228,311)(148,260,229,312)(149,261,230,313)(150,262,231,314)(151,263,232,315)(152,264,233,316)(153,265,234,317)(154,266,235,318)(155,267,236,319)(156,268,237,320)(157,269,238,305)(158,270,239,306)(159,271,240,307)(160,272,225,308), (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)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304)(305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320) );
G=PermutationGroup([[(1,88,219,151,65,242,193,177,232,33),(2,152,194,34,220,243,233,89,66,178),(3,35,234,179,195,244,67,153,221,90),(4,180,68,91,235,245,222,36,196,154),(5,92,223,155,69,246,197,181,236,37),(6,156,198,38,224,247,237,93,70,182),(7,39,238,183,199,248,71,157,209,94),(8,184,72,95,239,249,210,40,200,158),(9,96,211,159,73,250,201,185,240,41),(10,160,202,42,212,251,225,81,74,186),(11,43,226,187,203,252,75,145,213,82),(12,188,76,83,227,253,214,44,204,146),(13,84,215,147,77,254,205,189,228,45),(14,148,206,46,216,255,229,85,78,190),(15,47,230,191,207,256,79,149,217,86),(16,192,80,87,231,241,218,48,208,150),(17,110,130,314,173,277,61,120,262,298),(18,315,62,299,131,278,263,111,174,121),(19,300,264,122,63,279,175,316,132,112),(20,123,176,97,265,280,133,301,64,317),(21,98,134,318,161,281,49,124,266,302),(22,319,50,303,135,282,267,99,162,125),(23,304,268,126,51,283,163,320,136,100),(24,127,164,101,269,284,137,289,52,305),(25,102,138,306,165,285,53,128,270,290),(26,307,54,291,139,286,271,103,166,113),(27,292,272,114,55,287,167,308,140,104),(28,115,168,105,257,288,141,293,56,309),(29,106,142,310,169,273,57,116,258,294),(30,311,58,295,143,274,259,107,170,117),(31,296,260,118,59,275,171,312,144,108),(32,119,172,109,261,276,129,297,60,313)], [(1,121,242,131),(2,122,243,132),(3,123,244,133),(4,124,245,134),(5,125,246,135),(6,126,247,136),(7,127,248,137),(8,128,249,138),(9,113,250,139),(10,114,251,140),(11,115,252,141),(12,116,253,142),(13,117,254,143),(14,118,255,144),(15,119,256,129),(16,120,241,130),(17,80,277,48),(18,65,278,33),(19,66,279,34),(20,67,280,35),(21,68,281,36),(22,69,282,37),(23,70,283,38),(24,71,284,39),(25,72,285,40),(26,73,286,41),(27,74,287,42),(28,75,288,43),(29,76,273,44),(30,77,274,45),(31,78,275,46),(32,79,276,47),(49,222,98,180),(50,223,99,181),(51,224,100,182),(52,209,101,183),(53,210,102,184),(54,211,103,185),(55,212,104,186),(56,213,105,187),(57,214,106,188),(58,215,107,189),(59,216,108,190),(60,217,109,191),(61,218,110,192),(62,219,111,177),(63,220,112,178),(64,221,97,179),(81,167,202,292),(82,168,203,293),(83,169,204,294),(84,170,205,295),(85,171,206,296),(86,172,207,297),(87,173,208,298),(88,174,193,299),(89,175,194,300),(90,176,195,301),(91,161,196,302),(92,162,197,303),(93,163,198,304),(94,164,199,289),(95,165,200,290),(96,166,201,291),(145,257,226,309),(146,258,227,310),(147,259,228,311),(148,260,229,312),(149,261,230,313),(150,262,231,314),(151,263,232,315),(152,264,233,316),(153,265,234,317),(154,266,235,318),(155,267,236,319),(156,268,237,320),(157,269,238,305),(158,270,239,306),(159,271,240,307),(160,272,225,308)], [(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),(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256),(257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272),(273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288),(289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304),(305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320)]])
80 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 5 | 8A | ··· | 8H | 8I | ··· | 8P | 10A | 10B | 10C | 16A | ··· | 16AF | 20A | 20B | 20C | 20D | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 8 | ··· | 8 | 8 | ··· | 8 | 10 | 10 | 10 | 16 | ··· | 16 | 20 | 20 | 20 | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5 | ··· | 5 | 4 | 1 | ··· | 1 | 5 | ··· | 5 | 4 | 4 | 4 | 5 | ··· | 5 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | |||||||||
| image | C1 | C2 | C2 | C4 | C4 | C4 | C8 | C8 | C16 | F5 | C5⋊C8 | C2×F5 | C4×F5 | D5⋊C8 | D5⋊C16 |
| kernel | Dic5⋊C16 | C8×Dic5 | C2×C5⋊C16 | C5⋊C16 | C4×Dic5 | C2×C40 | C40 | C2×Dic5 | Dic5 | C2×C8 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 1 | 2 | 8 | 2 | 2 | 8 | 8 | 32 | 1 | 2 | 1 | 2 | 2 | 8 |
Matrix representation of Dic5⋊C16 ►in GL5(𝔽241)
| 240 | 0 | 0 | 0 | 0 |
| 0 | 240 | 1 | 0 | 0 |
| 0 | 240 | 0 | 1 | 0 |
| 0 | 240 | 0 | 0 | 1 |
| 0 | 240 | 0 | 0 | 0 |
| 64 | 0 | 0 | 0 | 0 |
| 0 | 164 | 66 | 13 | 38 |
| 0 | 230 | 79 | 51 | 239 |
| 0 | 2 | 117 | 11 | 162 |
| 0 | 40 | 77 | 175 | 228 |
| 240 | 0 | 0 | 0 | 0 |
| 0 | 81 | 88 | 2 | 90 |
| 0 | 83 | 178 | 223 | 171 |
| 0 | 63 | 18 | 70 | 173 |
| 0 | 151 | 20 | 160 | 153 |
G:=sub<GL(5,GF(241))| [240,0,0,0,0,0,240,240,240,240,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0],[64,0,0,0,0,0,164,230,2,40,0,66,79,117,77,0,13,51,11,175,0,38,239,162,228],[240,0,0,0,0,0,81,83,63,151,0,88,178,18,20,0,2,223,70,160,0,90,171,173,153] >;
Dic5⋊C16 in GAP, Magma, Sage, TeX
{\rm Dic}_5\rtimes C_{16} % in TeX
G:=Group("Dic5:C16"); // GroupNames label
G:=SmallGroup(320,223);
// by ID
G=gap.SmallGroup(320,223);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,176,100,102,6278,3156]);
// Polycyclic
G:=Group<a,b,c|a^10=c^16=1,b^2=a^5,b*a*b^-1=a^-1,c*a*c^-1=a^3,b*c=c*b>;
// generators/relations
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