direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C5×C9⋊C8, C9⋊C40, C45⋊4C8, C18.C20, C90.4C4, C20.4D9, C36.2C10, C180.5C2, C60.12S3, C10.3Dic9, C30.9Dic3, C4.2(C5×D9), C2.(C5×Dic9), C15.3(C3⋊C8), C12.4(C5×S3), C6.1(C5×Dic3), C3.(C5×C3⋊C8), SmallGroup(360,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C9 — C5×C9⋊C8 |
Generators and relations for C5×C9⋊C8
G = < a,b,c | a5=b9=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C5×C9⋊C8
►Regular action on 360 points
Generators in S360
(1 151 115 79 43)(2 152 116 80 44)(3 153 117 81 45)(4 145 109 73 37)(5 146 110 74 38)(6 147 111 75 39)(7 148 112 76 40)(8 149 113 77 41)(9 150 114 78 42)(10 154 118 82 46)(11 155 119 83 47)(12 156 120 84 48)(13 157 121 85 49)(14 158 122 86 50)(15 159 123 87 51)(16 160 124 88 52)(17 161 125 89 53)(18 162 126 90 54)(19 163 127 91 55)(20 164 128 92 56)(21 165 129 93 57)(22 166 130 94 58)(23 167 131 95 59)(24 168 132 96 60)(25 169 133 97 61)(26 170 134 98 62)(27 171 135 99 63)(28 172 136 100 64)(29 173 137 101 65)(30 174 138 102 66)(31 175 139 103 67)(32 176 140 104 68)(33 177 141 105 69)(34 178 142 106 70)(35 179 143 107 71)(36 180 144 108 72)(181 325 289 253 217)(182 326 290 254 218)(183 327 291 255 219)(184 328 292 256 220)(185 329 293 257 221)(186 330 294 258 222)(187 331 295 259 223)(188 332 296 260 224)(189 333 297 261 225)(190 334 298 262 226)(191 335 299 263 227)(192 336 300 264 228)(193 337 301 265 229)(194 338 302 266 230)(195 339 303 267 231)(196 340 304 268 232)(197 341 305 269 233)(198 342 306 270 234)(199 343 307 271 235)(200 344 308 272 236)(201 345 309 273 237)(202 346 310 274 238)(203 347 311 275 239)(204 348 312 276 240)(205 349 313 277 241)(206 350 314 278 242)(207 351 315 279 243)(208 352 316 280 244)(209 353 317 281 245)(210 354 318 282 246)(211 355 319 283 247)(212 356 320 284 248)(213 357 321 285 249)(214 358 322 286 250)(215 359 323 287 251)(216 360 324 288 252)
(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)(316 317 318 319 320 321 322 323 324)(325 326 327 328 329 330 331 332 333)(334 335 336 337 338 339 340 341 342)(343 344 345 346 347 348 349 350 351)(352 353 354 355 356 357 358 359 360)
(1 209 34 191 16 200 25 182)(2 208 35 190 17 199 26 181)(3 216 36 198 18 207 27 189)(4 215 28 197 10 206 19 188)(5 214 29 196 11 205 20 187)(6 213 30 195 12 204 21 186)(7 212 31 194 13 203 22 185)(8 211 32 193 14 202 23 184)(9 210 33 192 15 201 24 183)(37 251 64 233 46 242 55 224)(38 250 65 232 47 241 56 223)(39 249 66 231 48 240 57 222)(40 248 67 230 49 239 58 221)(41 247 68 229 50 238 59 220)(42 246 69 228 51 237 60 219)(43 245 70 227 52 236 61 218)(44 244 71 226 53 235 62 217)(45 252 72 234 54 243 63 225)(73 287 100 269 82 278 91 260)(74 286 101 268 83 277 92 259)(75 285 102 267 84 276 93 258)(76 284 103 266 85 275 94 257)(77 283 104 265 86 274 95 256)(78 282 105 264 87 273 96 255)(79 281 106 263 88 272 97 254)(80 280 107 262 89 271 98 253)(81 288 108 270 90 279 99 261)(109 323 136 305 118 314 127 296)(110 322 137 304 119 313 128 295)(111 321 138 303 120 312 129 294)(112 320 139 302 121 311 130 293)(113 319 140 301 122 310 131 292)(114 318 141 300 123 309 132 291)(115 317 142 299 124 308 133 290)(116 316 143 298 125 307 134 289)(117 324 144 306 126 315 135 297)(145 359 172 341 154 350 163 332)(146 358 173 340 155 349 164 331)(147 357 174 339 156 348 165 330)(148 356 175 338 157 347 166 329)(149 355 176 337 158 346 167 328)(150 354 177 336 159 345 168 327)(151 353 178 335 160 344 169 326)(152 352 179 334 161 343 170 325)(153 360 180 342 162 351 171 333)
G:=sub<Sym(360)| (1,151,115,79,43)(2,152,116,80,44)(3,153,117,81,45)(4,145,109,73,37)(5,146,110,74,38)(6,147,111,75,39)(7,148,112,76,40)(8,149,113,77,41)(9,150,114,78,42)(10,154,118,82,46)(11,155,119,83,47)(12,156,120,84,48)(13,157,121,85,49)(14,158,122,86,50)(15,159,123,87,51)(16,160,124,88,52)(17,161,125,89,53)(18,162,126,90,54)(19,163,127,91,55)(20,164,128,92,56)(21,165,129,93,57)(22,166,130,94,58)(23,167,131,95,59)(24,168,132,96,60)(25,169,133,97,61)(26,170,134,98,62)(27,171,135,99,63)(28,172,136,100,64)(29,173,137,101,65)(30,174,138,102,66)(31,175,139,103,67)(32,176,140,104,68)(33,177,141,105,69)(34,178,142,106,70)(35,179,143,107,71)(36,180,144,108,72)(181,325,289,253,217)(182,326,290,254,218)(183,327,291,255,219)(184,328,292,256,220)(185,329,293,257,221)(186,330,294,258,222)(187,331,295,259,223)(188,332,296,260,224)(189,333,297,261,225)(190,334,298,262,226)(191,335,299,263,227)(192,336,300,264,228)(193,337,301,265,229)(194,338,302,266,230)(195,339,303,267,231)(196,340,304,268,232)(197,341,305,269,233)(198,342,306,270,234)(199,343,307,271,235)(200,344,308,272,236)(201,345,309,273,237)(202,346,310,274,238)(203,347,311,275,239)(204,348,312,276,240)(205,349,313,277,241)(206,350,314,278,242)(207,351,315,279,243)(208,352,316,280,244)(209,353,317,281,245)(210,354,318,282,246)(211,355,319,283,247)(212,356,320,284,248)(213,357,321,285,249)(214,358,322,286,250)(215,359,323,287,251)(216,360,324,288,252), (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)(316,317,318,319,320,321,322,323,324)(325,326,327,328,329,330,331,332,333)(334,335,336,337,338,339,340,341,342)(343,344,345,346,347,348,349,350,351)(352,353,354,355,356,357,358,359,360), (1,209,34,191,16,200,25,182)(2,208,35,190,17,199,26,181)(3,216,36,198,18,207,27,189)(4,215,28,197,10,206,19,188)(5,214,29,196,11,205,20,187)(6,213,30,195,12,204,21,186)(7,212,31,194,13,203,22,185)(8,211,32,193,14,202,23,184)(9,210,33,192,15,201,24,183)(37,251,64,233,46,242,55,224)(38,250,65,232,47,241,56,223)(39,249,66,231,48,240,57,222)(40,248,67,230,49,239,58,221)(41,247,68,229,50,238,59,220)(42,246,69,228,51,237,60,219)(43,245,70,227,52,236,61,218)(44,244,71,226,53,235,62,217)(45,252,72,234,54,243,63,225)(73,287,100,269,82,278,91,260)(74,286,101,268,83,277,92,259)(75,285,102,267,84,276,93,258)(76,284,103,266,85,275,94,257)(77,283,104,265,86,274,95,256)(78,282,105,264,87,273,96,255)(79,281,106,263,88,272,97,254)(80,280,107,262,89,271,98,253)(81,288,108,270,90,279,99,261)(109,323,136,305,118,314,127,296)(110,322,137,304,119,313,128,295)(111,321,138,303,120,312,129,294)(112,320,139,302,121,311,130,293)(113,319,140,301,122,310,131,292)(114,318,141,300,123,309,132,291)(115,317,142,299,124,308,133,290)(116,316,143,298,125,307,134,289)(117,324,144,306,126,315,135,297)(145,359,172,341,154,350,163,332)(146,358,173,340,155,349,164,331)(147,357,174,339,156,348,165,330)(148,356,175,338,157,347,166,329)(149,355,176,337,158,346,167,328)(150,354,177,336,159,345,168,327)(151,353,178,335,160,344,169,326)(152,352,179,334,161,343,170,325)(153,360,180,342,162,351,171,333)>;
G:=Group( (1,151,115,79,43)(2,152,116,80,44)(3,153,117,81,45)(4,145,109,73,37)(5,146,110,74,38)(6,147,111,75,39)(7,148,112,76,40)(8,149,113,77,41)(9,150,114,78,42)(10,154,118,82,46)(11,155,119,83,47)(12,156,120,84,48)(13,157,121,85,49)(14,158,122,86,50)(15,159,123,87,51)(16,160,124,88,52)(17,161,125,89,53)(18,162,126,90,54)(19,163,127,91,55)(20,164,128,92,56)(21,165,129,93,57)(22,166,130,94,58)(23,167,131,95,59)(24,168,132,96,60)(25,169,133,97,61)(26,170,134,98,62)(27,171,135,99,63)(28,172,136,100,64)(29,173,137,101,65)(30,174,138,102,66)(31,175,139,103,67)(32,176,140,104,68)(33,177,141,105,69)(34,178,142,106,70)(35,179,143,107,71)(36,180,144,108,72)(181,325,289,253,217)(182,326,290,254,218)(183,327,291,255,219)(184,328,292,256,220)(185,329,293,257,221)(186,330,294,258,222)(187,331,295,259,223)(188,332,296,260,224)(189,333,297,261,225)(190,334,298,262,226)(191,335,299,263,227)(192,336,300,264,228)(193,337,301,265,229)(194,338,302,266,230)(195,339,303,267,231)(196,340,304,268,232)(197,341,305,269,233)(198,342,306,270,234)(199,343,307,271,235)(200,344,308,272,236)(201,345,309,273,237)(202,346,310,274,238)(203,347,311,275,239)(204,348,312,276,240)(205,349,313,277,241)(206,350,314,278,242)(207,351,315,279,243)(208,352,316,280,244)(209,353,317,281,245)(210,354,318,282,246)(211,355,319,283,247)(212,356,320,284,248)(213,357,321,285,249)(214,358,322,286,250)(215,359,323,287,251)(216,360,324,288,252), (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)(316,317,318,319,320,321,322,323,324)(325,326,327,328,329,330,331,332,333)(334,335,336,337,338,339,340,341,342)(343,344,345,346,347,348,349,350,351)(352,353,354,355,356,357,358,359,360), (1,209,34,191,16,200,25,182)(2,208,35,190,17,199,26,181)(3,216,36,198,18,207,27,189)(4,215,28,197,10,206,19,188)(5,214,29,196,11,205,20,187)(6,213,30,195,12,204,21,186)(7,212,31,194,13,203,22,185)(8,211,32,193,14,202,23,184)(9,210,33,192,15,201,24,183)(37,251,64,233,46,242,55,224)(38,250,65,232,47,241,56,223)(39,249,66,231,48,240,57,222)(40,248,67,230,49,239,58,221)(41,247,68,229,50,238,59,220)(42,246,69,228,51,237,60,219)(43,245,70,227,52,236,61,218)(44,244,71,226,53,235,62,217)(45,252,72,234,54,243,63,225)(73,287,100,269,82,278,91,260)(74,286,101,268,83,277,92,259)(75,285,102,267,84,276,93,258)(76,284,103,266,85,275,94,257)(77,283,104,265,86,274,95,256)(78,282,105,264,87,273,96,255)(79,281,106,263,88,272,97,254)(80,280,107,262,89,271,98,253)(81,288,108,270,90,279,99,261)(109,323,136,305,118,314,127,296)(110,322,137,304,119,313,128,295)(111,321,138,303,120,312,129,294)(112,320,139,302,121,311,130,293)(113,319,140,301,122,310,131,292)(114,318,141,300,123,309,132,291)(115,317,142,299,124,308,133,290)(116,316,143,298,125,307,134,289)(117,324,144,306,126,315,135,297)(145,359,172,341,154,350,163,332)(146,358,173,340,155,349,164,331)(147,357,174,339,156,348,165,330)(148,356,175,338,157,347,166,329)(149,355,176,337,158,346,167,328)(150,354,177,336,159,345,168,327)(151,353,178,335,160,344,169,326)(152,352,179,334,161,343,170,325)(153,360,180,342,162,351,171,333) );
G=PermutationGroup([[(1,151,115,79,43),(2,152,116,80,44),(3,153,117,81,45),(4,145,109,73,37),(5,146,110,74,38),(6,147,111,75,39),(7,148,112,76,40),(8,149,113,77,41),(9,150,114,78,42),(10,154,118,82,46),(11,155,119,83,47),(12,156,120,84,48),(13,157,121,85,49),(14,158,122,86,50),(15,159,123,87,51),(16,160,124,88,52),(17,161,125,89,53),(18,162,126,90,54),(19,163,127,91,55),(20,164,128,92,56),(21,165,129,93,57),(22,166,130,94,58),(23,167,131,95,59),(24,168,132,96,60),(25,169,133,97,61),(26,170,134,98,62),(27,171,135,99,63),(28,172,136,100,64),(29,173,137,101,65),(30,174,138,102,66),(31,175,139,103,67),(32,176,140,104,68),(33,177,141,105,69),(34,178,142,106,70),(35,179,143,107,71),(36,180,144,108,72),(181,325,289,253,217),(182,326,290,254,218),(183,327,291,255,219),(184,328,292,256,220),(185,329,293,257,221),(186,330,294,258,222),(187,331,295,259,223),(188,332,296,260,224),(189,333,297,261,225),(190,334,298,262,226),(191,335,299,263,227),(192,336,300,264,228),(193,337,301,265,229),(194,338,302,266,230),(195,339,303,267,231),(196,340,304,268,232),(197,341,305,269,233),(198,342,306,270,234),(199,343,307,271,235),(200,344,308,272,236),(201,345,309,273,237),(202,346,310,274,238),(203,347,311,275,239),(204,348,312,276,240),(205,349,313,277,241),(206,350,314,278,242),(207,351,315,279,243),(208,352,316,280,244),(209,353,317,281,245),(210,354,318,282,246),(211,355,319,283,247),(212,356,320,284,248),(213,357,321,285,249),(214,358,322,286,250),(215,359,323,287,251),(216,360,324,288,252)], [(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),(316,317,318,319,320,321,322,323,324),(325,326,327,328,329,330,331,332,333),(334,335,336,337,338,339,340,341,342),(343,344,345,346,347,348,349,350,351),(352,353,354,355,356,357,358,359,360)], [(1,209,34,191,16,200,25,182),(2,208,35,190,17,199,26,181),(3,216,36,198,18,207,27,189),(4,215,28,197,10,206,19,188),(5,214,29,196,11,205,20,187),(6,213,30,195,12,204,21,186),(7,212,31,194,13,203,22,185),(8,211,32,193,14,202,23,184),(9,210,33,192,15,201,24,183),(37,251,64,233,46,242,55,224),(38,250,65,232,47,241,56,223),(39,249,66,231,48,240,57,222),(40,248,67,230,49,239,58,221),(41,247,68,229,50,238,59,220),(42,246,69,228,51,237,60,219),(43,245,70,227,52,236,61,218),(44,244,71,226,53,235,62,217),(45,252,72,234,54,243,63,225),(73,287,100,269,82,278,91,260),(74,286,101,268,83,277,92,259),(75,285,102,267,84,276,93,258),(76,284,103,266,85,275,94,257),(77,283,104,265,86,274,95,256),(78,282,105,264,87,273,96,255),(79,281,106,263,88,272,97,254),(80,280,107,262,89,271,98,253),(81,288,108,270,90,279,99,261),(109,323,136,305,118,314,127,296),(110,322,137,304,119,313,128,295),(111,321,138,303,120,312,129,294),(112,320,139,302,121,311,130,293),(113,319,140,301,122,310,131,292),(114,318,141,300,123,309,132,291),(115,317,142,299,124,308,133,290),(116,316,143,298,125,307,134,289),(117,324,144,306,126,315,135,297),(145,359,172,341,154,350,163,332),(146,358,173,340,155,349,164,331),(147,357,174,339,156,348,165,330),(148,356,175,338,157,347,166,329),(149,355,176,337,158,346,167,328),(150,354,177,336,159,345,168,327),(151,353,178,335,160,344,169,326),(152,352,179,334,161,343,170,325),(153,360,180,342,162,351,171,333)]])
120 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 5A | 5B | 5C | 5D | 6 | 8A | 8B | 8C | 8D | 9A | 9B | 9C | 10A | 10B | 10C | 10D | 12A | 12B | 15A | 15B | 15C | 15D | 18A | 18B | 18C | 20A | ··· | 20H | 30A | 30B | 30C | 30D | 36A | ··· | 36F | 40A | ··· | 40P | 45A | ··· | 45L | 60A | ··· | 60H | 90A | ··· | 90L | 180A | ··· | 180X |
| order | 1 | 2 | 3 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 8 | 8 | 8 | 8 | 9 | 9 | 9 | 10 | 10 | 10 | 10 | 12 | 12 | 15 | 15 | 15 | 15 | 18 | 18 | 18 | 20 | ··· | 20 | 30 | 30 | 30 | 30 | 36 | ··· | 36 | 40 | ··· | 40 | 45 | ··· | 45 | 60 | ··· | 60 | 90 | ··· | 90 | 180 | ··· | 180 |
| size | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 9 | 9 | 9 | 9 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 9 | ··· | 9 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
120 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | - | ||||||||||||||
| image | C1 | C2 | C4 | C5 | C8 | C10 | C20 | C40 | S3 | Dic3 | D9 | C3⋊C8 | C5×S3 | Dic9 | C5×Dic3 | C9⋊C8 | C5×D9 | C5×C3⋊C8 | C5×Dic9 | C5×C9⋊C8 |
| kernel | C5×C9⋊C8 | C180 | C90 | C9⋊C8 | C45 | C36 | C18 | C9 | C60 | C30 | C20 | C15 | C12 | C10 | C6 | C5 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 4 | 4 | 8 | 16 | 1 | 1 | 3 | 2 | 4 | 3 | 4 | 6 | 12 | 8 | 12 | 24 |
Matrix representation of C5×C9⋊C8 ►in GL2(𝔽1801) generated by
| 350 | 0 |
| 0 | 350 |
| 1365 | 1503 |
| 298 | 1067 |
| 512 | 361 |
| 873 | 1289 |
G:=sub<GL(2,GF(1801))| [350,0,0,350],[1365,298,1503,1067],[512,873,361,1289] >;
C5×C9⋊C8 in GAP, Magma, Sage, TeX
C_5\times C_9\rtimes C_8
% in TeX
G:=Group("C5xC9:C8"); // GroupNames label
G:=SmallGroup(360,1);
// by ID
G=gap.SmallGroup(360,1);
# by ID
G:=PCGroup([6,-2,-5,-2,-2,-3,-3,60,50,6004,208,8645]);
// Polycyclic
G:=Group<a,b,c|a^5=b^9=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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