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G = C9×C5⋊C8order 360 = 23·32·5

Direct product of C9 and C5⋊C8

direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: C9×C5⋊C8, C5⋊C72, C452C8, C10.C36, C15.C24, C90.2C4, C18.2F5, C30.2C12, Dic5.2C18, C2.(C9×F5), C6.2(C3×F5), (C9×Dic5).4C2, (C3×Dic5).6C6, C3.(C3×C5⋊C8), (C3×C5⋊C8).C3, SmallGroup(360,5)

Series: Derived Chief Lower central Upper central

C1C5 — C9×C5⋊C8
C1C5C10C30C3×Dic5C9×Dic5 — C9×C5⋊C8
C5 — C9×C5⋊C8
C1C18

Generators and relations for C9×C5⋊C8
 G = < a,b,c | a9=b5=c8=1, ab=ba, ac=ca, cbc-1=b3 >

5C4
5C8
5C12
5C24
5C36
5C72

Smallest permutation representation of C9×C5⋊C8
Regular action on 360 points
Generators in S360
(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 54 171 203 189)(2 46 163 204 181)(3 47 164 205 182)(4 48 165 206 183)(5 49 166 207 184)(6 50 167 199 185)(7 51 168 200 186)(8 52 169 201 187)(9 53 170 202 188)(10 141 356 341 302)(11 142 357 342 303)(12 143 358 334 304)(13 144 359 335 305)(14 136 360 336 306)(15 137 352 337 298)(16 138 353 338 299)(17 139 354 339 300)(18 140 355 340 301)(19 210 283 273 327)(20 211 284 274 328)(21 212 285 275 329)(22 213 286 276 330)(23 214 287 277 331)(24 215 288 278 332)(25 216 280 279 333)(26 208 281 271 325)(27 209 282 272 326)(28 320 107 172 309)(29 321 108 173 310)(30 322 100 174 311)(31 323 101 175 312)(32 324 102 176 313)(33 316 103 177 314)(34 317 104 178 315)(35 318 105 179 307)(36 319 106 180 308)(37 88 153 109 197)(38 89 145 110 198)(39 90 146 111 190)(40 82 147 112 191)(41 83 148 113 192)(42 84 149 114 193)(43 85 150 115 194)(44 86 151 116 195)(45 87 152 117 196)(55 292 225 71 239)(56 293 217 72 240)(57 294 218 64 241)(58 295 219 65 242)(59 296 220 66 243)(60 297 221 67 235)(61 289 222 68 236)(62 290 223 69 237)(63 291 224 70 238)(73 119 226 135 343)(74 120 227 127 344)(75 121 228 128 345)(76 122 229 129 346)(77 123 230 130 347)(78 124 231 131 348)(79 125 232 132 349)(80 126 233 133 350)(81 118 234 134 351)(91 154 253 246 269)(92 155 254 247 270)(93 156 255 248 262)(94 157 256 249 263)(95 158 257 250 264)(96 159 258 251 265)(97 160 259 252 266)(98 161 260 244 267)(99 162 261 245 268)
(1 340 31 23 196 120 263 297)(2 341 32 24 197 121 264 289)(3 342 33 25 198 122 265 290)(4 334 34 26 190 123 266 291)(5 335 35 27 191 124 267 292)(6 336 36 19 192 125 268 293)(7 337 28 20 193 126 269 294)(8 338 29 21 194 118 270 295)(9 339 30 22 195 119 262 296)(10 313 278 37 128 250 236 46)(11 314 279 38 129 251 237 47)(12 315 271 39 130 252 238 48)(13 307 272 40 131 244 239 49)(14 308 273 41 132 245 240 50)(15 309 274 42 133 246 241 51)(16 310 275 43 134 247 242 52)(17 311 276 44 135 248 243 53)(18 312 277 45 127 249 235 54)(55 207 305 105 326 147 231 161)(56 199 306 106 327 148 232 162)(57 200 298 107 328 149 233 154)(58 201 299 108 329 150 234 155)(59 202 300 100 330 151 226 156)(60 203 301 101 331 152 227 157)(61 204 302 102 332 153 228 158)(62 205 303 103 333 145 229 159)(63 206 304 104 325 146 230 160)(64 186 137 320 284 114 350 91)(65 187 138 321 285 115 351 92)(66 188 139 322 286 116 343 93)(67 189 140 323 287 117 344 94)(68 181 141 324 288 109 345 95)(69 182 142 316 280 110 346 96)(70 183 143 317 281 111 347 97)(71 184 144 318 282 112 348 98)(72 185 136 319 283 113 349 99)(73 255 220 170 354 174 213 86)(74 256 221 171 355 175 214 87)(75 257 222 163 356 176 215 88)(76 258 223 164 357 177 216 89)(77 259 224 165 358 178 208 90)(78 260 225 166 359 179 209 82)(79 261 217 167 360 180 210 83)(80 253 218 168 352 172 211 84)(81 254 219 169 353 173 212 85)

G:=sub<Sym(360)| (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), (1,54,171,203,189)(2,46,163,204,181)(3,47,164,205,182)(4,48,165,206,183)(5,49,166,207,184)(6,50,167,199,185)(7,51,168,200,186)(8,52,169,201,187)(9,53,170,202,188)(10,141,356,341,302)(11,142,357,342,303)(12,143,358,334,304)(13,144,359,335,305)(14,136,360,336,306)(15,137,352,337,298)(16,138,353,338,299)(17,139,354,339,300)(18,140,355,340,301)(19,210,283,273,327)(20,211,284,274,328)(21,212,285,275,329)(22,213,286,276,330)(23,214,287,277,331)(24,215,288,278,332)(25,216,280,279,333)(26,208,281,271,325)(27,209,282,272,326)(28,320,107,172,309)(29,321,108,173,310)(30,322,100,174,311)(31,323,101,175,312)(32,324,102,176,313)(33,316,103,177,314)(34,317,104,178,315)(35,318,105,179,307)(36,319,106,180,308)(37,88,153,109,197)(38,89,145,110,198)(39,90,146,111,190)(40,82,147,112,191)(41,83,148,113,192)(42,84,149,114,193)(43,85,150,115,194)(44,86,151,116,195)(45,87,152,117,196)(55,292,225,71,239)(56,293,217,72,240)(57,294,218,64,241)(58,295,219,65,242)(59,296,220,66,243)(60,297,221,67,235)(61,289,222,68,236)(62,290,223,69,237)(63,291,224,70,238)(73,119,226,135,343)(74,120,227,127,344)(75,121,228,128,345)(76,122,229,129,346)(77,123,230,130,347)(78,124,231,131,348)(79,125,232,132,349)(80,126,233,133,350)(81,118,234,134,351)(91,154,253,246,269)(92,155,254,247,270)(93,156,255,248,262)(94,157,256,249,263)(95,158,257,250,264)(96,159,258,251,265)(97,160,259,252,266)(98,161,260,244,267)(99,162,261,245,268), (1,340,31,23,196,120,263,297)(2,341,32,24,197,121,264,289)(3,342,33,25,198,122,265,290)(4,334,34,26,190,123,266,291)(5,335,35,27,191,124,267,292)(6,336,36,19,192,125,268,293)(7,337,28,20,193,126,269,294)(8,338,29,21,194,118,270,295)(9,339,30,22,195,119,262,296)(10,313,278,37,128,250,236,46)(11,314,279,38,129,251,237,47)(12,315,271,39,130,252,238,48)(13,307,272,40,131,244,239,49)(14,308,273,41,132,245,240,50)(15,309,274,42,133,246,241,51)(16,310,275,43,134,247,242,52)(17,311,276,44,135,248,243,53)(18,312,277,45,127,249,235,54)(55,207,305,105,326,147,231,161)(56,199,306,106,327,148,232,162)(57,200,298,107,328,149,233,154)(58,201,299,108,329,150,234,155)(59,202,300,100,330,151,226,156)(60,203,301,101,331,152,227,157)(61,204,302,102,332,153,228,158)(62,205,303,103,333,145,229,159)(63,206,304,104,325,146,230,160)(64,186,137,320,284,114,350,91)(65,187,138,321,285,115,351,92)(66,188,139,322,286,116,343,93)(67,189,140,323,287,117,344,94)(68,181,141,324,288,109,345,95)(69,182,142,316,280,110,346,96)(70,183,143,317,281,111,347,97)(71,184,144,318,282,112,348,98)(72,185,136,319,283,113,349,99)(73,255,220,170,354,174,213,86)(74,256,221,171,355,175,214,87)(75,257,222,163,356,176,215,88)(76,258,223,164,357,177,216,89)(77,259,224,165,358,178,208,90)(78,260,225,166,359,179,209,82)(79,261,217,167,360,180,210,83)(80,253,218,168,352,172,211,84)(81,254,219,169,353,173,212,85)>;

G:=Group( (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), (1,54,171,203,189)(2,46,163,204,181)(3,47,164,205,182)(4,48,165,206,183)(5,49,166,207,184)(6,50,167,199,185)(7,51,168,200,186)(8,52,169,201,187)(9,53,170,202,188)(10,141,356,341,302)(11,142,357,342,303)(12,143,358,334,304)(13,144,359,335,305)(14,136,360,336,306)(15,137,352,337,298)(16,138,353,338,299)(17,139,354,339,300)(18,140,355,340,301)(19,210,283,273,327)(20,211,284,274,328)(21,212,285,275,329)(22,213,286,276,330)(23,214,287,277,331)(24,215,288,278,332)(25,216,280,279,333)(26,208,281,271,325)(27,209,282,272,326)(28,320,107,172,309)(29,321,108,173,310)(30,322,100,174,311)(31,323,101,175,312)(32,324,102,176,313)(33,316,103,177,314)(34,317,104,178,315)(35,318,105,179,307)(36,319,106,180,308)(37,88,153,109,197)(38,89,145,110,198)(39,90,146,111,190)(40,82,147,112,191)(41,83,148,113,192)(42,84,149,114,193)(43,85,150,115,194)(44,86,151,116,195)(45,87,152,117,196)(55,292,225,71,239)(56,293,217,72,240)(57,294,218,64,241)(58,295,219,65,242)(59,296,220,66,243)(60,297,221,67,235)(61,289,222,68,236)(62,290,223,69,237)(63,291,224,70,238)(73,119,226,135,343)(74,120,227,127,344)(75,121,228,128,345)(76,122,229,129,346)(77,123,230,130,347)(78,124,231,131,348)(79,125,232,132,349)(80,126,233,133,350)(81,118,234,134,351)(91,154,253,246,269)(92,155,254,247,270)(93,156,255,248,262)(94,157,256,249,263)(95,158,257,250,264)(96,159,258,251,265)(97,160,259,252,266)(98,161,260,244,267)(99,162,261,245,268), (1,340,31,23,196,120,263,297)(2,341,32,24,197,121,264,289)(3,342,33,25,198,122,265,290)(4,334,34,26,190,123,266,291)(5,335,35,27,191,124,267,292)(6,336,36,19,192,125,268,293)(7,337,28,20,193,126,269,294)(8,338,29,21,194,118,270,295)(9,339,30,22,195,119,262,296)(10,313,278,37,128,250,236,46)(11,314,279,38,129,251,237,47)(12,315,271,39,130,252,238,48)(13,307,272,40,131,244,239,49)(14,308,273,41,132,245,240,50)(15,309,274,42,133,246,241,51)(16,310,275,43,134,247,242,52)(17,311,276,44,135,248,243,53)(18,312,277,45,127,249,235,54)(55,207,305,105,326,147,231,161)(56,199,306,106,327,148,232,162)(57,200,298,107,328,149,233,154)(58,201,299,108,329,150,234,155)(59,202,300,100,330,151,226,156)(60,203,301,101,331,152,227,157)(61,204,302,102,332,153,228,158)(62,205,303,103,333,145,229,159)(63,206,304,104,325,146,230,160)(64,186,137,320,284,114,350,91)(65,187,138,321,285,115,351,92)(66,188,139,322,286,116,343,93)(67,189,140,323,287,117,344,94)(68,181,141,324,288,109,345,95)(69,182,142,316,280,110,346,96)(70,183,143,317,281,111,347,97)(71,184,144,318,282,112,348,98)(72,185,136,319,283,113,349,99)(73,255,220,170,354,174,213,86)(74,256,221,171,355,175,214,87)(75,257,222,163,356,176,215,88)(76,258,223,164,357,177,216,89)(77,259,224,165,358,178,208,90)(78,260,225,166,359,179,209,82)(79,261,217,167,360,180,210,83)(80,253,218,168,352,172,211,84)(81,254,219,169,353,173,212,85) );

G=PermutationGroup([(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)], [(1,54,171,203,189),(2,46,163,204,181),(3,47,164,205,182),(4,48,165,206,183),(5,49,166,207,184),(6,50,167,199,185),(7,51,168,200,186),(8,52,169,201,187),(9,53,170,202,188),(10,141,356,341,302),(11,142,357,342,303),(12,143,358,334,304),(13,144,359,335,305),(14,136,360,336,306),(15,137,352,337,298),(16,138,353,338,299),(17,139,354,339,300),(18,140,355,340,301),(19,210,283,273,327),(20,211,284,274,328),(21,212,285,275,329),(22,213,286,276,330),(23,214,287,277,331),(24,215,288,278,332),(25,216,280,279,333),(26,208,281,271,325),(27,209,282,272,326),(28,320,107,172,309),(29,321,108,173,310),(30,322,100,174,311),(31,323,101,175,312),(32,324,102,176,313),(33,316,103,177,314),(34,317,104,178,315),(35,318,105,179,307),(36,319,106,180,308),(37,88,153,109,197),(38,89,145,110,198),(39,90,146,111,190),(40,82,147,112,191),(41,83,148,113,192),(42,84,149,114,193),(43,85,150,115,194),(44,86,151,116,195),(45,87,152,117,196),(55,292,225,71,239),(56,293,217,72,240),(57,294,218,64,241),(58,295,219,65,242),(59,296,220,66,243),(60,297,221,67,235),(61,289,222,68,236),(62,290,223,69,237),(63,291,224,70,238),(73,119,226,135,343),(74,120,227,127,344),(75,121,228,128,345),(76,122,229,129,346),(77,123,230,130,347),(78,124,231,131,348),(79,125,232,132,349),(80,126,233,133,350),(81,118,234,134,351),(91,154,253,246,269),(92,155,254,247,270),(93,156,255,248,262),(94,157,256,249,263),(95,158,257,250,264),(96,159,258,251,265),(97,160,259,252,266),(98,161,260,244,267),(99,162,261,245,268)], [(1,340,31,23,196,120,263,297),(2,341,32,24,197,121,264,289),(3,342,33,25,198,122,265,290),(4,334,34,26,190,123,266,291),(5,335,35,27,191,124,267,292),(6,336,36,19,192,125,268,293),(7,337,28,20,193,126,269,294),(8,338,29,21,194,118,270,295),(9,339,30,22,195,119,262,296),(10,313,278,37,128,250,236,46),(11,314,279,38,129,251,237,47),(12,315,271,39,130,252,238,48),(13,307,272,40,131,244,239,49),(14,308,273,41,132,245,240,50),(15,309,274,42,133,246,241,51),(16,310,275,43,134,247,242,52),(17,311,276,44,135,248,243,53),(18,312,277,45,127,249,235,54),(55,207,305,105,326,147,231,161),(56,199,306,106,327,148,232,162),(57,200,298,107,328,149,233,154),(58,201,299,108,329,150,234,155),(59,202,300,100,330,151,226,156),(60,203,301,101,331,152,227,157),(61,204,302,102,332,153,228,158),(62,205,303,103,333,145,229,159),(63,206,304,104,325,146,230,160),(64,186,137,320,284,114,350,91),(65,187,138,321,285,115,351,92),(66,188,139,322,286,116,343,93),(67,189,140,323,287,117,344,94),(68,181,141,324,288,109,345,95),(69,182,142,316,280,110,346,96),(70,183,143,317,281,111,347,97),(71,184,144,318,282,112,348,98),(72,185,136,319,283,113,349,99),(73,255,220,170,354,174,213,86),(74,256,221,171,355,175,214,87),(75,257,222,163,356,176,215,88),(76,258,223,164,357,177,216,89),(77,259,224,165,358,178,208,90),(78,260,225,166,359,179,209,82),(79,261,217,167,360,180,210,83),(80,253,218,168,352,172,211,84),(81,254,219,169,353,173,212,85)])

90 conjugacy classes

class 1  2 3A3B4A4B 5 6A6B8A8B8C8D9A···9F 10 12A12B12C12D15A15B18A···18F24A···24H30A30B36A···36L45A···45F72A···72X90A···90F
order12334456688889···91012121212151518···1824···24303036···3645···4572···7290···90
size11115541155551···145555441···15···5445···54···45···54···4

90 irreducible representations

dim111111111111444444
type+++-
imageC1C2C3C4C6C8C9C12C18C24C36C72F5C5⋊C8C3×F5C3×C5⋊C8C9×F5C9×C5⋊C8
kernelC9×C5⋊C8C9×Dic5C3×C5⋊C8C90C3×Dic5C45C5⋊C8C30Dic5C15C10C5C18C9C6C3C2C1
# reps11222464681224112266

Matrix representation of C9×C5⋊C8 in GL5(𝔽1801)

10000
0144000
0014400
0001440
0000144
,
10000
00001800
01001800
00101800
00011800
,
4640000
08827368771785
01759720199866
0108116029351743
0166789191065

G:=sub<GL(5,GF(1801))| [1,0,0,0,0,0,144,0,0,0,0,0,144,0,0,0,0,0,144,0,0,0,0,0,144],[1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1800,1800,1800,1800],[464,0,0,0,0,0,882,1759,1081,16,0,736,720,1602,678,0,877,199,935,919,0,1785,866,1743,1065] >;

C9×C5⋊C8 in GAP, Magma, Sage, TeX

C_9\times C_5\rtimes C_8
% in TeX

G:=Group("C9xC5:C8");
// GroupNames label

G:=SmallGroup(360,5);
// by ID

G=gap.SmallGroup(360,5);
# by ID

G:=PCGroup([6,-2,-3,-2,-3,-2,-5,36,79,122,5189,1745]);
// Polycyclic

G:=Group<a,b,c|a^9=b^5=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^3>;
// generators/relations

Export

Subgroup lattice of C9×C5⋊C8 in TeX

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