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G = C9×C52C8order 360 = 23·32·5

Direct product of C9 and C52C8

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

Aliases: C9×C52C8, C52C72, C455C8, C90.5C4, C60.7C6, C36.4D5, C20.2C18, C180.6C2, C30.6C12, C15.2C24, C10.2C36, C18.2Dic5, C4.2(C9×D5), C2.(C9×Dic5), C12.6(C3×D5), C6.2(C3×Dic5), C3.(C3×C52C8), (C3×C52C8).C3, SmallGroup(360,2)

Series: Derived Chief Lower central Upper central

C1C5 — C9×C52C8
C1C5C10C30C60C180 — C9×C52C8
C5 — C9×C52C8
C1C36

Generators and relations for C9×C52C8
 G = < a,b,c | a9=b5=c8=1, ab=ba, ac=ca, cbc-1=b-1 >

5C8
5C24
5C72

Smallest permutation representation of C9×C52C8
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)
(1 165 161 193 189)(2 166 162 194 181)(3 167 154 195 182)(4 168 155 196 183)(5 169 156 197 184)(6 170 157 198 185)(7 171 158 190 186)(8 163 159 191 187)(9 164 160 192 188)(10 294 277 331 214)(11 295 278 332 215)(12 296 279 333 216)(13 297 271 325 208)(14 289 272 326 209)(15 290 273 327 210)(16 291 274 328 211)(17 292 275 329 212)(18 293 276 330 213)(19 62 223 227 240)(20 63 224 228 241)(21 55 225 229 242)(22 56 217 230 243)(23 57 218 231 235)(24 58 219 232 236)(25 59 220 233 237)(26 60 221 234 238)(27 61 222 226 239)(28 266 253 200 100)(29 267 254 201 101)(30 268 255 202 102)(31 269 256 203 103)(32 270 257 204 104)(33 262 258 205 105)(34 263 259 206 106)(35 264 260 207 107)(36 265 261 199 108)(37 86 91 47 315)(38 87 92 48 307)(39 88 93 49 308)(40 89 94 50 309)(41 90 95 51 310)(42 82 96 52 311)(43 83 97 53 312)(44 84 98 54 313)(45 85 99 46 314)(64 77 130 334 347)(65 78 131 335 348)(66 79 132 336 349)(67 80 133 337 350)(68 81 134 338 351)(69 73 135 339 343)(70 74 127 340 344)(71 75 128 341 345)(72 76 129 342 346)(109 321 149 249 173)(110 322 150 250 174)(111 323 151 251 175)(112 324 152 252 176)(113 316 153 244 177)(114 317 145 245 178)(115 318 146 246 179)(116 319 147 247 180)(117 320 148 248 172)(118 288 139 300 354)(119 280 140 301 355)(120 281 141 302 356)(121 282 142 303 357)(122 283 143 304 358)(123 284 144 305 359)(124 285 136 306 360)(125 286 137 298 352)(126 287 138 299 353)
(1 280 151 13 307 130 263 238)(2 281 152 14 308 131 264 239)(3 282 153 15 309 132 265 240)(4 283 145 16 310 133 266 241)(5 284 146 17 311 134 267 242)(6 285 147 18 312 135 268 243)(7 286 148 10 313 127 269 235)(8 287 149 11 314 128 270 236)(9 288 150 12 315 129 262 237)(19 182 142 316 290 50 336 36)(20 183 143 317 291 51 337 28)(21 184 144 318 292 52 338 29)(22 185 136 319 293 53 339 30)(23 186 137 320 294 54 340 31)(24 187 138 321 295 46 341 32)(25 188 139 322 296 47 342 33)(26 189 140 323 297 48 334 34)(27 181 141 324 289 49 335 35)(37 76 258 233 164 118 250 216)(38 77 259 234 165 119 251 208)(39 78 260 226 166 120 252 209)(40 79 261 227 167 121 244 210)(41 80 253 228 168 122 245 211)(42 81 254 229 169 123 246 212)(43 73 255 230 170 124 247 213)(44 74 256 231 171 125 248 214)(45 75 257 232 163 126 249 215)(55 197 305 115 275 96 351 101)(56 198 306 116 276 97 343 102)(57 190 298 117 277 98 344 103)(58 191 299 109 278 99 345 104)(59 192 300 110 279 91 346 105)(60 193 301 111 271 92 347 106)(61 194 302 112 272 93 348 107)(62 195 303 113 273 94 349 108)(63 196 304 114 274 95 350 100)(64 206 221 161 355 175 325 87)(65 207 222 162 356 176 326 88)(66 199 223 154 357 177 327 89)(67 200 224 155 358 178 328 90)(68 201 225 156 359 179 329 82)(69 202 217 157 360 180 330 83)(70 203 218 158 352 172 331 84)(71 204 219 159 353 173 332 85)(72 205 220 160 354 174 333 86)

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

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

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

144 conjugacy classes

class 1  2 3A3B4A4B5A5B6A6B8A8B8C8D9A···9F10A10B12A12B12C12D15A15B15C15D18A···18F20A20B20C20D24A···24H30A30B30C30D36A···36L45A···45L60A···60H72A···72X90A···90L180A···180X
order123344556688889···91010121212121515151518···182020202024···243030303036···3645···4560···6072···7290···90180···180
size111111221155551···122111122221···122225···522221···12···22···25···52···22···2

144 irreducible representations

dim111111111111222222222
type+++-
imageC1C2C3C4C6C8C9C12C18C24C36C72D5Dic5C3×D5C52C8C3×Dic5C9×D5C3×C52C8C9×Dic5C9×C52C8
kernelC9×C52C8C180C3×C52C8C90C60C45C52C8C30C20C15C10C5C36C18C12C9C6C4C3C2C1
# reps11222464681224224441281224

Matrix representation of C9×C52C8 in GL2(𝔽1801) generated by

8880
0888
,
13741800
10
,
1021557
12271699
G:=sub<GL(2,GF(1801))| [888,0,0,888],[1374,1,1800,0],[102,1227,1557,1699] >;

C9×C52C8 in GAP, Magma, Sage, TeX

C_9\times C_5\rtimes_2C_8
% in TeX

G:=Group("C9xC5:2C8");
// GroupNames label

G:=SmallGroup(360,2);
// by ID

G=gap.SmallGroup(360,2);
# by ID

G:=PCGroup([6,-2,-3,-2,-3,-2,-5,36,79,122,10373]);
// 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^-1>;
// generators/relations

Export

Subgroup lattice of C9×C52C8 in TeX

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