direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C18×Dic5, C90⋊5C4, C10⋊2C36, C30.7C12, C18.16D10, C90.21C22, C5⋊3(C2×C36), C45⋊12(C2×C4), (C2×C10).C18, C3.(C6×Dic5), C22.(C9×D5), (C2×C30).5C6, (C2×C90).3C2, C2.2(D5×C18), (C2×C18).2D5, C6.16(C6×D5), (C6×Dic5).C3, C15.3(C2×C12), C30.16(C2×C6), C10.4(C2×C18), C6.3(C3×Dic5), (C3×Dic5).9C6, (C2×C6).4(C3×D5), SmallGroup(360,18)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — C18×Dic5 |
Generators and relations for C18×Dic5
G = < a,b,c | a18=b10=1, c2=b5, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C18×Dic5
►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)
(1 186 23 265 217 318 104 294 176 47)(2 187 24 266 218 319 105 295 177 48)(3 188 25 267 219 320 106 296 178 49)(4 189 26 268 220 321 107 297 179 50)(5 190 27 269 221 322 108 298 180 51)(6 191 28 270 222 323 91 299 163 52)(7 192 29 253 223 324 92 300 164 53)(8 193 30 254 224 307 93 301 165 54)(9 194 31 255 225 308 94 302 166 37)(10 195 32 256 226 309 95 303 167 38)(11 196 33 257 227 310 96 304 168 39)(12 197 34 258 228 311 97 305 169 40)(13 198 35 259 229 312 98 306 170 41)(14 181 36 260 230 313 99 289 171 42)(15 182 19 261 231 314 100 290 172 43)(16 183 20 262 232 315 101 291 173 44)(17 184 21 263 233 316 102 292 174 45)(18 185 22 264 234 317 103 293 175 46)(55 156 284 114 144 330 206 344 240 73)(56 157 285 115 127 331 207 345 241 74)(57 158 286 116 128 332 208 346 242 75)(58 159 287 117 129 333 209 347 243 76)(59 160 288 118 130 334 210 348 244 77)(60 161 271 119 131 335 211 349 245 78)(61 162 272 120 132 336 212 350 246 79)(62 145 273 121 133 337 213 351 247 80)(63 146 274 122 134 338 214 352 248 81)(64 147 275 123 135 339 215 353 249 82)(65 148 276 124 136 340 216 354 250 83)(66 149 277 125 137 341 199 355 251 84)(67 150 278 126 138 342 200 356 252 85)(68 151 279 109 139 325 201 357 235 86)(69 152 280 110 140 326 202 358 236 87)(70 153 281 111 141 327 203 359 237 88)(71 154 282 112 142 328 204 360 238 89)(72 155 283 113 143 329 205 343 239 90)
(1 59 318 334)(2 60 319 335)(3 61 320 336)(4 62 321 337)(5 63 322 338)(6 64 323 339)(7 65 324 340)(8 66 307 341)(9 67 308 342)(10 68 309 325)(11 69 310 326)(12 70 311 327)(13 71 312 328)(14 72 313 329)(15 55 314 330)(16 56 315 331)(17 57 316 332)(18 58 317 333)(19 240 290 114)(20 241 291 115)(21 242 292 116)(22 243 293 117)(23 244 294 118)(24 245 295 119)(25 246 296 120)(26 247 297 121)(27 248 298 122)(28 249 299 123)(29 250 300 124)(30 251 301 125)(31 252 302 126)(32 235 303 109)(33 236 304 110)(34 237 305 111)(35 238 306 112)(36 239 289 113)(37 150 225 200)(38 151 226 201)(39 152 227 202)(40 153 228 203)(41 154 229 204)(42 155 230 205)(43 156 231 206)(44 157 232 207)(45 158 233 208)(46 159 234 209)(47 160 217 210)(48 161 218 211)(49 162 219 212)(50 145 220 213)(51 146 221 214)(52 147 222 215)(53 148 223 216)(54 149 224 199)(73 100 144 182)(74 101 127 183)(75 102 128 184)(76 103 129 185)(77 104 130 186)(78 105 131 187)(79 106 132 188)(80 107 133 189)(81 108 134 190)(82 91 135 191)(83 92 136 192)(84 93 137 193)(85 94 138 194)(86 95 139 195)(87 96 140 196)(88 97 141 197)(89 98 142 198)(90 99 143 181)(163 275 270 353)(164 276 253 354)(165 277 254 355)(166 278 255 356)(167 279 256 357)(168 280 257 358)(169 281 258 359)(170 282 259 360)(171 283 260 343)(172 284 261 344)(173 285 262 345)(174 286 263 346)(175 287 264 347)(176 288 265 348)(177 271 266 349)(178 272 267 350)(179 273 268 351)(180 274 269 352)
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), (1,186,23,265,217,318,104,294,176,47)(2,187,24,266,218,319,105,295,177,48)(3,188,25,267,219,320,106,296,178,49)(4,189,26,268,220,321,107,297,179,50)(5,190,27,269,221,322,108,298,180,51)(6,191,28,270,222,323,91,299,163,52)(7,192,29,253,223,324,92,300,164,53)(8,193,30,254,224,307,93,301,165,54)(9,194,31,255,225,308,94,302,166,37)(10,195,32,256,226,309,95,303,167,38)(11,196,33,257,227,310,96,304,168,39)(12,197,34,258,228,311,97,305,169,40)(13,198,35,259,229,312,98,306,170,41)(14,181,36,260,230,313,99,289,171,42)(15,182,19,261,231,314,100,290,172,43)(16,183,20,262,232,315,101,291,173,44)(17,184,21,263,233,316,102,292,174,45)(18,185,22,264,234,317,103,293,175,46)(55,156,284,114,144,330,206,344,240,73)(56,157,285,115,127,331,207,345,241,74)(57,158,286,116,128,332,208,346,242,75)(58,159,287,117,129,333,209,347,243,76)(59,160,288,118,130,334,210,348,244,77)(60,161,271,119,131,335,211,349,245,78)(61,162,272,120,132,336,212,350,246,79)(62,145,273,121,133,337,213,351,247,80)(63,146,274,122,134,338,214,352,248,81)(64,147,275,123,135,339,215,353,249,82)(65,148,276,124,136,340,216,354,250,83)(66,149,277,125,137,341,199,355,251,84)(67,150,278,126,138,342,200,356,252,85)(68,151,279,109,139,325,201,357,235,86)(69,152,280,110,140,326,202,358,236,87)(70,153,281,111,141,327,203,359,237,88)(71,154,282,112,142,328,204,360,238,89)(72,155,283,113,143,329,205,343,239,90), (1,59,318,334)(2,60,319,335)(3,61,320,336)(4,62,321,337)(5,63,322,338)(6,64,323,339)(7,65,324,340)(8,66,307,341)(9,67,308,342)(10,68,309,325)(11,69,310,326)(12,70,311,327)(13,71,312,328)(14,72,313,329)(15,55,314,330)(16,56,315,331)(17,57,316,332)(18,58,317,333)(19,240,290,114)(20,241,291,115)(21,242,292,116)(22,243,293,117)(23,244,294,118)(24,245,295,119)(25,246,296,120)(26,247,297,121)(27,248,298,122)(28,249,299,123)(29,250,300,124)(30,251,301,125)(31,252,302,126)(32,235,303,109)(33,236,304,110)(34,237,305,111)(35,238,306,112)(36,239,289,113)(37,150,225,200)(38,151,226,201)(39,152,227,202)(40,153,228,203)(41,154,229,204)(42,155,230,205)(43,156,231,206)(44,157,232,207)(45,158,233,208)(46,159,234,209)(47,160,217,210)(48,161,218,211)(49,162,219,212)(50,145,220,213)(51,146,221,214)(52,147,222,215)(53,148,223,216)(54,149,224,199)(73,100,144,182)(74,101,127,183)(75,102,128,184)(76,103,129,185)(77,104,130,186)(78,105,131,187)(79,106,132,188)(80,107,133,189)(81,108,134,190)(82,91,135,191)(83,92,136,192)(84,93,137,193)(85,94,138,194)(86,95,139,195)(87,96,140,196)(88,97,141,197)(89,98,142,198)(90,99,143,181)(163,275,270,353)(164,276,253,354)(165,277,254,355)(166,278,255,356)(167,279,256,357)(168,280,257,358)(169,281,258,359)(170,282,259,360)(171,283,260,343)(172,284,261,344)(173,285,262,345)(174,286,263,346)(175,287,264,347)(176,288,265,348)(177,271,266,349)(178,272,267,350)(179,273,268,351)(180,274,269,352)>;
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), (1,186,23,265,217,318,104,294,176,47)(2,187,24,266,218,319,105,295,177,48)(3,188,25,267,219,320,106,296,178,49)(4,189,26,268,220,321,107,297,179,50)(5,190,27,269,221,322,108,298,180,51)(6,191,28,270,222,323,91,299,163,52)(7,192,29,253,223,324,92,300,164,53)(8,193,30,254,224,307,93,301,165,54)(9,194,31,255,225,308,94,302,166,37)(10,195,32,256,226,309,95,303,167,38)(11,196,33,257,227,310,96,304,168,39)(12,197,34,258,228,311,97,305,169,40)(13,198,35,259,229,312,98,306,170,41)(14,181,36,260,230,313,99,289,171,42)(15,182,19,261,231,314,100,290,172,43)(16,183,20,262,232,315,101,291,173,44)(17,184,21,263,233,316,102,292,174,45)(18,185,22,264,234,317,103,293,175,46)(55,156,284,114,144,330,206,344,240,73)(56,157,285,115,127,331,207,345,241,74)(57,158,286,116,128,332,208,346,242,75)(58,159,287,117,129,333,209,347,243,76)(59,160,288,118,130,334,210,348,244,77)(60,161,271,119,131,335,211,349,245,78)(61,162,272,120,132,336,212,350,246,79)(62,145,273,121,133,337,213,351,247,80)(63,146,274,122,134,338,214,352,248,81)(64,147,275,123,135,339,215,353,249,82)(65,148,276,124,136,340,216,354,250,83)(66,149,277,125,137,341,199,355,251,84)(67,150,278,126,138,342,200,356,252,85)(68,151,279,109,139,325,201,357,235,86)(69,152,280,110,140,326,202,358,236,87)(70,153,281,111,141,327,203,359,237,88)(71,154,282,112,142,328,204,360,238,89)(72,155,283,113,143,329,205,343,239,90), (1,59,318,334)(2,60,319,335)(3,61,320,336)(4,62,321,337)(5,63,322,338)(6,64,323,339)(7,65,324,340)(8,66,307,341)(9,67,308,342)(10,68,309,325)(11,69,310,326)(12,70,311,327)(13,71,312,328)(14,72,313,329)(15,55,314,330)(16,56,315,331)(17,57,316,332)(18,58,317,333)(19,240,290,114)(20,241,291,115)(21,242,292,116)(22,243,293,117)(23,244,294,118)(24,245,295,119)(25,246,296,120)(26,247,297,121)(27,248,298,122)(28,249,299,123)(29,250,300,124)(30,251,301,125)(31,252,302,126)(32,235,303,109)(33,236,304,110)(34,237,305,111)(35,238,306,112)(36,239,289,113)(37,150,225,200)(38,151,226,201)(39,152,227,202)(40,153,228,203)(41,154,229,204)(42,155,230,205)(43,156,231,206)(44,157,232,207)(45,158,233,208)(46,159,234,209)(47,160,217,210)(48,161,218,211)(49,162,219,212)(50,145,220,213)(51,146,221,214)(52,147,222,215)(53,148,223,216)(54,149,224,199)(73,100,144,182)(74,101,127,183)(75,102,128,184)(76,103,129,185)(77,104,130,186)(78,105,131,187)(79,106,132,188)(80,107,133,189)(81,108,134,190)(82,91,135,191)(83,92,136,192)(84,93,137,193)(85,94,138,194)(86,95,139,195)(87,96,140,196)(88,97,141,197)(89,98,142,198)(90,99,143,181)(163,275,270,353)(164,276,253,354)(165,277,254,355)(166,278,255,356)(167,279,256,357)(168,280,257,358)(169,281,258,359)(170,282,259,360)(171,283,260,343)(172,284,261,344)(173,285,262,345)(174,286,263,346)(175,287,264,347)(176,288,265,348)(177,271,266,349)(178,272,267,350)(179,273,268,351)(180,274,269,352) );
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)], [(1,186,23,265,217,318,104,294,176,47),(2,187,24,266,218,319,105,295,177,48),(3,188,25,267,219,320,106,296,178,49),(4,189,26,268,220,321,107,297,179,50),(5,190,27,269,221,322,108,298,180,51),(6,191,28,270,222,323,91,299,163,52),(7,192,29,253,223,324,92,300,164,53),(8,193,30,254,224,307,93,301,165,54),(9,194,31,255,225,308,94,302,166,37),(10,195,32,256,226,309,95,303,167,38),(11,196,33,257,227,310,96,304,168,39),(12,197,34,258,228,311,97,305,169,40),(13,198,35,259,229,312,98,306,170,41),(14,181,36,260,230,313,99,289,171,42),(15,182,19,261,231,314,100,290,172,43),(16,183,20,262,232,315,101,291,173,44),(17,184,21,263,233,316,102,292,174,45),(18,185,22,264,234,317,103,293,175,46),(55,156,284,114,144,330,206,344,240,73),(56,157,285,115,127,331,207,345,241,74),(57,158,286,116,128,332,208,346,242,75),(58,159,287,117,129,333,209,347,243,76),(59,160,288,118,130,334,210,348,244,77),(60,161,271,119,131,335,211,349,245,78),(61,162,272,120,132,336,212,350,246,79),(62,145,273,121,133,337,213,351,247,80),(63,146,274,122,134,338,214,352,248,81),(64,147,275,123,135,339,215,353,249,82),(65,148,276,124,136,340,216,354,250,83),(66,149,277,125,137,341,199,355,251,84),(67,150,278,126,138,342,200,356,252,85),(68,151,279,109,139,325,201,357,235,86),(69,152,280,110,140,326,202,358,236,87),(70,153,281,111,141,327,203,359,237,88),(71,154,282,112,142,328,204,360,238,89),(72,155,283,113,143,329,205,343,239,90)], [(1,59,318,334),(2,60,319,335),(3,61,320,336),(4,62,321,337),(5,63,322,338),(6,64,323,339),(7,65,324,340),(8,66,307,341),(9,67,308,342),(10,68,309,325),(11,69,310,326),(12,70,311,327),(13,71,312,328),(14,72,313,329),(15,55,314,330),(16,56,315,331),(17,57,316,332),(18,58,317,333),(19,240,290,114),(20,241,291,115),(21,242,292,116),(22,243,293,117),(23,244,294,118),(24,245,295,119),(25,246,296,120),(26,247,297,121),(27,248,298,122),(28,249,299,123),(29,250,300,124),(30,251,301,125),(31,252,302,126),(32,235,303,109),(33,236,304,110),(34,237,305,111),(35,238,306,112),(36,239,289,113),(37,150,225,200),(38,151,226,201),(39,152,227,202),(40,153,228,203),(41,154,229,204),(42,155,230,205),(43,156,231,206),(44,157,232,207),(45,158,233,208),(46,159,234,209),(47,160,217,210),(48,161,218,211),(49,162,219,212),(50,145,220,213),(51,146,221,214),(52,147,222,215),(53,148,223,216),(54,149,224,199),(73,100,144,182),(74,101,127,183),(75,102,128,184),(76,103,129,185),(77,104,130,186),(78,105,131,187),(79,106,132,188),(80,107,133,189),(81,108,134,190),(82,91,135,191),(83,92,136,192),(84,93,137,193),(85,94,138,194),(86,95,139,195),(87,96,140,196),(88,97,141,197),(89,98,142,198),(90,99,143,181),(163,275,270,353),(164,276,253,354),(165,277,254,355),(166,278,255,356),(167,279,256,357),(168,280,257,358),(169,281,258,359),(170,282,259,360),(171,283,260,343),(172,284,261,344),(173,285,262,345),(174,286,263,346),(175,287,264,347),(176,288,265,348),(177,271,266,349),(178,272,267,350),(179,273,268,351),(180,274,269,352)]])
144 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | 4B | 4C | 4D | 5A | 5B | 6A | ··· | 6F | 9A | ··· | 9F | 10A | ··· | 10F | 12A | ··· | 12H | 15A | 15B | 15C | 15D | 18A | ··· | 18R | 30A | ··· | 30L | 36A | ··· | 36X | 45A | ··· | 45L | 90A | ··· | 90AJ |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 9 | ··· | 9 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 18 | ··· | 18 | 30 | ··· | 30 | 36 | ··· | 36 | 45 | ··· | 45 | 90 | ··· | 90 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 5 | ··· | 5 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 5 | ··· | 5 | 2 | ··· | 2 | 2 | ··· | 2 |
144 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |||||||||||||||
| image | C1 | C2 | C2 | C3 | C4 | C6 | C6 | C9 | C12 | C18 | C18 | C36 | D5 | Dic5 | D10 | C3×D5 | C3×Dic5 | C6×D5 | C9×D5 | C9×Dic5 | D5×C18 |
| kernel | C18×Dic5 | C9×Dic5 | C2×C90 | C6×Dic5 | C90 | C3×Dic5 | C2×C30 | C2×Dic5 | C30 | Dic5 | C2×C10 | C10 | C2×C18 | C18 | C18 | C2×C6 | C6 | C6 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 4 | 4 | 2 | 6 | 8 | 12 | 6 | 24 | 2 | 4 | 2 | 4 | 8 | 4 | 12 | 24 | 12 |
Matrix representation of C18×Dic5 ►in GL4(𝔽181) generated by
| 49 | 0 | 0 | 0 |
| 0 | 180 | 0 | 0 |
| 0 | 0 | 62 | 0 |
| 0 | 0 | 0 | 62 |
| 1 | 0 | 0 | 0 |
| 0 | 180 | 0 | 0 |
| 0 | 0 | 180 | 1 |
| 0 | 0 | 12 | 168 |
| 1 | 0 | 0 | 0 |
| 0 | 19 | 0 | 0 |
| 0 | 0 | 141 | 157 |
| 0 | 0 | 44 | 40 |
G:=sub<GL(4,GF(181))| [49,0,0,0,0,180,0,0,0,0,62,0,0,0,0,62],[1,0,0,0,0,180,0,0,0,0,180,12,0,0,1,168],[1,0,0,0,0,19,0,0,0,0,141,44,0,0,157,40] >;
C18×Dic5 in GAP, Magma, Sage, TeX
C_{18}\times {\rm Dic}_5 % in TeX
G:=Group("C18xDic5"); // GroupNames label
G:=SmallGroup(360,18);
// by ID
G=gap.SmallGroup(360,18);
# by ID
G:=PCGroup([6,-2,-2,-3,-2,-3,-5,72,122,10373]);
// Polycyclic
G:=Group<a,b,c|a^18=b^10=1,c^2=b^5,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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