direct product, metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C9×Dic10, C45⋊4Q8, C60.3C6, C36.3D5, C180.4C2, C20.1C18, C18.13D10, C90.18C22, Dic5.1C18, C5⋊(Q8×C9), C4.(C9×D5), C15.(C3×Q8), C12.3(C3×D5), C6.13(C6×D5), C2.3(D5×C18), C3.(C3×Dic10), C30.13(C2×C6), C10.1(C2×C18), (C3×Dic10).C3, (C3×Dic5).2C6, (C9×Dic5).3C2, SmallGroup(360,15)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C9×Dic10
G = < a,b,c | a9=b20=1, c2=b10, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C9×Dic10
►Regular action on 360 points
Generators in S360
(1 206 55 109 100 324 224 129 197)(2 207 56 110 81 325 225 130 198)(3 208 57 111 82 326 226 131 199)(4 209 58 112 83 327 227 132 200)(5 210 59 113 84 328 228 133 181)(6 211 60 114 85 329 229 134 182)(7 212 41 115 86 330 230 135 183)(8 213 42 116 87 331 231 136 184)(9 214 43 117 88 332 232 137 185)(10 215 44 118 89 333 233 138 186)(11 216 45 119 90 334 234 139 187)(12 217 46 120 91 335 235 140 188)(13 218 47 101 92 336 236 121 189)(14 219 48 102 93 337 237 122 190)(15 220 49 103 94 338 238 123 191)(16 201 50 104 95 339 239 124 192)(17 202 51 105 96 340 240 125 193)(18 203 52 106 97 321 221 126 194)(19 204 53 107 98 322 222 127 195)(20 205 54 108 99 323 223 128 196)(21 154 64 316 245 354 282 274 163)(22 155 65 317 246 355 283 275 164)(23 156 66 318 247 356 284 276 165)(24 157 67 319 248 357 285 277 166)(25 158 68 320 249 358 286 278 167)(26 159 69 301 250 359 287 279 168)(27 160 70 302 251 360 288 280 169)(28 141 71 303 252 341 289 261 170)(29 142 72 304 253 342 290 262 171)(30 143 73 305 254 343 291 263 172)(31 144 74 306 255 344 292 264 173)(32 145 75 307 256 345 293 265 174)(33 146 76 308 257 346 294 266 175)(34 147 77 309 258 347 295 267 176)(35 148 78 310 259 348 296 268 177)(36 149 79 311 260 349 297 269 178)(37 150 80 312 241 350 298 270 179)(38 151 61 313 242 351 299 271 180)(39 152 62 314 243 352 300 272 161)(40 153 63 315 244 353 281 273 162)
(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)
(1 265 11 275)(2 264 12 274)(3 263 13 273)(4 262 14 272)(5 261 15 271)(6 280 16 270)(7 279 17 269)(8 278 18 268)(9 277 19 267)(10 276 20 266)(21 56 31 46)(22 55 32 45)(23 54 33 44)(24 53 34 43)(25 52 35 42)(26 51 36 41)(27 50 37 60)(28 49 38 59)(29 48 39 58)(30 47 40 57)(61 84 71 94)(62 83 72 93)(63 82 73 92)(64 81 74 91)(65 100 75 90)(66 99 76 89)(67 98 77 88)(68 97 78 87)(69 96 79 86)(70 95 80 85)(101 153 111 143)(102 152 112 142)(103 151 113 141)(104 150 114 160)(105 149 115 159)(106 148 116 158)(107 147 117 157)(108 146 118 156)(109 145 119 155)(110 144 120 154)(121 353 131 343)(122 352 132 342)(123 351 133 341)(124 350 134 360)(125 349 135 359)(126 348 136 358)(127 347 137 357)(128 346 138 356)(129 345 139 355)(130 344 140 354)(161 209 171 219)(162 208 172 218)(163 207 173 217)(164 206 174 216)(165 205 175 215)(166 204 176 214)(167 203 177 213)(168 202 178 212)(169 201 179 211)(170 220 180 210)(181 289 191 299)(182 288 192 298)(183 287 193 297)(184 286 194 296)(185 285 195 295)(186 284 196 294)(187 283 197 293)(188 282 198 292)(189 281 199 291)(190 300 200 290)(221 259 231 249)(222 258 232 248)(223 257 233 247)(224 256 234 246)(225 255 235 245)(226 254 236 244)(227 253 237 243)(228 252 238 242)(229 251 239 241)(230 250 240 260)(301 340 311 330)(302 339 312 329)(303 338 313 328)(304 337 314 327)(305 336 315 326)(306 335 316 325)(307 334 317 324)(308 333 318 323)(309 332 319 322)(310 331 320 321)
G:=sub<Sym(360)| (1,206,55,109,100,324,224,129,197)(2,207,56,110,81,325,225,130,198)(3,208,57,111,82,326,226,131,199)(4,209,58,112,83,327,227,132,200)(5,210,59,113,84,328,228,133,181)(6,211,60,114,85,329,229,134,182)(7,212,41,115,86,330,230,135,183)(8,213,42,116,87,331,231,136,184)(9,214,43,117,88,332,232,137,185)(10,215,44,118,89,333,233,138,186)(11,216,45,119,90,334,234,139,187)(12,217,46,120,91,335,235,140,188)(13,218,47,101,92,336,236,121,189)(14,219,48,102,93,337,237,122,190)(15,220,49,103,94,338,238,123,191)(16,201,50,104,95,339,239,124,192)(17,202,51,105,96,340,240,125,193)(18,203,52,106,97,321,221,126,194)(19,204,53,107,98,322,222,127,195)(20,205,54,108,99,323,223,128,196)(21,154,64,316,245,354,282,274,163)(22,155,65,317,246,355,283,275,164)(23,156,66,318,247,356,284,276,165)(24,157,67,319,248,357,285,277,166)(25,158,68,320,249,358,286,278,167)(26,159,69,301,250,359,287,279,168)(27,160,70,302,251,360,288,280,169)(28,141,71,303,252,341,289,261,170)(29,142,72,304,253,342,290,262,171)(30,143,73,305,254,343,291,263,172)(31,144,74,306,255,344,292,264,173)(32,145,75,307,256,345,293,265,174)(33,146,76,308,257,346,294,266,175)(34,147,77,309,258,347,295,267,176)(35,148,78,310,259,348,296,268,177)(36,149,79,311,260,349,297,269,178)(37,150,80,312,241,350,298,270,179)(38,151,61,313,242,351,299,271,180)(39,152,62,314,243,352,300,272,161)(40,153,63,315,244,353,281,273,162), (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), (1,265,11,275)(2,264,12,274)(3,263,13,273)(4,262,14,272)(5,261,15,271)(6,280,16,270)(7,279,17,269)(8,278,18,268)(9,277,19,267)(10,276,20,266)(21,56,31,46)(22,55,32,45)(23,54,33,44)(24,53,34,43)(25,52,35,42)(26,51,36,41)(27,50,37,60)(28,49,38,59)(29,48,39,58)(30,47,40,57)(61,84,71,94)(62,83,72,93)(63,82,73,92)(64,81,74,91)(65,100,75,90)(66,99,76,89)(67,98,77,88)(68,97,78,87)(69,96,79,86)(70,95,80,85)(101,153,111,143)(102,152,112,142)(103,151,113,141)(104,150,114,160)(105,149,115,159)(106,148,116,158)(107,147,117,157)(108,146,118,156)(109,145,119,155)(110,144,120,154)(121,353,131,343)(122,352,132,342)(123,351,133,341)(124,350,134,360)(125,349,135,359)(126,348,136,358)(127,347,137,357)(128,346,138,356)(129,345,139,355)(130,344,140,354)(161,209,171,219)(162,208,172,218)(163,207,173,217)(164,206,174,216)(165,205,175,215)(166,204,176,214)(167,203,177,213)(168,202,178,212)(169,201,179,211)(170,220,180,210)(181,289,191,299)(182,288,192,298)(183,287,193,297)(184,286,194,296)(185,285,195,295)(186,284,196,294)(187,283,197,293)(188,282,198,292)(189,281,199,291)(190,300,200,290)(221,259,231,249)(222,258,232,248)(223,257,233,247)(224,256,234,246)(225,255,235,245)(226,254,236,244)(227,253,237,243)(228,252,238,242)(229,251,239,241)(230,250,240,260)(301,340,311,330)(302,339,312,329)(303,338,313,328)(304,337,314,327)(305,336,315,326)(306,335,316,325)(307,334,317,324)(308,333,318,323)(309,332,319,322)(310,331,320,321)>;
G:=Group( (1,206,55,109,100,324,224,129,197)(2,207,56,110,81,325,225,130,198)(3,208,57,111,82,326,226,131,199)(4,209,58,112,83,327,227,132,200)(5,210,59,113,84,328,228,133,181)(6,211,60,114,85,329,229,134,182)(7,212,41,115,86,330,230,135,183)(8,213,42,116,87,331,231,136,184)(9,214,43,117,88,332,232,137,185)(10,215,44,118,89,333,233,138,186)(11,216,45,119,90,334,234,139,187)(12,217,46,120,91,335,235,140,188)(13,218,47,101,92,336,236,121,189)(14,219,48,102,93,337,237,122,190)(15,220,49,103,94,338,238,123,191)(16,201,50,104,95,339,239,124,192)(17,202,51,105,96,340,240,125,193)(18,203,52,106,97,321,221,126,194)(19,204,53,107,98,322,222,127,195)(20,205,54,108,99,323,223,128,196)(21,154,64,316,245,354,282,274,163)(22,155,65,317,246,355,283,275,164)(23,156,66,318,247,356,284,276,165)(24,157,67,319,248,357,285,277,166)(25,158,68,320,249,358,286,278,167)(26,159,69,301,250,359,287,279,168)(27,160,70,302,251,360,288,280,169)(28,141,71,303,252,341,289,261,170)(29,142,72,304,253,342,290,262,171)(30,143,73,305,254,343,291,263,172)(31,144,74,306,255,344,292,264,173)(32,145,75,307,256,345,293,265,174)(33,146,76,308,257,346,294,266,175)(34,147,77,309,258,347,295,267,176)(35,148,78,310,259,348,296,268,177)(36,149,79,311,260,349,297,269,178)(37,150,80,312,241,350,298,270,179)(38,151,61,313,242,351,299,271,180)(39,152,62,314,243,352,300,272,161)(40,153,63,315,244,353,281,273,162), (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), (1,265,11,275)(2,264,12,274)(3,263,13,273)(4,262,14,272)(5,261,15,271)(6,280,16,270)(7,279,17,269)(8,278,18,268)(9,277,19,267)(10,276,20,266)(21,56,31,46)(22,55,32,45)(23,54,33,44)(24,53,34,43)(25,52,35,42)(26,51,36,41)(27,50,37,60)(28,49,38,59)(29,48,39,58)(30,47,40,57)(61,84,71,94)(62,83,72,93)(63,82,73,92)(64,81,74,91)(65,100,75,90)(66,99,76,89)(67,98,77,88)(68,97,78,87)(69,96,79,86)(70,95,80,85)(101,153,111,143)(102,152,112,142)(103,151,113,141)(104,150,114,160)(105,149,115,159)(106,148,116,158)(107,147,117,157)(108,146,118,156)(109,145,119,155)(110,144,120,154)(121,353,131,343)(122,352,132,342)(123,351,133,341)(124,350,134,360)(125,349,135,359)(126,348,136,358)(127,347,137,357)(128,346,138,356)(129,345,139,355)(130,344,140,354)(161,209,171,219)(162,208,172,218)(163,207,173,217)(164,206,174,216)(165,205,175,215)(166,204,176,214)(167,203,177,213)(168,202,178,212)(169,201,179,211)(170,220,180,210)(181,289,191,299)(182,288,192,298)(183,287,193,297)(184,286,194,296)(185,285,195,295)(186,284,196,294)(187,283,197,293)(188,282,198,292)(189,281,199,291)(190,300,200,290)(221,259,231,249)(222,258,232,248)(223,257,233,247)(224,256,234,246)(225,255,235,245)(226,254,236,244)(227,253,237,243)(228,252,238,242)(229,251,239,241)(230,250,240,260)(301,340,311,330)(302,339,312,329)(303,338,313,328)(304,337,314,327)(305,336,315,326)(306,335,316,325)(307,334,317,324)(308,333,318,323)(309,332,319,322)(310,331,320,321) );
G=PermutationGroup([[(1,206,55,109,100,324,224,129,197),(2,207,56,110,81,325,225,130,198),(3,208,57,111,82,326,226,131,199),(4,209,58,112,83,327,227,132,200),(5,210,59,113,84,328,228,133,181),(6,211,60,114,85,329,229,134,182),(7,212,41,115,86,330,230,135,183),(8,213,42,116,87,331,231,136,184),(9,214,43,117,88,332,232,137,185),(10,215,44,118,89,333,233,138,186),(11,216,45,119,90,334,234,139,187),(12,217,46,120,91,335,235,140,188),(13,218,47,101,92,336,236,121,189),(14,219,48,102,93,337,237,122,190),(15,220,49,103,94,338,238,123,191),(16,201,50,104,95,339,239,124,192),(17,202,51,105,96,340,240,125,193),(18,203,52,106,97,321,221,126,194),(19,204,53,107,98,322,222,127,195),(20,205,54,108,99,323,223,128,196),(21,154,64,316,245,354,282,274,163),(22,155,65,317,246,355,283,275,164),(23,156,66,318,247,356,284,276,165),(24,157,67,319,248,357,285,277,166),(25,158,68,320,249,358,286,278,167),(26,159,69,301,250,359,287,279,168),(27,160,70,302,251,360,288,280,169),(28,141,71,303,252,341,289,261,170),(29,142,72,304,253,342,290,262,171),(30,143,73,305,254,343,291,263,172),(31,144,74,306,255,344,292,264,173),(32,145,75,307,256,345,293,265,174),(33,146,76,308,257,346,294,266,175),(34,147,77,309,258,347,295,267,176),(35,148,78,310,259,348,296,268,177),(36,149,79,311,260,349,297,269,178),(37,150,80,312,241,350,298,270,179),(38,151,61,313,242,351,299,271,180),(39,152,62,314,243,352,300,272,161),(40,153,63,315,244,353,281,273,162)], [(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)], [(1,265,11,275),(2,264,12,274),(3,263,13,273),(4,262,14,272),(5,261,15,271),(6,280,16,270),(7,279,17,269),(8,278,18,268),(9,277,19,267),(10,276,20,266),(21,56,31,46),(22,55,32,45),(23,54,33,44),(24,53,34,43),(25,52,35,42),(26,51,36,41),(27,50,37,60),(28,49,38,59),(29,48,39,58),(30,47,40,57),(61,84,71,94),(62,83,72,93),(63,82,73,92),(64,81,74,91),(65,100,75,90),(66,99,76,89),(67,98,77,88),(68,97,78,87),(69,96,79,86),(70,95,80,85),(101,153,111,143),(102,152,112,142),(103,151,113,141),(104,150,114,160),(105,149,115,159),(106,148,116,158),(107,147,117,157),(108,146,118,156),(109,145,119,155),(110,144,120,154),(121,353,131,343),(122,352,132,342),(123,351,133,341),(124,350,134,360),(125,349,135,359),(126,348,136,358),(127,347,137,357),(128,346,138,356),(129,345,139,355),(130,344,140,354),(161,209,171,219),(162,208,172,218),(163,207,173,217),(164,206,174,216),(165,205,175,215),(166,204,176,214),(167,203,177,213),(168,202,178,212),(169,201,179,211),(170,220,180,210),(181,289,191,299),(182,288,192,298),(183,287,193,297),(184,286,194,296),(185,285,195,295),(186,284,196,294),(187,283,197,293),(188,282,198,292),(189,281,199,291),(190,300,200,290),(221,259,231,249),(222,258,232,248),(223,257,233,247),(224,256,234,246),(225,255,235,245),(226,254,236,244),(227,253,237,243),(228,252,238,242),(229,251,239,241),(230,250,240,260),(301,340,311,330),(302,339,312,329),(303,338,313,328),(304,337,314,327),(305,336,315,326),(306,335,316,325),(307,334,317,324),(308,333,318,323),(309,332,319,322),(310,331,320,321)]])
117 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 4C | 5A | 5B | 6A | 6B | 9A | ··· | 9F | 10A | 10B | 12A | 12B | 12C | 12D | 12E | 12F | 15A | 15B | 15C | 15D | 18A | ··· | 18F | 20A | 20B | 20C | 20D | 30A | 30B | 30C | 30D | 36A | ··· | 36F | 36G | ··· | 36R | 45A | ··· | 45L | 60A | ··· | 60H | 90A | ··· | 90L | 180A | ··· | 180X |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 9 | ··· | 9 | 10 | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 18 | ··· | 18 | 20 | 20 | 20 | 20 | 30 | 30 | 30 | 30 | 36 | ··· | 36 | 36 | ··· | 36 | 45 | ··· | 45 | 60 | ··· | 60 | 90 | ··· | 90 | 180 | ··· | 180 |
| size | 1 | 1 | 1 | 1 | 2 | 10 | 10 | 2 | 2 | 1 | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 10 | ··· | 10 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
117 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | + | - | ||||||||||||||
| image | C1 | C2 | C2 | C3 | C6 | C6 | C9 | C18 | C18 | Q8 | D5 | D10 | C3×Q8 | C3×D5 | Dic10 | C6×D5 | Q8×C9 | C9×D5 | C3×Dic10 | D5×C18 | C9×Dic10 |
| kernel | C9×Dic10 | C9×Dic5 | C180 | C3×Dic10 | C3×Dic5 | C60 | Dic10 | Dic5 | C20 | C45 | C36 | C18 | C15 | C12 | C9 | C6 | C5 | C4 | C3 | C2 | C1 |
| # reps | 1 | 2 | 1 | 2 | 4 | 2 | 6 | 12 | 6 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 6 | 12 | 8 | 12 | 24 |
Matrix representation of C9×Dic10 ►in GL2(𝔽19) generated by
| 6 | 0 |
| 0 | 6 |
| 11 | 17 |
| 10 | 0 |
| 6 | 7 |
| 11 | 13 |
G:=sub<GL(2,GF(19))| [6,0,0,6],[11,10,17,0],[6,11,7,13] >;
C9×Dic10 in GAP, Magma, Sage, TeX
C_9\times {\rm Dic}_{10} % in TeX
G:=Group("C9xDic10"); // GroupNames label
G:=SmallGroup(360,15);
// by ID
G=gap.SmallGroup(360,15);
# by ID
G:=PCGroup([6,-2,-2,-3,-2,-3,-5,72,169,79,122,10373]);
// Polycyclic
G:=Group<a,b,c|a^9=b^20=1,c^2=b^10,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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