metabelian, supersoluble, monomial
Aliases: C15⋊1Dic6, C30.15D6, C32⋊5Dic10, (C3×C15)⋊4Q8, C3⋊2(C15⋊Q8), C6.22(S3×D5), (C3×C6).26D10, C3⋊Dic3.2D5, C5⋊1(C32⋊4Q8), C3⋊Dic15.3C2, (C3×Dic5).5S3, Dic5.1(C3⋊S3), (C3×C30).14C22, (C32×Dic5).2C2, C2.7(D5×C3⋊S3), C10.7(C2×C3⋊S3), (C5×C3⋊Dic3).1C2, SmallGroup(360,71)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C15⋊Dic6
G = < a,b,c | a15=b12=1, c2=b6, bab-1=a4, cac-1=a11, cbc-1=b-1 >
Subgroups: 368 in 72 conjugacy classes, 34 normal (14 characteristic)
C1, C2, C3, C4, C5, C6, Q8, C32, C10, Dic3, C12, C15, C3×C6, Dic5, Dic5, C20, Dic6, C30, C3⋊Dic3, C3⋊Dic3, C3×C12, Dic10, C3×C15, C5×Dic3, C3×Dic5, Dic15, C32⋊4Q8, C3×C30, C15⋊Q8, C32×Dic5, C5×C3⋊Dic3, C3⋊Dic15, C15⋊Dic6
Quotients: C1, C2, C22, S3, Q8, D5, D6, C3⋊S3, D10, Dic6, C2×C3⋊S3, Dic10, S3×D5, C32⋊4Q8, C15⋊Q8, D5×C3⋊S3, C15⋊Dic6
►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)
(1 263 69 194 31 254 50 220 16 239 84 209)(2 267 70 183 32 243 51 224 17 228 85 198)(3 256 71 187 33 247 52 213 18 232 86 202)(4 260 72 191 34 251 53 217 19 236 87 206)(5 264 73 195 35 255 54 221 20 240 88 210)(6 268 74 184 36 244 55 225 21 229 89 199)(7 257 75 188 37 248 56 214 22 233 90 203)(8 261 61 192 38 252 57 218 23 237 76 207)(9 265 62 181 39 241 58 222 24 226 77 196)(10 269 63 185 40 245 59 211 25 230 78 200)(11 258 64 189 41 249 60 215 26 234 79 204)(12 262 65 193 42 253 46 219 27 238 80 208)(13 266 66 182 43 242 47 223 28 227 81 197)(14 270 67 186 44 246 48 212 29 231 82 201)(15 259 68 190 45 250 49 216 30 235 83 205)(91 336 177 277 114 356 145 290 125 329 162 311)(92 340 178 281 115 360 146 294 126 318 163 315)(93 344 179 285 116 349 147 298 127 322 164 304)(94 333 180 274 117 353 148 287 128 326 165 308)(95 337 166 278 118 357 149 291 129 330 151 312)(96 341 167 282 119 346 150 295 130 319 152 301)(97 345 168 271 120 350 136 299 131 323 153 305)(98 334 169 275 106 354 137 288 132 327 154 309)(99 338 170 279 107 358 138 292 133 316 155 313)(100 342 171 283 108 347 139 296 134 320 156 302)(101 331 172 272 109 351 140 300 135 324 157 306)(102 335 173 276 110 355 141 289 121 328 158 310)(103 339 174 280 111 359 142 293 122 317 159 314)(104 343 175 284 112 348 143 297 123 321 160 303)(105 332 176 273 113 352 144 286 124 325 161 307)
(1 145 50 91)(2 141 51 102)(3 137 52 98)(4 148 53 94)(5 144 54 105)(6 140 55 101)(7 136 56 97)(8 147 57 93)(9 143 58 104)(10 139 59 100)(11 150 60 96)(12 146 46 92)(13 142 47 103)(14 138 48 99)(15 149 49 95)(16 162 69 114)(17 158 70 110)(18 154 71 106)(19 165 72 117)(20 161 73 113)(21 157 74 109)(22 153 75 120)(23 164 61 116)(24 160 62 112)(25 156 63 108)(26 152 64 119)(27 163 65 115)(28 159 66 111)(29 155 67 107)(30 151 68 118)(31 177 84 125)(32 173 85 121)(33 169 86 132)(34 180 87 128)(35 176 88 124)(36 172 89 135)(37 168 90 131)(38 179 76 127)(39 175 77 123)(40 171 78 134)(41 167 79 130)(42 178 80 126)(43 174 81 122)(44 170 82 133)(45 166 83 129)(181 284 226 321)(182 280 227 317)(183 276 228 328)(184 272 229 324)(185 283 230 320)(186 279 231 316)(187 275 232 327)(188 271 233 323)(189 282 234 319)(190 278 235 330)(191 274 236 326)(192 285 237 322)(193 281 238 318)(194 277 239 329)(195 273 240 325)(196 297 241 343)(197 293 242 339)(198 289 243 335)(199 300 244 331)(200 296 245 342)(201 292 246 338)(202 288 247 334)(203 299 248 345)(204 295 249 341)(205 291 250 337)(206 287 251 333)(207 298 252 344)(208 294 253 340)(209 290 254 336)(210 286 255 332)(211 302 269 347)(212 313 270 358)(213 309 256 354)(214 305 257 350)(215 301 258 346)(216 312 259 357)(217 308 260 353)(218 304 261 349)(219 315 262 360)(220 311 263 356)(221 307 264 352)(222 303 265 348)(223 314 266 359)(224 310 267 355)(225 306 268 351)
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), (1,263,69,194,31,254,50,220,16,239,84,209)(2,267,70,183,32,243,51,224,17,228,85,198)(3,256,71,187,33,247,52,213,18,232,86,202)(4,260,72,191,34,251,53,217,19,236,87,206)(5,264,73,195,35,255,54,221,20,240,88,210)(6,268,74,184,36,244,55,225,21,229,89,199)(7,257,75,188,37,248,56,214,22,233,90,203)(8,261,61,192,38,252,57,218,23,237,76,207)(9,265,62,181,39,241,58,222,24,226,77,196)(10,269,63,185,40,245,59,211,25,230,78,200)(11,258,64,189,41,249,60,215,26,234,79,204)(12,262,65,193,42,253,46,219,27,238,80,208)(13,266,66,182,43,242,47,223,28,227,81,197)(14,270,67,186,44,246,48,212,29,231,82,201)(15,259,68,190,45,250,49,216,30,235,83,205)(91,336,177,277,114,356,145,290,125,329,162,311)(92,340,178,281,115,360,146,294,126,318,163,315)(93,344,179,285,116,349,147,298,127,322,164,304)(94,333,180,274,117,353,148,287,128,326,165,308)(95,337,166,278,118,357,149,291,129,330,151,312)(96,341,167,282,119,346,150,295,130,319,152,301)(97,345,168,271,120,350,136,299,131,323,153,305)(98,334,169,275,106,354,137,288,132,327,154,309)(99,338,170,279,107,358,138,292,133,316,155,313)(100,342,171,283,108,347,139,296,134,320,156,302)(101,331,172,272,109,351,140,300,135,324,157,306)(102,335,173,276,110,355,141,289,121,328,158,310)(103,339,174,280,111,359,142,293,122,317,159,314)(104,343,175,284,112,348,143,297,123,321,160,303)(105,332,176,273,113,352,144,286,124,325,161,307), (1,145,50,91)(2,141,51,102)(3,137,52,98)(4,148,53,94)(5,144,54,105)(6,140,55,101)(7,136,56,97)(8,147,57,93)(9,143,58,104)(10,139,59,100)(11,150,60,96)(12,146,46,92)(13,142,47,103)(14,138,48,99)(15,149,49,95)(16,162,69,114)(17,158,70,110)(18,154,71,106)(19,165,72,117)(20,161,73,113)(21,157,74,109)(22,153,75,120)(23,164,61,116)(24,160,62,112)(25,156,63,108)(26,152,64,119)(27,163,65,115)(28,159,66,111)(29,155,67,107)(30,151,68,118)(31,177,84,125)(32,173,85,121)(33,169,86,132)(34,180,87,128)(35,176,88,124)(36,172,89,135)(37,168,90,131)(38,179,76,127)(39,175,77,123)(40,171,78,134)(41,167,79,130)(42,178,80,126)(43,174,81,122)(44,170,82,133)(45,166,83,129)(181,284,226,321)(182,280,227,317)(183,276,228,328)(184,272,229,324)(185,283,230,320)(186,279,231,316)(187,275,232,327)(188,271,233,323)(189,282,234,319)(190,278,235,330)(191,274,236,326)(192,285,237,322)(193,281,238,318)(194,277,239,329)(195,273,240,325)(196,297,241,343)(197,293,242,339)(198,289,243,335)(199,300,244,331)(200,296,245,342)(201,292,246,338)(202,288,247,334)(203,299,248,345)(204,295,249,341)(205,291,250,337)(206,287,251,333)(207,298,252,344)(208,294,253,340)(209,290,254,336)(210,286,255,332)(211,302,269,347)(212,313,270,358)(213,309,256,354)(214,305,257,350)(215,301,258,346)(216,312,259,357)(217,308,260,353)(218,304,261,349)(219,315,262,360)(220,311,263,356)(221,307,264,352)(222,303,265,348)(223,314,266,359)(224,310,267,355)(225,306,268,351)>;
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), (1,263,69,194,31,254,50,220,16,239,84,209)(2,267,70,183,32,243,51,224,17,228,85,198)(3,256,71,187,33,247,52,213,18,232,86,202)(4,260,72,191,34,251,53,217,19,236,87,206)(5,264,73,195,35,255,54,221,20,240,88,210)(6,268,74,184,36,244,55,225,21,229,89,199)(7,257,75,188,37,248,56,214,22,233,90,203)(8,261,61,192,38,252,57,218,23,237,76,207)(9,265,62,181,39,241,58,222,24,226,77,196)(10,269,63,185,40,245,59,211,25,230,78,200)(11,258,64,189,41,249,60,215,26,234,79,204)(12,262,65,193,42,253,46,219,27,238,80,208)(13,266,66,182,43,242,47,223,28,227,81,197)(14,270,67,186,44,246,48,212,29,231,82,201)(15,259,68,190,45,250,49,216,30,235,83,205)(91,336,177,277,114,356,145,290,125,329,162,311)(92,340,178,281,115,360,146,294,126,318,163,315)(93,344,179,285,116,349,147,298,127,322,164,304)(94,333,180,274,117,353,148,287,128,326,165,308)(95,337,166,278,118,357,149,291,129,330,151,312)(96,341,167,282,119,346,150,295,130,319,152,301)(97,345,168,271,120,350,136,299,131,323,153,305)(98,334,169,275,106,354,137,288,132,327,154,309)(99,338,170,279,107,358,138,292,133,316,155,313)(100,342,171,283,108,347,139,296,134,320,156,302)(101,331,172,272,109,351,140,300,135,324,157,306)(102,335,173,276,110,355,141,289,121,328,158,310)(103,339,174,280,111,359,142,293,122,317,159,314)(104,343,175,284,112,348,143,297,123,321,160,303)(105,332,176,273,113,352,144,286,124,325,161,307), (1,145,50,91)(2,141,51,102)(3,137,52,98)(4,148,53,94)(5,144,54,105)(6,140,55,101)(7,136,56,97)(8,147,57,93)(9,143,58,104)(10,139,59,100)(11,150,60,96)(12,146,46,92)(13,142,47,103)(14,138,48,99)(15,149,49,95)(16,162,69,114)(17,158,70,110)(18,154,71,106)(19,165,72,117)(20,161,73,113)(21,157,74,109)(22,153,75,120)(23,164,61,116)(24,160,62,112)(25,156,63,108)(26,152,64,119)(27,163,65,115)(28,159,66,111)(29,155,67,107)(30,151,68,118)(31,177,84,125)(32,173,85,121)(33,169,86,132)(34,180,87,128)(35,176,88,124)(36,172,89,135)(37,168,90,131)(38,179,76,127)(39,175,77,123)(40,171,78,134)(41,167,79,130)(42,178,80,126)(43,174,81,122)(44,170,82,133)(45,166,83,129)(181,284,226,321)(182,280,227,317)(183,276,228,328)(184,272,229,324)(185,283,230,320)(186,279,231,316)(187,275,232,327)(188,271,233,323)(189,282,234,319)(190,278,235,330)(191,274,236,326)(192,285,237,322)(193,281,238,318)(194,277,239,329)(195,273,240,325)(196,297,241,343)(197,293,242,339)(198,289,243,335)(199,300,244,331)(200,296,245,342)(201,292,246,338)(202,288,247,334)(203,299,248,345)(204,295,249,341)(205,291,250,337)(206,287,251,333)(207,298,252,344)(208,294,253,340)(209,290,254,336)(210,286,255,332)(211,302,269,347)(212,313,270,358)(213,309,256,354)(214,305,257,350)(215,301,258,346)(216,312,259,357)(217,308,260,353)(218,304,261,349)(219,315,262,360)(220,311,263,356)(221,307,264,352)(222,303,265,348)(223,314,266,359)(224,310,267,355)(225,306,268,351) );
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)], [(1,263,69,194,31,254,50,220,16,239,84,209),(2,267,70,183,32,243,51,224,17,228,85,198),(3,256,71,187,33,247,52,213,18,232,86,202),(4,260,72,191,34,251,53,217,19,236,87,206),(5,264,73,195,35,255,54,221,20,240,88,210),(6,268,74,184,36,244,55,225,21,229,89,199),(7,257,75,188,37,248,56,214,22,233,90,203),(8,261,61,192,38,252,57,218,23,237,76,207),(9,265,62,181,39,241,58,222,24,226,77,196),(10,269,63,185,40,245,59,211,25,230,78,200),(11,258,64,189,41,249,60,215,26,234,79,204),(12,262,65,193,42,253,46,219,27,238,80,208),(13,266,66,182,43,242,47,223,28,227,81,197),(14,270,67,186,44,246,48,212,29,231,82,201),(15,259,68,190,45,250,49,216,30,235,83,205),(91,336,177,277,114,356,145,290,125,329,162,311),(92,340,178,281,115,360,146,294,126,318,163,315),(93,344,179,285,116,349,147,298,127,322,164,304),(94,333,180,274,117,353,148,287,128,326,165,308),(95,337,166,278,118,357,149,291,129,330,151,312),(96,341,167,282,119,346,150,295,130,319,152,301),(97,345,168,271,120,350,136,299,131,323,153,305),(98,334,169,275,106,354,137,288,132,327,154,309),(99,338,170,279,107,358,138,292,133,316,155,313),(100,342,171,283,108,347,139,296,134,320,156,302),(101,331,172,272,109,351,140,300,135,324,157,306),(102,335,173,276,110,355,141,289,121,328,158,310),(103,339,174,280,111,359,142,293,122,317,159,314),(104,343,175,284,112,348,143,297,123,321,160,303),(105,332,176,273,113,352,144,286,124,325,161,307)], [(1,145,50,91),(2,141,51,102),(3,137,52,98),(4,148,53,94),(5,144,54,105),(6,140,55,101),(7,136,56,97),(8,147,57,93),(9,143,58,104),(10,139,59,100),(11,150,60,96),(12,146,46,92),(13,142,47,103),(14,138,48,99),(15,149,49,95),(16,162,69,114),(17,158,70,110),(18,154,71,106),(19,165,72,117),(20,161,73,113),(21,157,74,109),(22,153,75,120),(23,164,61,116),(24,160,62,112),(25,156,63,108),(26,152,64,119),(27,163,65,115),(28,159,66,111),(29,155,67,107),(30,151,68,118),(31,177,84,125),(32,173,85,121),(33,169,86,132),(34,180,87,128),(35,176,88,124),(36,172,89,135),(37,168,90,131),(38,179,76,127),(39,175,77,123),(40,171,78,134),(41,167,79,130),(42,178,80,126),(43,174,81,122),(44,170,82,133),(45,166,83,129),(181,284,226,321),(182,280,227,317),(183,276,228,328),(184,272,229,324),(185,283,230,320),(186,279,231,316),(187,275,232,327),(188,271,233,323),(189,282,234,319),(190,278,235,330),(191,274,236,326),(192,285,237,322),(193,281,238,318),(194,277,239,329),(195,273,240,325),(196,297,241,343),(197,293,242,339),(198,289,243,335),(199,300,244,331),(200,296,245,342),(201,292,246,338),(202,288,247,334),(203,299,248,345),(204,295,249,341),(205,291,250,337),(206,287,251,333),(207,298,252,344),(208,294,253,340),(209,290,254,336),(210,286,255,332),(211,302,269,347),(212,313,270,358),(213,309,256,354),(214,305,257,350),(215,301,258,346),(216,312,259,357),(217,308,260,353),(218,304,261,349),(219,315,262,360),(220,311,263,356),(221,307,264,352),(222,303,265,348),(223,314,266,359),(224,310,267,355),(225,306,268,351)]])
45 conjugacy classes
| class | 1 | 2 | 3A | 3B | 3C | 3D | 4A | 4B | 4C | 5A | 5B | 6A | 6B | 6C | 6D | 10A | 10B | 12A | ··· | 12H | 15A | ··· | 15H | 20A | 20B | 20C | 20D | 30A | ··· | 30H |
| order | 1 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 10 | 10 | 12 | ··· | 12 | 15 | ··· | 15 | 20 | 20 | 20 | 20 | 30 | ··· | 30 |
| size | 1 | 1 | 2 | 2 | 2 | 2 | 10 | 18 | 90 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 10 | ··· | 10 | 4 | ··· | 4 | 18 | 18 | 18 | 18 | 4 | ··· | 4 |
45 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | - | + | + | + | - | - | + | - |
| image | C1 | C2 | C2 | C2 | S3 | Q8 | D5 | D6 | D10 | Dic6 | Dic10 | S3×D5 | C15⋊Q8 |
| kernel | C15⋊Dic6 | C32×Dic5 | C5×C3⋊Dic3 | C3⋊Dic15 | C3×Dic5 | C3×C15 | C3⋊Dic3 | C30 | C3×C6 | C15 | C32 | C6 | C3 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 2 | 4 | 2 | 8 | 4 | 8 | 8 |
Matrix representation of C15⋊Dic6 ►in GL6(𝔽61)
| 13 | 0 | 0 | 0 | 0 | 0 |
| 12 | 47 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 0 | 0 | 0 |
| 0 | 0 | 59 | 47 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 17 |
| 0 | 0 | 0 | 0 | 44 | 44 |
| 21 | 0 | 0 | 0 | 0 | 0 |
| 29 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 45 | 14 |
| 0 | 0 | 0 | 0 | 47 | 16 |
| 27 | 46 | 0 | 0 | 0 | 0 |
| 8 | 34 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 37 | 0 | 0 |
| 0 | 0 | 1 | 56 | 0 | 0 |
| 0 | 0 | 0 | 0 | 29 | 54 |
| 0 | 0 | 0 | 0 | 7 | 32 |
G:=sub<GL(6,GF(61))| [13,12,0,0,0,0,0,47,0,0,0,0,0,0,13,59,0,0,0,0,0,47,0,0,0,0,0,0,60,44,0,0,0,0,17,44],[21,29,0,0,0,0,0,32,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,45,47,0,0,0,0,14,16],[27,8,0,0,0,0,46,34,0,0,0,0,0,0,5,1,0,0,0,0,37,56,0,0,0,0,0,0,29,7,0,0,0,0,54,32] >;
C15⋊Dic6 in GAP, Magma, Sage, TeX
C_{15}\rtimes {\rm Dic}_6 % in TeX
G:=Group("C15:Dic6"); // GroupNames label
G:=SmallGroup(360,71);
// by ID
G=gap.SmallGroup(360,71);
# by ID
G:=PCGroup([6,-2,-2,-2,-3,-3,-5,24,73,31,201,730,10373]);
// Polycyclic
G:=Group<a,b,c|a^15=b^12=1,c^2=b^6,b*a*b^-1=a^4,c*a*c^-1=a^11,c*b*c^-1=b^-1>;
// generators/relations