Copied to
clipboard

G = C60.S3order 360 = 23·32·5

6th non-split extension by C60 of S3 acting via S3/C3=C2

metabelian, supersoluble, monomial, A-group

Aliases: C60.6S3, C12.6D15, C30.7Dic3, C6.3Dic15, C153(C3⋊C8), C3⋊(C153C8), (C3×C15)⋊10C8, (C3×C30).7C4, (C3×C60).3C2, (C3×C12).4D5, C20.2(C3⋊S3), C4.2(C3⋊D15), C324(C52C8), C52(C324C8), C2.(C3⋊Dic15), (C3×C6).3Dic5, C10.2(C3⋊Dic3), SmallGroup(360,37)

Series: Derived Chief Lower central Upper central

C1C3×C15 — C60.S3
C1C5C15C3×C15C3×C30C3×C60 — C60.S3
C3×C15 — C60.S3
C1C4

Generators and relations for C60.S3
 G = < a,b,c | a60=b3=1, c2=a45, ab=ba, cac-1=a29, cbc-1=b-1 >

45C8
15C3⋊C8
15C3⋊C8
15C3⋊C8
15C3⋊C8
9C52C8
5C324C8
3C153C8
3C153C8
3C153C8
3C153C8

Smallest permutation representation of C60.S3
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)
(1 177 88)(2 178 89)(3 179 90)(4 180 91)(5 121 92)(6 122 93)(7 123 94)(8 124 95)(9 125 96)(10 126 97)(11 127 98)(12 128 99)(13 129 100)(14 130 101)(15 131 102)(16 132 103)(17 133 104)(18 134 105)(19 135 106)(20 136 107)(21 137 108)(22 138 109)(23 139 110)(24 140 111)(25 141 112)(26 142 113)(27 143 114)(28 144 115)(29 145 116)(30 146 117)(31 147 118)(32 148 119)(33 149 120)(34 150 61)(35 151 62)(36 152 63)(37 153 64)(38 154 65)(39 155 66)(40 156 67)(41 157 68)(42 158 69)(43 159 70)(44 160 71)(45 161 72)(46 162 73)(47 163 74)(48 164 75)(49 165 76)(50 166 77)(51 167 78)(52 168 79)(53 169 80)(54 170 81)(55 171 82)(56 172 83)(57 173 84)(58 174 85)(59 175 86)(60 176 87)(181 256 359)(182 257 360)(183 258 301)(184 259 302)(185 260 303)(186 261 304)(187 262 305)(188 263 306)(189 264 307)(190 265 308)(191 266 309)(192 267 310)(193 268 311)(194 269 312)(195 270 313)(196 271 314)(197 272 315)(198 273 316)(199 274 317)(200 275 318)(201 276 319)(202 277 320)(203 278 321)(204 279 322)(205 280 323)(206 281 324)(207 282 325)(208 283 326)(209 284 327)(210 285 328)(211 286 329)(212 287 330)(213 288 331)(214 289 332)(215 290 333)(216 291 334)(217 292 335)(218 293 336)(219 294 337)(220 295 338)(221 296 339)(222 297 340)(223 298 341)(224 299 342)(225 300 343)(226 241 344)(227 242 345)(228 243 346)(229 244 347)(230 245 348)(231 246 349)(232 247 350)(233 248 351)(234 249 352)(235 250 353)(236 251 354)(237 252 355)(238 253 356)(239 254 357)(240 255 358)
(1 269 46 254 31 299 16 284)(2 298 47 283 32 268 17 253)(3 267 48 252 33 297 18 282)(4 296 49 281 34 266 19 251)(5 265 50 250 35 295 20 280)(6 294 51 279 36 264 21 249)(7 263 52 248 37 293 22 278)(8 292 53 277 38 262 23 247)(9 261 54 246 39 291 24 276)(10 290 55 275 40 260 25 245)(11 259 56 244 41 289 26 274)(12 288 57 273 42 258 27 243)(13 257 58 242 43 287 28 272)(14 286 59 271 44 256 29 241)(15 255 60 300 45 285 30 270)(61 309 106 354 91 339 76 324)(62 338 107 323 92 308 77 353)(63 307 108 352 93 337 78 322)(64 336 109 321 94 306 79 351)(65 305 110 350 95 335 80 320)(66 334 111 319 96 304 81 349)(67 303 112 348 97 333 82 318)(68 332 113 317 98 302 83 347)(69 301 114 346 99 331 84 316)(70 330 115 315 100 360 85 345)(71 359 116 344 101 329 86 314)(72 328 117 313 102 358 87 343)(73 357 118 342 103 327 88 312)(74 326 119 311 104 356 89 341)(75 355 120 340 105 325 90 310)(121 190 166 235 151 220 136 205)(122 219 167 204 152 189 137 234)(123 188 168 233 153 218 138 203)(124 217 169 202 154 187 139 232)(125 186 170 231 155 216 140 201)(126 215 171 200 156 185 141 230)(127 184 172 229 157 214 142 199)(128 213 173 198 158 183 143 228)(129 182 174 227 159 212 144 197)(130 211 175 196 160 181 145 226)(131 240 176 225 161 210 146 195)(132 209 177 194 162 239 147 224)(133 238 178 223 163 208 148 193)(134 207 179 192 164 237 149 222)(135 236 180 221 165 206 150 191)

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

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

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

96 conjugacy classes

class 1  2 3A3B3C3D4A4B5A5B6A6B6C6D8A8B8C8D10A10B12A···12H15A···15P20A20B20C20D30A···30P60A···60AF
order123333445566668888101012···1215···152020202030···3060···60
size1122221122222245454545222···22···222222···22···2

96 irreducible representations

dim1111222222222
type++++--+-
imageC1C2C4C8S3D5Dic3Dic5C3⋊C8D15C52C8Dic15C153C8
kernelC60.S3C3×C60C3×C30C3×C15C60C3×C12C30C3×C6C15C12C32C6C3
# reps1124424281641632

Matrix representation of C60.S3 in GL5(𝔽241)

1770000
018918900
052100
00017316
00022564
,
10000
01773000
02116300
00063211
00030177
,
2110000
02216300
01392000
000163169
00012878

G:=sub<GL(5,GF(241))| [177,0,0,0,0,0,189,52,0,0,0,189,1,0,0,0,0,0,173,225,0,0,0,16,64],[1,0,0,0,0,0,177,211,0,0,0,30,63,0,0,0,0,0,63,30,0,0,0,211,177],[211,0,0,0,0,0,221,139,0,0,0,63,20,0,0,0,0,0,163,128,0,0,0,169,78] >;

C60.S3 in GAP, Magma, Sage, TeX

C_{60}.S_3
% in TeX

G:=Group("C60.S3");
// GroupNames label

G:=SmallGroup(360,37);
// by ID

G=gap.SmallGroup(360,37);
# by ID

G:=PCGroup([6,-2,-2,-2,-3,-3,-5,12,31,387,1444,10373]);
// Polycyclic

G:=Group<a,b,c|a^60=b^3=1,c^2=a^45,a*b=b*a,c*a*c^-1=a^29,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C60.S3 in TeX

׿
×
𝔽