direct product, abelian, monomial, 5-elementary
Aliases: C52×C15, SmallGroup(375,7)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C52×C15 |
| C1 — C52×C15 |
| C1 — C52×C15 |
Generators and relations for C52×C15
G = < a,b,c | a5=b5=c15=1, ab=ba, ac=ca, bc=cb >
Subgroups: 128, all normal (4 characteristic)
C1, C3, C5, C15, C52, C5×C15, C53, C52×C15
Quotients: C1, C3, C5, C15, C52, C5×C15, C53, C52×C15
►Regular action on 375 points
Generators in S375
(1 328 194 235 170)(2 329 195 236 171)(3 330 181 237 172)(4 316 182 238 173)(5 317 183 239 174)(6 318 184 240 175)(7 319 185 226 176)(8 320 186 227 177)(9 321 187 228 178)(10 322 188 229 179)(11 323 189 230 180)(12 324 190 231 166)(13 325 191 232 167)(14 326 192 233 168)(15 327 193 234 169)(16 216 151 84 336)(17 217 152 85 337)(18 218 153 86 338)(19 219 154 87 339)(20 220 155 88 340)(21 221 156 89 341)(22 222 157 90 342)(23 223 158 76 343)(24 224 159 77 344)(25 225 160 78 345)(26 211 161 79 331)(27 212 162 80 332)(28 213 163 81 333)(29 214 164 82 334)(30 215 165 83 335)(31 360 202 141 134)(32 346 203 142 135)(33 347 204 143 121)(34 348 205 144 122)(35 349 206 145 123)(36 350 207 146 124)(37 351 208 147 125)(38 352 209 148 126)(39 353 210 149 127)(40 354 196 150 128)(41 355 197 136 129)(42 356 198 137 130)(43 357 199 138 131)(44 358 200 139 132)(45 359 201 140 133)(46 314 260 285 109)(47 315 261 271 110)(48 301 262 272 111)(49 302 263 273 112)(50 303 264 274 113)(51 304 265 275 114)(52 305 266 276 115)(53 306 267 277 116)(54 307 268 278 117)(55 308 269 279 118)(56 309 270 280 119)(57 310 256 281 120)(58 311 257 282 106)(59 312 258 283 107)(60 313 259 284 108)(61 246 370 95 298)(62 247 371 96 299)(63 248 372 97 300)(64 249 373 98 286)(65 250 374 99 287)(66 251 375 100 288)(67 252 361 101 289)(68 253 362 102 290)(69 254 363 103 291)(70 255 364 104 292)(71 241 365 105 293)(72 242 366 91 294)(73 243 367 92 295)(74 244 368 93 296)(75 245 369 94 297)
(1 21 312 361 124)(2 22 313 362 125)(3 23 314 363 126)(4 24 315 364 127)(5 25 301 365 128)(6 26 302 366 129)(7 27 303 367 130)(8 28 304 368 131)(9 29 305 369 132)(10 30 306 370 133)(11 16 307 371 134)(12 17 308 372 135)(13 18 309 373 121)(14 19 310 374 122)(15 20 311 375 123)(31 323 216 268 96)(32 324 217 269 97)(33 325 218 270 98)(34 326 219 256 99)(35 327 220 257 100)(36 328 221 258 101)(37 329 222 259 102)(38 330 223 260 103)(39 316 224 261 104)(40 317 225 262 105)(41 318 211 263 91)(42 319 212 264 92)(43 320 213 265 93)(44 321 214 266 94)(45 322 215 267 95)(46 254 148 172 343)(47 255 149 173 344)(48 241 150 174 345)(49 242 136 175 331)(50 243 137 176 332)(51 244 138 177 333)(52 245 139 178 334)(53 246 140 179 335)(54 247 141 180 336)(55 248 142 166 337)(56 249 143 167 338)(57 250 144 168 339)(58 251 145 169 340)(59 252 146 170 341)(60 253 147 171 342)(61 201 229 83 116)(62 202 230 84 117)(63 203 231 85 118)(64 204 232 86 119)(65 205 233 87 120)(66 206 234 88 106)(67 207 235 89 107)(68 208 236 90 108)(69 209 237 76 109)(70 210 238 77 110)(71 196 239 78 111)(72 197 240 79 112)(73 198 226 80 113)(74 199 227 81 114)(75 200 228 82 115)(151 278 299 360 189)(152 279 300 346 190)(153 280 286 347 191)(154 281 287 348 192)(155 282 288 349 193)(156 283 289 350 194)(157 284 290 351 195)(158 285 291 352 181)(159 271 292 353 182)(160 272 293 354 183)(161 273 294 355 184)(162 274 295 356 185)(163 275 296 357 186)(164 276 297 358 187)(165 277 298 359 188)
(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)(361 362 363 364 365 366 367 368 369 370 371 372 373 374 375)
G:=sub<Sym(375)| (1,328,194,235,170)(2,329,195,236,171)(3,330,181,237,172)(4,316,182,238,173)(5,317,183,239,174)(6,318,184,240,175)(7,319,185,226,176)(8,320,186,227,177)(9,321,187,228,178)(10,322,188,229,179)(11,323,189,230,180)(12,324,190,231,166)(13,325,191,232,167)(14,326,192,233,168)(15,327,193,234,169)(16,216,151,84,336)(17,217,152,85,337)(18,218,153,86,338)(19,219,154,87,339)(20,220,155,88,340)(21,221,156,89,341)(22,222,157,90,342)(23,223,158,76,343)(24,224,159,77,344)(25,225,160,78,345)(26,211,161,79,331)(27,212,162,80,332)(28,213,163,81,333)(29,214,164,82,334)(30,215,165,83,335)(31,360,202,141,134)(32,346,203,142,135)(33,347,204,143,121)(34,348,205,144,122)(35,349,206,145,123)(36,350,207,146,124)(37,351,208,147,125)(38,352,209,148,126)(39,353,210,149,127)(40,354,196,150,128)(41,355,197,136,129)(42,356,198,137,130)(43,357,199,138,131)(44,358,200,139,132)(45,359,201,140,133)(46,314,260,285,109)(47,315,261,271,110)(48,301,262,272,111)(49,302,263,273,112)(50,303,264,274,113)(51,304,265,275,114)(52,305,266,276,115)(53,306,267,277,116)(54,307,268,278,117)(55,308,269,279,118)(56,309,270,280,119)(57,310,256,281,120)(58,311,257,282,106)(59,312,258,283,107)(60,313,259,284,108)(61,246,370,95,298)(62,247,371,96,299)(63,248,372,97,300)(64,249,373,98,286)(65,250,374,99,287)(66,251,375,100,288)(67,252,361,101,289)(68,253,362,102,290)(69,254,363,103,291)(70,255,364,104,292)(71,241,365,105,293)(72,242,366,91,294)(73,243,367,92,295)(74,244,368,93,296)(75,245,369,94,297), (1,21,312,361,124)(2,22,313,362,125)(3,23,314,363,126)(4,24,315,364,127)(5,25,301,365,128)(6,26,302,366,129)(7,27,303,367,130)(8,28,304,368,131)(9,29,305,369,132)(10,30,306,370,133)(11,16,307,371,134)(12,17,308,372,135)(13,18,309,373,121)(14,19,310,374,122)(15,20,311,375,123)(31,323,216,268,96)(32,324,217,269,97)(33,325,218,270,98)(34,326,219,256,99)(35,327,220,257,100)(36,328,221,258,101)(37,329,222,259,102)(38,330,223,260,103)(39,316,224,261,104)(40,317,225,262,105)(41,318,211,263,91)(42,319,212,264,92)(43,320,213,265,93)(44,321,214,266,94)(45,322,215,267,95)(46,254,148,172,343)(47,255,149,173,344)(48,241,150,174,345)(49,242,136,175,331)(50,243,137,176,332)(51,244,138,177,333)(52,245,139,178,334)(53,246,140,179,335)(54,247,141,180,336)(55,248,142,166,337)(56,249,143,167,338)(57,250,144,168,339)(58,251,145,169,340)(59,252,146,170,341)(60,253,147,171,342)(61,201,229,83,116)(62,202,230,84,117)(63,203,231,85,118)(64,204,232,86,119)(65,205,233,87,120)(66,206,234,88,106)(67,207,235,89,107)(68,208,236,90,108)(69,209,237,76,109)(70,210,238,77,110)(71,196,239,78,111)(72,197,240,79,112)(73,198,226,80,113)(74,199,227,81,114)(75,200,228,82,115)(151,278,299,360,189)(152,279,300,346,190)(153,280,286,347,191)(154,281,287,348,192)(155,282,288,349,193)(156,283,289,350,194)(157,284,290,351,195)(158,285,291,352,181)(159,271,292,353,182)(160,272,293,354,183)(161,273,294,355,184)(162,274,295,356,185)(163,275,296,357,186)(164,276,297,358,187)(165,277,298,359,188), (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)(361,362,363,364,365,366,367,368,369,370,371,372,373,374,375)>;
G:=Group( (1,328,194,235,170)(2,329,195,236,171)(3,330,181,237,172)(4,316,182,238,173)(5,317,183,239,174)(6,318,184,240,175)(7,319,185,226,176)(8,320,186,227,177)(9,321,187,228,178)(10,322,188,229,179)(11,323,189,230,180)(12,324,190,231,166)(13,325,191,232,167)(14,326,192,233,168)(15,327,193,234,169)(16,216,151,84,336)(17,217,152,85,337)(18,218,153,86,338)(19,219,154,87,339)(20,220,155,88,340)(21,221,156,89,341)(22,222,157,90,342)(23,223,158,76,343)(24,224,159,77,344)(25,225,160,78,345)(26,211,161,79,331)(27,212,162,80,332)(28,213,163,81,333)(29,214,164,82,334)(30,215,165,83,335)(31,360,202,141,134)(32,346,203,142,135)(33,347,204,143,121)(34,348,205,144,122)(35,349,206,145,123)(36,350,207,146,124)(37,351,208,147,125)(38,352,209,148,126)(39,353,210,149,127)(40,354,196,150,128)(41,355,197,136,129)(42,356,198,137,130)(43,357,199,138,131)(44,358,200,139,132)(45,359,201,140,133)(46,314,260,285,109)(47,315,261,271,110)(48,301,262,272,111)(49,302,263,273,112)(50,303,264,274,113)(51,304,265,275,114)(52,305,266,276,115)(53,306,267,277,116)(54,307,268,278,117)(55,308,269,279,118)(56,309,270,280,119)(57,310,256,281,120)(58,311,257,282,106)(59,312,258,283,107)(60,313,259,284,108)(61,246,370,95,298)(62,247,371,96,299)(63,248,372,97,300)(64,249,373,98,286)(65,250,374,99,287)(66,251,375,100,288)(67,252,361,101,289)(68,253,362,102,290)(69,254,363,103,291)(70,255,364,104,292)(71,241,365,105,293)(72,242,366,91,294)(73,243,367,92,295)(74,244,368,93,296)(75,245,369,94,297), (1,21,312,361,124)(2,22,313,362,125)(3,23,314,363,126)(4,24,315,364,127)(5,25,301,365,128)(6,26,302,366,129)(7,27,303,367,130)(8,28,304,368,131)(9,29,305,369,132)(10,30,306,370,133)(11,16,307,371,134)(12,17,308,372,135)(13,18,309,373,121)(14,19,310,374,122)(15,20,311,375,123)(31,323,216,268,96)(32,324,217,269,97)(33,325,218,270,98)(34,326,219,256,99)(35,327,220,257,100)(36,328,221,258,101)(37,329,222,259,102)(38,330,223,260,103)(39,316,224,261,104)(40,317,225,262,105)(41,318,211,263,91)(42,319,212,264,92)(43,320,213,265,93)(44,321,214,266,94)(45,322,215,267,95)(46,254,148,172,343)(47,255,149,173,344)(48,241,150,174,345)(49,242,136,175,331)(50,243,137,176,332)(51,244,138,177,333)(52,245,139,178,334)(53,246,140,179,335)(54,247,141,180,336)(55,248,142,166,337)(56,249,143,167,338)(57,250,144,168,339)(58,251,145,169,340)(59,252,146,170,341)(60,253,147,171,342)(61,201,229,83,116)(62,202,230,84,117)(63,203,231,85,118)(64,204,232,86,119)(65,205,233,87,120)(66,206,234,88,106)(67,207,235,89,107)(68,208,236,90,108)(69,209,237,76,109)(70,210,238,77,110)(71,196,239,78,111)(72,197,240,79,112)(73,198,226,80,113)(74,199,227,81,114)(75,200,228,82,115)(151,278,299,360,189)(152,279,300,346,190)(153,280,286,347,191)(154,281,287,348,192)(155,282,288,349,193)(156,283,289,350,194)(157,284,290,351,195)(158,285,291,352,181)(159,271,292,353,182)(160,272,293,354,183)(161,273,294,355,184)(162,274,295,356,185)(163,275,296,357,186)(164,276,297,358,187)(165,277,298,359,188), (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)(361,362,363,364,365,366,367,368,369,370,371,372,373,374,375) );
G=PermutationGroup([[(1,328,194,235,170),(2,329,195,236,171),(3,330,181,237,172),(4,316,182,238,173),(5,317,183,239,174),(6,318,184,240,175),(7,319,185,226,176),(8,320,186,227,177),(9,321,187,228,178),(10,322,188,229,179),(11,323,189,230,180),(12,324,190,231,166),(13,325,191,232,167),(14,326,192,233,168),(15,327,193,234,169),(16,216,151,84,336),(17,217,152,85,337),(18,218,153,86,338),(19,219,154,87,339),(20,220,155,88,340),(21,221,156,89,341),(22,222,157,90,342),(23,223,158,76,343),(24,224,159,77,344),(25,225,160,78,345),(26,211,161,79,331),(27,212,162,80,332),(28,213,163,81,333),(29,214,164,82,334),(30,215,165,83,335),(31,360,202,141,134),(32,346,203,142,135),(33,347,204,143,121),(34,348,205,144,122),(35,349,206,145,123),(36,350,207,146,124),(37,351,208,147,125),(38,352,209,148,126),(39,353,210,149,127),(40,354,196,150,128),(41,355,197,136,129),(42,356,198,137,130),(43,357,199,138,131),(44,358,200,139,132),(45,359,201,140,133),(46,314,260,285,109),(47,315,261,271,110),(48,301,262,272,111),(49,302,263,273,112),(50,303,264,274,113),(51,304,265,275,114),(52,305,266,276,115),(53,306,267,277,116),(54,307,268,278,117),(55,308,269,279,118),(56,309,270,280,119),(57,310,256,281,120),(58,311,257,282,106),(59,312,258,283,107),(60,313,259,284,108),(61,246,370,95,298),(62,247,371,96,299),(63,248,372,97,300),(64,249,373,98,286),(65,250,374,99,287),(66,251,375,100,288),(67,252,361,101,289),(68,253,362,102,290),(69,254,363,103,291),(70,255,364,104,292),(71,241,365,105,293),(72,242,366,91,294),(73,243,367,92,295),(74,244,368,93,296),(75,245,369,94,297)], [(1,21,312,361,124),(2,22,313,362,125),(3,23,314,363,126),(4,24,315,364,127),(5,25,301,365,128),(6,26,302,366,129),(7,27,303,367,130),(8,28,304,368,131),(9,29,305,369,132),(10,30,306,370,133),(11,16,307,371,134),(12,17,308,372,135),(13,18,309,373,121),(14,19,310,374,122),(15,20,311,375,123),(31,323,216,268,96),(32,324,217,269,97),(33,325,218,270,98),(34,326,219,256,99),(35,327,220,257,100),(36,328,221,258,101),(37,329,222,259,102),(38,330,223,260,103),(39,316,224,261,104),(40,317,225,262,105),(41,318,211,263,91),(42,319,212,264,92),(43,320,213,265,93),(44,321,214,266,94),(45,322,215,267,95),(46,254,148,172,343),(47,255,149,173,344),(48,241,150,174,345),(49,242,136,175,331),(50,243,137,176,332),(51,244,138,177,333),(52,245,139,178,334),(53,246,140,179,335),(54,247,141,180,336),(55,248,142,166,337),(56,249,143,167,338),(57,250,144,168,339),(58,251,145,169,340),(59,252,146,170,341),(60,253,147,171,342),(61,201,229,83,116),(62,202,230,84,117),(63,203,231,85,118),(64,204,232,86,119),(65,205,233,87,120),(66,206,234,88,106),(67,207,235,89,107),(68,208,236,90,108),(69,209,237,76,109),(70,210,238,77,110),(71,196,239,78,111),(72,197,240,79,112),(73,198,226,80,113),(74,199,227,81,114),(75,200,228,82,115),(151,278,299,360,189),(152,279,300,346,190),(153,280,286,347,191),(154,281,287,348,192),(155,282,288,349,193),(156,283,289,350,194),(157,284,290,351,195),(158,285,291,352,181),(159,271,292,353,182),(160,272,293,354,183),(161,273,294,355,184),(162,274,295,356,185),(163,275,296,357,186),(164,276,297,358,187),(165,277,298,359,188)], [(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),(361,362,363,364,365,366,367,368,369,370,371,372,373,374,375)]])
375 conjugacy classes
| class | 1 | 3A | 3B | 5A | ··· | 5DT | 15A | ··· | 15IN |
| order | 1 | 3 | 3 | 5 | ··· | 5 | 15 | ··· | 15 |
| size | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
375 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C3 | C5 | C15 |
| kernel | C52×C15 | C53 | C5×C15 | C52 |
| # reps | 1 | 2 | 124 | 248 |
Matrix representation of C52×C15 ►in GL3(𝔽31) generated by
| 1 | 0 | 0 |
| 0 | 16 | 0 |
| 0 | 0 | 4 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 4 |
| 16 | 0 | 0 |
| 0 | 16 | 0 |
| 0 | 0 | 9 |
G:=sub<GL(3,GF(31))| [1,0,0,0,16,0,0,0,4],[1,0,0,0,1,0,0,0,4],[16,0,0,0,16,0,0,0,9] >;
C52×C15 in GAP, Magma, Sage, TeX
C_5^2\times C_{15} % in TeX
G:=Group("C5^2xC15"); // GroupNames label
G:=SmallGroup(375,7);
// by ID
G=gap.SmallGroup(375,7);
# by ID
G:=PCGroup([4,-3,-5,-5,-5]);
// Polycyclic
G:=Group<a,b,c|a^5=b^5=c^15=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations