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G = C52×C15order 375 = 3·53

Abelian group of type [5,5,15]

direct product, abelian, monomial, 5-elementary

Aliases: C52×C15, SmallGroup(375,7)

Series: Derived Chief Lower central Upper central

C1 — C52×C15
C1C5C52C53 — 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 [×31], C15 [×31], C52 [×31], C5×C15 [×31], C53, C52×C15
Quotients: C1, C3, C5 [×31], C15 [×31], C52 [×31], C5×C15 [×31], C53, C52×C15

Smallest permutation representation of C52×C15
Regular action on 375 points
Generators in S375
(1 236 339 182 80)(2 237 340 183 81)(3 238 341 184 82)(4 239 342 185 83)(5 240 343 186 84)(6 226 344 187 85)(7 227 345 188 86)(8 228 331 189 87)(9 229 332 190 88)(10 230 333 191 89)(11 231 334 192 90)(12 232 335 193 76)(13 233 336 194 77)(14 234 337 195 78)(15 235 338 181 79)(16 112 174 52 254)(17 113 175 53 255)(18 114 176 54 241)(19 115 177 55 242)(20 116 178 56 243)(21 117 179 57 244)(22 118 180 58 245)(23 119 166 59 246)(24 120 167 60 247)(25 106 168 46 248)(26 107 169 47 249)(27 108 170 48 250)(28 109 171 49 251)(29 110 172 50 252)(30 111 173 51 253)(31 197 352 299 123)(32 198 353 300 124)(33 199 354 286 125)(34 200 355 287 126)(35 201 356 288 127)(36 202 357 289 128)(37 203 358 290 129)(38 204 359 291 130)(39 205 360 292 131)(40 206 346 293 132)(41 207 347 294 133)(42 208 348 295 134)(43 209 349 296 135)(44 210 350 297 121)(45 196 351 298 122)(61 281 304 319 374)(62 282 305 320 375)(63 283 306 321 361)(64 284 307 322 362)(65 285 308 323 363)(66 271 309 324 364)(67 272 310 325 365)(68 273 311 326 366)(69 274 312 327 367)(70 275 313 328 368)(71 276 314 329 369)(72 277 315 330 370)(73 278 301 316 371)(74 279 302 317 372)(75 280 303 318 373)(91 216 158 264 138)(92 217 159 265 139)(93 218 160 266 140)(94 219 161 267 141)(95 220 162 268 142)(96 221 163 269 143)(97 222 164 270 144)(98 223 165 256 145)(99 224 151 257 146)(100 225 152 258 147)(101 211 153 259 148)(102 212 154 260 149)(103 213 155 261 150)(104 214 156 262 136)(105 215 157 263 137)
(1 45 24 145 371)(2 31 25 146 372)(3 32 26 147 373)(4 33 27 148 374)(5 34 28 149 375)(6 35 29 150 361)(7 36 30 136 362)(8 37 16 137 363)(9 38 17 138 364)(10 39 18 139 365)(11 40 19 140 366)(12 41 20 141 367)(13 42 21 142 368)(14 43 22 143 369)(15 44 23 144 370)(46 151 302 183 299)(47 152 303 184 300)(48 153 304 185 286)(49 154 305 186 287)(50 155 306 187 288)(51 156 307 188 289)(52 157 308 189 290)(53 158 309 190 291)(54 159 310 191 292)(55 160 311 192 293)(56 161 312 193 294)(57 162 313 194 295)(58 163 314 195 296)(59 164 315 181 297)(60 165 301 182 298)(61 239 199 108 101)(62 240 200 109 102)(63 226 201 110 103)(64 227 202 111 104)(65 228 203 112 105)(66 229 204 113 91)(67 230 205 114 92)(68 231 206 115 93)(69 232 207 116 94)(70 233 208 117 95)(71 234 209 118 96)(72 235 210 119 97)(73 236 196 120 98)(74 237 197 106 99)(75 238 198 107 100)(76 133 243 267 327)(77 134 244 268 328)(78 135 245 269 329)(79 121 246 270 330)(80 122 247 256 316)(81 123 248 257 317)(82 124 249 258 318)(83 125 250 259 319)(84 126 251 260 320)(85 127 252 261 321)(86 128 253 262 322)(87 129 254 263 323)(88 130 255 264 324)(89 131 241 265 325)(90 132 242 266 326)(166 222 277 338 350)(167 223 278 339 351)(168 224 279 340 352)(169 225 280 341 353)(170 211 281 342 354)(171 212 282 343 355)(172 213 283 344 356)(173 214 284 345 357)(174 215 285 331 358)(175 216 271 332 359)(176 217 272 333 360)(177 218 273 334 346)(178 219 274 335 347)(179 220 275 336 348)(180 221 276 337 349)
(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)| (1,236,339,182,80)(2,237,340,183,81)(3,238,341,184,82)(4,239,342,185,83)(5,240,343,186,84)(6,226,344,187,85)(7,227,345,188,86)(8,228,331,189,87)(9,229,332,190,88)(10,230,333,191,89)(11,231,334,192,90)(12,232,335,193,76)(13,233,336,194,77)(14,234,337,195,78)(15,235,338,181,79)(16,112,174,52,254)(17,113,175,53,255)(18,114,176,54,241)(19,115,177,55,242)(20,116,178,56,243)(21,117,179,57,244)(22,118,180,58,245)(23,119,166,59,246)(24,120,167,60,247)(25,106,168,46,248)(26,107,169,47,249)(27,108,170,48,250)(28,109,171,49,251)(29,110,172,50,252)(30,111,173,51,253)(31,197,352,299,123)(32,198,353,300,124)(33,199,354,286,125)(34,200,355,287,126)(35,201,356,288,127)(36,202,357,289,128)(37,203,358,290,129)(38,204,359,291,130)(39,205,360,292,131)(40,206,346,293,132)(41,207,347,294,133)(42,208,348,295,134)(43,209,349,296,135)(44,210,350,297,121)(45,196,351,298,122)(61,281,304,319,374)(62,282,305,320,375)(63,283,306,321,361)(64,284,307,322,362)(65,285,308,323,363)(66,271,309,324,364)(67,272,310,325,365)(68,273,311,326,366)(69,274,312,327,367)(70,275,313,328,368)(71,276,314,329,369)(72,277,315,330,370)(73,278,301,316,371)(74,279,302,317,372)(75,280,303,318,373)(91,216,158,264,138)(92,217,159,265,139)(93,218,160,266,140)(94,219,161,267,141)(95,220,162,268,142)(96,221,163,269,143)(97,222,164,270,144)(98,223,165,256,145)(99,224,151,257,146)(100,225,152,258,147)(101,211,153,259,148)(102,212,154,260,149)(103,213,155,261,150)(104,214,156,262,136)(105,215,157,263,137), (1,45,24,145,371)(2,31,25,146,372)(3,32,26,147,373)(4,33,27,148,374)(5,34,28,149,375)(6,35,29,150,361)(7,36,30,136,362)(8,37,16,137,363)(9,38,17,138,364)(10,39,18,139,365)(11,40,19,140,366)(12,41,20,141,367)(13,42,21,142,368)(14,43,22,143,369)(15,44,23,144,370)(46,151,302,183,299)(47,152,303,184,300)(48,153,304,185,286)(49,154,305,186,287)(50,155,306,187,288)(51,156,307,188,289)(52,157,308,189,290)(53,158,309,190,291)(54,159,310,191,292)(55,160,311,192,293)(56,161,312,193,294)(57,162,313,194,295)(58,163,314,195,296)(59,164,315,181,297)(60,165,301,182,298)(61,239,199,108,101)(62,240,200,109,102)(63,226,201,110,103)(64,227,202,111,104)(65,228,203,112,105)(66,229,204,113,91)(67,230,205,114,92)(68,231,206,115,93)(69,232,207,116,94)(70,233,208,117,95)(71,234,209,118,96)(72,235,210,119,97)(73,236,196,120,98)(74,237,197,106,99)(75,238,198,107,100)(76,133,243,267,327)(77,134,244,268,328)(78,135,245,269,329)(79,121,246,270,330)(80,122,247,256,316)(81,123,248,257,317)(82,124,249,258,318)(83,125,250,259,319)(84,126,251,260,320)(85,127,252,261,321)(86,128,253,262,322)(87,129,254,263,323)(88,130,255,264,324)(89,131,241,265,325)(90,132,242,266,326)(166,222,277,338,350)(167,223,278,339,351)(168,224,279,340,352)(169,225,280,341,353)(170,211,281,342,354)(171,212,282,343,355)(172,213,283,344,356)(173,214,284,345,357)(174,215,285,331,358)(175,216,271,332,359)(176,217,272,333,360)(177,218,273,334,346)(178,219,274,335,347)(179,220,275,336,348)(180,221,276,337,349), (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( (1,236,339,182,80)(2,237,340,183,81)(3,238,341,184,82)(4,239,342,185,83)(5,240,343,186,84)(6,226,344,187,85)(7,227,345,188,86)(8,228,331,189,87)(9,229,332,190,88)(10,230,333,191,89)(11,231,334,192,90)(12,232,335,193,76)(13,233,336,194,77)(14,234,337,195,78)(15,235,338,181,79)(16,112,174,52,254)(17,113,175,53,255)(18,114,176,54,241)(19,115,177,55,242)(20,116,178,56,243)(21,117,179,57,244)(22,118,180,58,245)(23,119,166,59,246)(24,120,167,60,247)(25,106,168,46,248)(26,107,169,47,249)(27,108,170,48,250)(28,109,171,49,251)(29,110,172,50,252)(30,111,173,51,253)(31,197,352,299,123)(32,198,353,300,124)(33,199,354,286,125)(34,200,355,287,126)(35,201,356,288,127)(36,202,357,289,128)(37,203,358,290,129)(38,204,359,291,130)(39,205,360,292,131)(40,206,346,293,132)(41,207,347,294,133)(42,208,348,295,134)(43,209,349,296,135)(44,210,350,297,121)(45,196,351,298,122)(61,281,304,319,374)(62,282,305,320,375)(63,283,306,321,361)(64,284,307,322,362)(65,285,308,323,363)(66,271,309,324,364)(67,272,310,325,365)(68,273,311,326,366)(69,274,312,327,367)(70,275,313,328,368)(71,276,314,329,369)(72,277,315,330,370)(73,278,301,316,371)(74,279,302,317,372)(75,280,303,318,373)(91,216,158,264,138)(92,217,159,265,139)(93,218,160,266,140)(94,219,161,267,141)(95,220,162,268,142)(96,221,163,269,143)(97,222,164,270,144)(98,223,165,256,145)(99,224,151,257,146)(100,225,152,258,147)(101,211,153,259,148)(102,212,154,260,149)(103,213,155,261,150)(104,214,156,262,136)(105,215,157,263,137), (1,45,24,145,371)(2,31,25,146,372)(3,32,26,147,373)(4,33,27,148,374)(5,34,28,149,375)(6,35,29,150,361)(7,36,30,136,362)(8,37,16,137,363)(9,38,17,138,364)(10,39,18,139,365)(11,40,19,140,366)(12,41,20,141,367)(13,42,21,142,368)(14,43,22,143,369)(15,44,23,144,370)(46,151,302,183,299)(47,152,303,184,300)(48,153,304,185,286)(49,154,305,186,287)(50,155,306,187,288)(51,156,307,188,289)(52,157,308,189,290)(53,158,309,190,291)(54,159,310,191,292)(55,160,311,192,293)(56,161,312,193,294)(57,162,313,194,295)(58,163,314,195,296)(59,164,315,181,297)(60,165,301,182,298)(61,239,199,108,101)(62,240,200,109,102)(63,226,201,110,103)(64,227,202,111,104)(65,228,203,112,105)(66,229,204,113,91)(67,230,205,114,92)(68,231,206,115,93)(69,232,207,116,94)(70,233,208,117,95)(71,234,209,118,96)(72,235,210,119,97)(73,236,196,120,98)(74,237,197,106,99)(75,238,198,107,100)(76,133,243,267,327)(77,134,244,268,328)(78,135,245,269,329)(79,121,246,270,330)(80,122,247,256,316)(81,123,248,257,317)(82,124,249,258,318)(83,125,250,259,319)(84,126,251,260,320)(85,127,252,261,321)(86,128,253,262,322)(87,129,254,263,323)(88,130,255,264,324)(89,131,241,265,325)(90,132,242,266,326)(166,222,277,338,350)(167,223,278,339,351)(168,224,279,340,352)(169,225,280,341,353)(170,211,281,342,354)(171,212,282,343,355)(172,213,283,344,356)(173,214,284,345,357)(174,215,285,331,358)(175,216,271,332,359)(176,217,272,333,360)(177,218,273,334,346)(178,219,274,335,347)(179,220,275,336,348)(180,221,276,337,349), (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([(1,236,339,182,80),(2,237,340,183,81),(3,238,341,184,82),(4,239,342,185,83),(5,240,343,186,84),(6,226,344,187,85),(7,227,345,188,86),(8,228,331,189,87),(9,229,332,190,88),(10,230,333,191,89),(11,231,334,192,90),(12,232,335,193,76),(13,233,336,194,77),(14,234,337,195,78),(15,235,338,181,79),(16,112,174,52,254),(17,113,175,53,255),(18,114,176,54,241),(19,115,177,55,242),(20,116,178,56,243),(21,117,179,57,244),(22,118,180,58,245),(23,119,166,59,246),(24,120,167,60,247),(25,106,168,46,248),(26,107,169,47,249),(27,108,170,48,250),(28,109,171,49,251),(29,110,172,50,252),(30,111,173,51,253),(31,197,352,299,123),(32,198,353,300,124),(33,199,354,286,125),(34,200,355,287,126),(35,201,356,288,127),(36,202,357,289,128),(37,203,358,290,129),(38,204,359,291,130),(39,205,360,292,131),(40,206,346,293,132),(41,207,347,294,133),(42,208,348,295,134),(43,209,349,296,135),(44,210,350,297,121),(45,196,351,298,122),(61,281,304,319,374),(62,282,305,320,375),(63,283,306,321,361),(64,284,307,322,362),(65,285,308,323,363),(66,271,309,324,364),(67,272,310,325,365),(68,273,311,326,366),(69,274,312,327,367),(70,275,313,328,368),(71,276,314,329,369),(72,277,315,330,370),(73,278,301,316,371),(74,279,302,317,372),(75,280,303,318,373),(91,216,158,264,138),(92,217,159,265,139),(93,218,160,266,140),(94,219,161,267,141),(95,220,162,268,142),(96,221,163,269,143),(97,222,164,270,144),(98,223,165,256,145),(99,224,151,257,146),(100,225,152,258,147),(101,211,153,259,148),(102,212,154,260,149),(103,213,155,261,150),(104,214,156,262,136),(105,215,157,263,137)], [(1,45,24,145,371),(2,31,25,146,372),(3,32,26,147,373),(4,33,27,148,374),(5,34,28,149,375),(6,35,29,150,361),(7,36,30,136,362),(8,37,16,137,363),(9,38,17,138,364),(10,39,18,139,365),(11,40,19,140,366),(12,41,20,141,367),(13,42,21,142,368),(14,43,22,143,369),(15,44,23,144,370),(46,151,302,183,299),(47,152,303,184,300),(48,153,304,185,286),(49,154,305,186,287),(50,155,306,187,288),(51,156,307,188,289),(52,157,308,189,290),(53,158,309,190,291),(54,159,310,191,292),(55,160,311,192,293),(56,161,312,193,294),(57,162,313,194,295),(58,163,314,195,296),(59,164,315,181,297),(60,165,301,182,298),(61,239,199,108,101),(62,240,200,109,102),(63,226,201,110,103),(64,227,202,111,104),(65,228,203,112,105),(66,229,204,113,91),(67,230,205,114,92),(68,231,206,115,93),(69,232,207,116,94),(70,233,208,117,95),(71,234,209,118,96),(72,235,210,119,97),(73,236,196,120,98),(74,237,197,106,99),(75,238,198,107,100),(76,133,243,267,327),(77,134,244,268,328),(78,135,245,269,329),(79,121,246,270,330),(80,122,247,256,316),(81,123,248,257,317),(82,124,249,258,318),(83,125,250,259,319),(84,126,251,260,320),(85,127,252,261,321),(86,128,253,262,322),(87,129,254,263,323),(88,130,255,264,324),(89,131,241,265,325),(90,132,242,266,326),(166,222,277,338,350),(167,223,278,339,351),(168,224,279,340,352),(169,225,280,341,353),(170,211,281,342,354),(171,212,282,343,355),(172,213,283,344,356),(173,214,284,345,357),(174,215,285,331,358),(175,216,271,332,359),(176,217,272,333,360),(177,218,273,334,346),(178,219,274,335,347),(179,220,275,336,348),(180,221,276,337,349)], [(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 3A3B5A···5DT15A···15IN
order1335···515···15
size1111···11···1

375 irreducible representations

dim1111
type+
imageC1C3C5C15
kernelC52×C15C53C5×C15C52
# reps12124248

Matrix representation of C52×C15 in GL3(𝔽31) generated by

100
0160
004
,
100
010
004
,
1600
0160
009
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

׿
×
𝔽