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G = Dic3×C37order 444 = 22·3·37

Direct product of C37 and Dic3

direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: Dic3×C37, C3⋊C148, C6.C74, C1115C4, C74.2S3, C222.3C2, C2.(S3×C37), SmallGroup(444,3)

Series: Derived Chief Lower central Upper central

C1C3 — Dic3×C37
C1C3C6C222 — Dic3×C37
C3 — Dic3×C37
C1C74

Generators and relations for Dic3×C37
 G = < a,b,c | a37=b6=1, c2=b3, ab=ba, ac=ca, cbc-1=b-1 >

3C4
3C148

Smallest permutation representation of Dic3×C37
Regular action on 444 points
Generators in S444
(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)(371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407)(408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444)
(1 226 79 284 348 54)(2 227 80 285 349 55)(3 228 81 286 350 56)(4 229 82 287 351 57)(5 230 83 288 352 58)(6 231 84 289 353 59)(7 232 85 290 354 60)(8 233 86 291 355 61)(9 234 87 292 356 62)(10 235 88 293 357 63)(11 236 89 294 358 64)(12 237 90 295 359 65)(13 238 91 296 360 66)(14 239 92 260 361 67)(15 240 93 261 362 68)(16 241 94 262 363 69)(17 242 95 263 364 70)(18 243 96 264 365 71)(19 244 97 265 366 72)(20 245 98 266 367 73)(21 246 99 267 368 74)(22 247 100 268 369 38)(23 248 101 269 370 39)(24 249 102 270 334 40)(25 250 103 271 335 41)(26 251 104 272 336 42)(27 252 105 273 337 43)(28 253 106 274 338 44)(29 254 107 275 339 45)(30 255 108 276 340 46)(31 256 109 277 341 47)(32 257 110 278 342 48)(33 258 111 279 343 49)(34 259 75 280 344 50)(35 223 76 281 345 51)(36 224 77 282 346 52)(37 225 78 283 347 53)(112 324 391 408 213 154)(113 325 392 409 214 155)(114 326 393 410 215 156)(115 327 394 411 216 157)(116 328 395 412 217 158)(117 329 396 413 218 159)(118 330 397 414 219 160)(119 331 398 415 220 161)(120 332 399 416 221 162)(121 333 400 417 222 163)(122 297 401 418 186 164)(123 298 402 419 187 165)(124 299 403 420 188 166)(125 300 404 421 189 167)(126 301 405 422 190 168)(127 302 406 423 191 169)(128 303 407 424 192 170)(129 304 371 425 193 171)(130 305 372 426 194 172)(131 306 373 427 195 173)(132 307 374 428 196 174)(133 308 375 429 197 175)(134 309 376 430 198 176)(135 310 377 431 199 177)(136 311 378 432 200 178)(137 312 379 433 201 179)(138 313 380 434 202 180)(139 314 381 435 203 181)(140 315 382 436 204 182)(141 316 383 437 205 183)(142 317 384 438 206 184)(143 318 385 439 207 185)(144 319 386 440 208 149)(145 320 387 441 209 150)(146 321 388 442 210 151)(147 322 389 443 211 152)(148 323 390 444 212 153)
(1 221 284 332)(2 222 285 333)(3 186 286 297)(4 187 287 298)(5 188 288 299)(6 189 289 300)(7 190 290 301)(8 191 291 302)(9 192 292 303)(10 193 293 304)(11 194 294 305)(12 195 295 306)(13 196 296 307)(14 197 260 308)(15 198 261 309)(16 199 262 310)(17 200 263 311)(18 201 264 312)(19 202 265 313)(20 203 266 314)(21 204 267 315)(22 205 268 316)(23 206 269 317)(24 207 270 318)(25 208 271 319)(26 209 272 320)(27 210 273 321)(28 211 274 322)(29 212 275 323)(30 213 276 324)(31 214 277 325)(32 215 278 326)(33 216 279 327)(34 217 280 328)(35 218 281 329)(36 219 282 330)(37 220 283 331)(38 183 100 383)(39 184 101 384)(40 185 102 385)(41 149 103 386)(42 150 104 387)(43 151 105 388)(44 152 106 389)(45 153 107 390)(46 154 108 391)(47 155 109 392)(48 156 110 393)(49 157 111 394)(50 158 75 395)(51 159 76 396)(52 160 77 397)(53 161 78 398)(54 162 79 399)(55 163 80 400)(56 164 81 401)(57 165 82 402)(58 166 83 403)(59 167 84 404)(60 168 85 405)(61 169 86 406)(62 170 87 407)(63 171 88 371)(64 172 89 372)(65 173 90 373)(66 174 91 374)(67 175 92 375)(68 176 93 376)(69 177 94 377)(70 178 95 378)(71 179 96 379)(72 180 97 380)(73 181 98 381)(74 182 99 382)(112 255 408 340)(113 256 409 341)(114 257 410 342)(115 258 411 343)(116 259 412 344)(117 223 413 345)(118 224 414 346)(119 225 415 347)(120 226 416 348)(121 227 417 349)(122 228 418 350)(123 229 419 351)(124 230 420 352)(125 231 421 353)(126 232 422 354)(127 233 423 355)(128 234 424 356)(129 235 425 357)(130 236 426 358)(131 237 427 359)(132 238 428 360)(133 239 429 361)(134 240 430 362)(135 241 431 363)(136 242 432 364)(137 243 433 365)(138 244 434 366)(139 245 435 367)(140 246 436 368)(141 247 437 369)(142 248 438 370)(143 249 439 334)(144 250 440 335)(145 251 441 336)(146 252 442 337)(147 253 443 338)(148 254 444 339)

G:=sub<Sym(444)| (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)(371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407)(408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444), (1,226,79,284,348,54)(2,227,80,285,349,55)(3,228,81,286,350,56)(4,229,82,287,351,57)(5,230,83,288,352,58)(6,231,84,289,353,59)(7,232,85,290,354,60)(8,233,86,291,355,61)(9,234,87,292,356,62)(10,235,88,293,357,63)(11,236,89,294,358,64)(12,237,90,295,359,65)(13,238,91,296,360,66)(14,239,92,260,361,67)(15,240,93,261,362,68)(16,241,94,262,363,69)(17,242,95,263,364,70)(18,243,96,264,365,71)(19,244,97,265,366,72)(20,245,98,266,367,73)(21,246,99,267,368,74)(22,247,100,268,369,38)(23,248,101,269,370,39)(24,249,102,270,334,40)(25,250,103,271,335,41)(26,251,104,272,336,42)(27,252,105,273,337,43)(28,253,106,274,338,44)(29,254,107,275,339,45)(30,255,108,276,340,46)(31,256,109,277,341,47)(32,257,110,278,342,48)(33,258,111,279,343,49)(34,259,75,280,344,50)(35,223,76,281,345,51)(36,224,77,282,346,52)(37,225,78,283,347,53)(112,324,391,408,213,154)(113,325,392,409,214,155)(114,326,393,410,215,156)(115,327,394,411,216,157)(116,328,395,412,217,158)(117,329,396,413,218,159)(118,330,397,414,219,160)(119,331,398,415,220,161)(120,332,399,416,221,162)(121,333,400,417,222,163)(122,297,401,418,186,164)(123,298,402,419,187,165)(124,299,403,420,188,166)(125,300,404,421,189,167)(126,301,405,422,190,168)(127,302,406,423,191,169)(128,303,407,424,192,170)(129,304,371,425,193,171)(130,305,372,426,194,172)(131,306,373,427,195,173)(132,307,374,428,196,174)(133,308,375,429,197,175)(134,309,376,430,198,176)(135,310,377,431,199,177)(136,311,378,432,200,178)(137,312,379,433,201,179)(138,313,380,434,202,180)(139,314,381,435,203,181)(140,315,382,436,204,182)(141,316,383,437,205,183)(142,317,384,438,206,184)(143,318,385,439,207,185)(144,319,386,440,208,149)(145,320,387,441,209,150)(146,321,388,442,210,151)(147,322,389,443,211,152)(148,323,390,444,212,153), (1,221,284,332)(2,222,285,333)(3,186,286,297)(4,187,287,298)(5,188,288,299)(6,189,289,300)(7,190,290,301)(8,191,291,302)(9,192,292,303)(10,193,293,304)(11,194,294,305)(12,195,295,306)(13,196,296,307)(14,197,260,308)(15,198,261,309)(16,199,262,310)(17,200,263,311)(18,201,264,312)(19,202,265,313)(20,203,266,314)(21,204,267,315)(22,205,268,316)(23,206,269,317)(24,207,270,318)(25,208,271,319)(26,209,272,320)(27,210,273,321)(28,211,274,322)(29,212,275,323)(30,213,276,324)(31,214,277,325)(32,215,278,326)(33,216,279,327)(34,217,280,328)(35,218,281,329)(36,219,282,330)(37,220,283,331)(38,183,100,383)(39,184,101,384)(40,185,102,385)(41,149,103,386)(42,150,104,387)(43,151,105,388)(44,152,106,389)(45,153,107,390)(46,154,108,391)(47,155,109,392)(48,156,110,393)(49,157,111,394)(50,158,75,395)(51,159,76,396)(52,160,77,397)(53,161,78,398)(54,162,79,399)(55,163,80,400)(56,164,81,401)(57,165,82,402)(58,166,83,403)(59,167,84,404)(60,168,85,405)(61,169,86,406)(62,170,87,407)(63,171,88,371)(64,172,89,372)(65,173,90,373)(66,174,91,374)(67,175,92,375)(68,176,93,376)(69,177,94,377)(70,178,95,378)(71,179,96,379)(72,180,97,380)(73,181,98,381)(74,182,99,382)(112,255,408,340)(113,256,409,341)(114,257,410,342)(115,258,411,343)(116,259,412,344)(117,223,413,345)(118,224,414,346)(119,225,415,347)(120,226,416,348)(121,227,417,349)(122,228,418,350)(123,229,419,351)(124,230,420,352)(125,231,421,353)(126,232,422,354)(127,233,423,355)(128,234,424,356)(129,235,425,357)(130,236,426,358)(131,237,427,359)(132,238,428,360)(133,239,429,361)(134,240,430,362)(135,241,431,363)(136,242,432,364)(137,243,433,365)(138,244,434,366)(139,245,435,367)(140,246,436,368)(141,247,437,369)(142,248,438,370)(143,249,439,334)(144,250,440,335)(145,251,441,336)(146,252,442,337)(147,253,443,338)(148,254,444,339)>;

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)(334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370)(371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407)(408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444), (1,226,79,284,348,54)(2,227,80,285,349,55)(3,228,81,286,350,56)(4,229,82,287,351,57)(5,230,83,288,352,58)(6,231,84,289,353,59)(7,232,85,290,354,60)(8,233,86,291,355,61)(9,234,87,292,356,62)(10,235,88,293,357,63)(11,236,89,294,358,64)(12,237,90,295,359,65)(13,238,91,296,360,66)(14,239,92,260,361,67)(15,240,93,261,362,68)(16,241,94,262,363,69)(17,242,95,263,364,70)(18,243,96,264,365,71)(19,244,97,265,366,72)(20,245,98,266,367,73)(21,246,99,267,368,74)(22,247,100,268,369,38)(23,248,101,269,370,39)(24,249,102,270,334,40)(25,250,103,271,335,41)(26,251,104,272,336,42)(27,252,105,273,337,43)(28,253,106,274,338,44)(29,254,107,275,339,45)(30,255,108,276,340,46)(31,256,109,277,341,47)(32,257,110,278,342,48)(33,258,111,279,343,49)(34,259,75,280,344,50)(35,223,76,281,345,51)(36,224,77,282,346,52)(37,225,78,283,347,53)(112,324,391,408,213,154)(113,325,392,409,214,155)(114,326,393,410,215,156)(115,327,394,411,216,157)(116,328,395,412,217,158)(117,329,396,413,218,159)(118,330,397,414,219,160)(119,331,398,415,220,161)(120,332,399,416,221,162)(121,333,400,417,222,163)(122,297,401,418,186,164)(123,298,402,419,187,165)(124,299,403,420,188,166)(125,300,404,421,189,167)(126,301,405,422,190,168)(127,302,406,423,191,169)(128,303,407,424,192,170)(129,304,371,425,193,171)(130,305,372,426,194,172)(131,306,373,427,195,173)(132,307,374,428,196,174)(133,308,375,429,197,175)(134,309,376,430,198,176)(135,310,377,431,199,177)(136,311,378,432,200,178)(137,312,379,433,201,179)(138,313,380,434,202,180)(139,314,381,435,203,181)(140,315,382,436,204,182)(141,316,383,437,205,183)(142,317,384,438,206,184)(143,318,385,439,207,185)(144,319,386,440,208,149)(145,320,387,441,209,150)(146,321,388,442,210,151)(147,322,389,443,211,152)(148,323,390,444,212,153), (1,221,284,332)(2,222,285,333)(3,186,286,297)(4,187,287,298)(5,188,288,299)(6,189,289,300)(7,190,290,301)(8,191,291,302)(9,192,292,303)(10,193,293,304)(11,194,294,305)(12,195,295,306)(13,196,296,307)(14,197,260,308)(15,198,261,309)(16,199,262,310)(17,200,263,311)(18,201,264,312)(19,202,265,313)(20,203,266,314)(21,204,267,315)(22,205,268,316)(23,206,269,317)(24,207,270,318)(25,208,271,319)(26,209,272,320)(27,210,273,321)(28,211,274,322)(29,212,275,323)(30,213,276,324)(31,214,277,325)(32,215,278,326)(33,216,279,327)(34,217,280,328)(35,218,281,329)(36,219,282,330)(37,220,283,331)(38,183,100,383)(39,184,101,384)(40,185,102,385)(41,149,103,386)(42,150,104,387)(43,151,105,388)(44,152,106,389)(45,153,107,390)(46,154,108,391)(47,155,109,392)(48,156,110,393)(49,157,111,394)(50,158,75,395)(51,159,76,396)(52,160,77,397)(53,161,78,398)(54,162,79,399)(55,163,80,400)(56,164,81,401)(57,165,82,402)(58,166,83,403)(59,167,84,404)(60,168,85,405)(61,169,86,406)(62,170,87,407)(63,171,88,371)(64,172,89,372)(65,173,90,373)(66,174,91,374)(67,175,92,375)(68,176,93,376)(69,177,94,377)(70,178,95,378)(71,179,96,379)(72,180,97,380)(73,181,98,381)(74,182,99,382)(112,255,408,340)(113,256,409,341)(114,257,410,342)(115,258,411,343)(116,259,412,344)(117,223,413,345)(118,224,414,346)(119,225,415,347)(120,226,416,348)(121,227,417,349)(122,228,418,350)(123,229,419,351)(124,230,420,352)(125,231,421,353)(126,232,422,354)(127,233,423,355)(128,234,424,356)(129,235,425,357)(130,236,426,358)(131,237,427,359)(132,238,428,360)(133,239,429,361)(134,240,430,362)(135,241,431,363)(136,242,432,364)(137,243,433,365)(138,244,434,366)(139,245,435,367)(140,246,436,368)(141,247,437,369)(142,248,438,370)(143,249,439,334)(144,250,440,335)(145,251,441,336)(146,252,442,337)(147,253,443,338)(148,254,444,339) );

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),(334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370),(371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407),(408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444)], [(1,226,79,284,348,54),(2,227,80,285,349,55),(3,228,81,286,350,56),(4,229,82,287,351,57),(5,230,83,288,352,58),(6,231,84,289,353,59),(7,232,85,290,354,60),(8,233,86,291,355,61),(9,234,87,292,356,62),(10,235,88,293,357,63),(11,236,89,294,358,64),(12,237,90,295,359,65),(13,238,91,296,360,66),(14,239,92,260,361,67),(15,240,93,261,362,68),(16,241,94,262,363,69),(17,242,95,263,364,70),(18,243,96,264,365,71),(19,244,97,265,366,72),(20,245,98,266,367,73),(21,246,99,267,368,74),(22,247,100,268,369,38),(23,248,101,269,370,39),(24,249,102,270,334,40),(25,250,103,271,335,41),(26,251,104,272,336,42),(27,252,105,273,337,43),(28,253,106,274,338,44),(29,254,107,275,339,45),(30,255,108,276,340,46),(31,256,109,277,341,47),(32,257,110,278,342,48),(33,258,111,279,343,49),(34,259,75,280,344,50),(35,223,76,281,345,51),(36,224,77,282,346,52),(37,225,78,283,347,53),(112,324,391,408,213,154),(113,325,392,409,214,155),(114,326,393,410,215,156),(115,327,394,411,216,157),(116,328,395,412,217,158),(117,329,396,413,218,159),(118,330,397,414,219,160),(119,331,398,415,220,161),(120,332,399,416,221,162),(121,333,400,417,222,163),(122,297,401,418,186,164),(123,298,402,419,187,165),(124,299,403,420,188,166),(125,300,404,421,189,167),(126,301,405,422,190,168),(127,302,406,423,191,169),(128,303,407,424,192,170),(129,304,371,425,193,171),(130,305,372,426,194,172),(131,306,373,427,195,173),(132,307,374,428,196,174),(133,308,375,429,197,175),(134,309,376,430,198,176),(135,310,377,431,199,177),(136,311,378,432,200,178),(137,312,379,433,201,179),(138,313,380,434,202,180),(139,314,381,435,203,181),(140,315,382,436,204,182),(141,316,383,437,205,183),(142,317,384,438,206,184),(143,318,385,439,207,185),(144,319,386,440,208,149),(145,320,387,441,209,150),(146,321,388,442,210,151),(147,322,389,443,211,152),(148,323,390,444,212,153)], [(1,221,284,332),(2,222,285,333),(3,186,286,297),(4,187,287,298),(5,188,288,299),(6,189,289,300),(7,190,290,301),(8,191,291,302),(9,192,292,303),(10,193,293,304),(11,194,294,305),(12,195,295,306),(13,196,296,307),(14,197,260,308),(15,198,261,309),(16,199,262,310),(17,200,263,311),(18,201,264,312),(19,202,265,313),(20,203,266,314),(21,204,267,315),(22,205,268,316),(23,206,269,317),(24,207,270,318),(25,208,271,319),(26,209,272,320),(27,210,273,321),(28,211,274,322),(29,212,275,323),(30,213,276,324),(31,214,277,325),(32,215,278,326),(33,216,279,327),(34,217,280,328),(35,218,281,329),(36,219,282,330),(37,220,283,331),(38,183,100,383),(39,184,101,384),(40,185,102,385),(41,149,103,386),(42,150,104,387),(43,151,105,388),(44,152,106,389),(45,153,107,390),(46,154,108,391),(47,155,109,392),(48,156,110,393),(49,157,111,394),(50,158,75,395),(51,159,76,396),(52,160,77,397),(53,161,78,398),(54,162,79,399),(55,163,80,400),(56,164,81,401),(57,165,82,402),(58,166,83,403),(59,167,84,404),(60,168,85,405),(61,169,86,406),(62,170,87,407),(63,171,88,371),(64,172,89,372),(65,173,90,373),(66,174,91,374),(67,175,92,375),(68,176,93,376),(69,177,94,377),(70,178,95,378),(71,179,96,379),(72,180,97,380),(73,181,98,381),(74,182,99,382),(112,255,408,340),(113,256,409,341),(114,257,410,342),(115,258,411,343),(116,259,412,344),(117,223,413,345),(118,224,414,346),(119,225,415,347),(120,226,416,348),(121,227,417,349),(122,228,418,350),(123,229,419,351),(124,230,420,352),(125,231,421,353),(126,232,422,354),(127,233,423,355),(128,234,424,356),(129,235,425,357),(130,236,426,358),(131,237,427,359),(132,238,428,360),(133,239,429,361),(134,240,430,362),(135,241,431,363),(136,242,432,364),(137,243,433,365),(138,244,434,366),(139,245,435,367),(140,246,436,368),(141,247,437,369),(142,248,438,370),(143,249,439,334),(144,250,440,335),(145,251,441,336),(146,252,442,337),(147,253,443,338),(148,254,444,339)])

222 conjugacy classes

class 1  2  3 4A4B 6 37A···37AJ74A···74AJ111A···111AJ148A···148BT222A···222AJ
order12344637···3774···74111···111148···148222···222
size1123321···11···12···23···32···2

222 irreducible representations

dim1111112222
type+++-
imageC1C2C4C37C74C148S3Dic3S3×C37Dic3×C37
kernelDic3×C37C222C111Dic3C6C3C74C37C2C1
# reps112363672113636

Matrix representation of Dic3×C37 in GL2(𝔽1777) generated by

6930
0693
,
11776
10
,
1529601
353248
G:=sub<GL(2,GF(1777))| [693,0,0,693],[1,1,1776,0],[1529,353,601,248] >;

Dic3×C37 in GAP, Magma, Sage, TeX

{\rm Dic}_3\times C_{37}
% in TeX

G:=Group("Dic3xC37");
// GroupNames label

G:=SmallGroup(444,3);
// by ID

G=gap.SmallGroup(444,3);
# by ID

G:=PCGroup([4,-2,-37,-2,-3,296,4739]);
// Polycyclic

G:=Group<a,b,c|a^37=b^6=1,c^2=b^3,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of Dic3×C37 in TeX

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