Copied to
clipboard

G = Q8×C47order 376 = 23·47

Direct product of C47 and Q8

direct product, metacyclic, nilpotent (class 2), monomial, 2-elementary

Aliases: Q8×C47, C4.C94, C188.3C2, C94.7C22, C2.2(C2×C94), SmallGroup(376,10)

Series: Derived Chief Lower central Upper central

C1C2 — Q8×C47
C1C2C94C188 — Q8×C47
C1C2 — Q8×C47
C1C94 — Q8×C47

Generators and relations for Q8×C47
 G = < a,b,c | a47=b4=1, c2=b2, ab=ba, ac=ca, cbc-1=b-1 >


Smallest permutation representation of Q8×C47
Regular action on 376 points
Generators in S376
(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)
(1 284 49 233)(2 285 50 234)(3 286 51 235)(4 287 52 189)(5 288 53 190)(6 289 54 191)(7 290 55 192)(8 291 56 193)(9 292 57 194)(10 293 58 195)(11 294 59 196)(12 295 60 197)(13 296 61 198)(14 297 62 199)(15 298 63 200)(16 299 64 201)(17 300 65 202)(18 301 66 203)(19 302 67 204)(20 303 68 205)(21 304 69 206)(22 305 70 207)(23 306 71 208)(24 307 72 209)(25 308 73 210)(26 309 74 211)(27 310 75 212)(28 311 76 213)(29 312 77 214)(30 313 78 215)(31 314 79 216)(32 315 80 217)(33 316 81 218)(34 317 82 219)(35 318 83 220)(36 319 84 221)(37 320 85 222)(38 321 86 223)(39 322 87 224)(40 323 88 225)(41 324 89 226)(42 325 90 227)(43 326 91 228)(44 327 92 229)(45 328 93 230)(46 329 94 231)(47 283 48 232)(95 177 345 255)(96 178 346 256)(97 179 347 257)(98 180 348 258)(99 181 349 259)(100 182 350 260)(101 183 351 261)(102 184 352 262)(103 185 353 263)(104 186 354 264)(105 187 355 265)(106 188 356 266)(107 142 357 267)(108 143 358 268)(109 144 359 269)(110 145 360 270)(111 146 361 271)(112 147 362 272)(113 148 363 273)(114 149 364 274)(115 150 365 275)(116 151 366 276)(117 152 367 277)(118 153 368 278)(119 154 369 279)(120 155 370 280)(121 156 371 281)(122 157 372 282)(123 158 373 236)(124 159 374 237)(125 160 375 238)(126 161 376 239)(127 162 330 240)(128 163 331 241)(129 164 332 242)(130 165 333 243)(131 166 334 244)(132 167 335 245)(133 168 336 246)(134 169 337 247)(135 170 338 248)(136 171 339 249)(137 172 340 250)(138 173 341 251)(139 174 342 252)(140 175 343 253)(141 176 344 254)
(1 269 49 144)(2 270 50 145)(3 271 51 146)(4 272 52 147)(5 273 53 148)(6 274 54 149)(7 275 55 150)(8 276 56 151)(9 277 57 152)(10 278 58 153)(11 279 59 154)(12 280 60 155)(13 281 61 156)(14 282 62 157)(15 236 63 158)(16 237 64 159)(17 238 65 160)(18 239 66 161)(19 240 67 162)(20 241 68 163)(21 242 69 164)(22 243 70 165)(23 244 71 166)(24 245 72 167)(25 246 73 168)(26 247 74 169)(27 248 75 170)(28 249 76 171)(29 250 77 172)(30 251 78 173)(31 252 79 174)(32 253 80 175)(33 254 81 176)(34 255 82 177)(35 256 83 178)(36 257 84 179)(37 258 85 180)(38 259 86 181)(39 260 87 182)(40 261 88 183)(41 262 89 184)(42 263 90 185)(43 264 91 186)(44 265 92 187)(45 266 93 188)(46 267 94 142)(47 268 48 143)(95 317 345 219)(96 318 346 220)(97 319 347 221)(98 320 348 222)(99 321 349 223)(100 322 350 224)(101 323 351 225)(102 324 352 226)(103 325 353 227)(104 326 354 228)(105 327 355 229)(106 328 356 230)(107 329 357 231)(108 283 358 232)(109 284 359 233)(110 285 360 234)(111 286 361 235)(112 287 362 189)(113 288 363 190)(114 289 364 191)(115 290 365 192)(116 291 366 193)(117 292 367 194)(118 293 368 195)(119 294 369 196)(120 295 370 197)(121 296 371 198)(122 297 372 199)(123 298 373 200)(124 299 374 201)(125 300 375 202)(126 301 376 203)(127 302 330 204)(128 303 331 205)(129 304 332 206)(130 305 333 207)(131 306 334 208)(132 307 335 209)(133 308 336 210)(134 309 337 211)(135 310 338 212)(136 311 339 213)(137 312 340 214)(138 313 341 215)(139 314 342 216)(140 315 343 217)(141 316 344 218)

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

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

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

235 conjugacy classes

class 1  2 4A4B4C47A···47AT94A···94AT188A···188EH
order1244447···4794···94188···188
size112221···11···12···2

235 irreducible representations

dim111122
type++-
imageC1C2C47C94Q8Q8×C47
kernelQ8×C47C188Q8C4C47C1
# reps1346138146

Matrix representation of Q8×C47 in GL2(𝔽941) generated by

6300
0630
,
361939
232580
,
730498
417211
G:=sub<GL(2,GF(941))| [630,0,0,630],[361,232,939,580],[730,417,498,211] >;

Q8×C47 in GAP, Magma, Sage, TeX

Q_8\times C_{47}
% in TeX

G:=Group("Q8xC47");
// GroupNames label

G:=SmallGroup(376,10);
// by ID

G=gap.SmallGroup(376,10);
# by ID

G:=PCGroup([4,-2,-2,-47,-2,752,1521,757]);
// Polycyclic

G:=Group<a,b,c|a^47=b^4=1,c^2=b^2,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of Q8×C47 in TeX

׿
×
𝔽