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
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)
(1 251 109 74)(2 252 110 75)(3 253 111 76)(4 254 112 77)(5 255 113 78)(6 256 114 79)(7 257 115 80)(8 258 116 81)(9 259 117 82)(10 260 118 83)(11 261 119 84)(12 262 120 85)(13 263 121 86)(14 264 122 87)(15 265 123 88)(16 266 124 89)(17 267 125 90)(18 268 126 91)(19 269 127 92)(20 270 128 93)(21 271 129 94)(22 272 130 48)(23 273 131 49)(24 274 132 50)(25 275 133 51)(26 276 134 52)(27 277 135 53)(28 278 136 54)(29 279 137 55)(30 280 138 56)(31 281 139 57)(32 282 140 58)(33 236 141 59)(34 237 95 60)(35 238 96 61)(36 239 97 62)(37 240 98 63)(38 241 99 64)(39 242 100 65)(40 243 101 66)(41 244 102 67)(42 245 103 68)(43 246 104 69)(44 247 105 70)(45 248 106 71)(46 249 107 72)(47 250 108 73)(142 290 351 191)(143 291 352 192)(144 292 353 193)(145 293 354 194)(146 294 355 195)(147 295 356 196)(148 296 357 197)(149 297 358 198)(150 298 359 199)(151 299 360 200)(152 300 361 201)(153 301 362 202)(154 302 363 203)(155 303 364 204)(156 304 365 205)(157 305 366 206)(158 306 367 207)(159 307 368 208)(160 308 369 209)(161 309 370 210)(162 310 371 211)(163 311 372 212)(164 312 373 213)(165 313 374 214)(166 314 375 215)(167 315 376 216)(168 316 330 217)(169 317 331 218)(170 318 332 219)(171 319 333 220)(172 320 334 221)(173 321 335 222)(174 322 336 223)(175 323 337 224)(176 324 338 225)(177 325 339 226)(178 326 340 227)(179 327 341 228)(180 328 342 229)(181 329 343 230)(182 283 344 231)(183 284 345 232)(184 285 346 233)(185 286 347 234)(186 287 348 235)(187 288 349 189)(188 289 350 190)
(1 336 109 174)(2 337 110 175)(3 338 111 176)(4 339 112 177)(5 340 113 178)(6 341 114 179)(7 342 115 180)(8 343 116 181)(9 344 117 182)(10 345 118 183)(11 346 119 184)(12 347 120 185)(13 348 121 186)(14 349 122 187)(15 350 123 188)(16 351 124 142)(17 352 125 143)(18 353 126 144)(19 354 127 145)(20 355 128 146)(21 356 129 147)(22 357 130 148)(23 358 131 149)(24 359 132 150)(25 360 133 151)(26 361 134 152)(27 362 135 153)(28 363 136 154)(29 364 137 155)(30 365 138 156)(31 366 139 157)(32 367 140 158)(33 368 141 159)(34 369 95 160)(35 370 96 161)(36 371 97 162)(37 372 98 163)(38 373 99 164)(39 374 100 165)(40 375 101 166)(41 376 102 167)(42 330 103 168)(43 331 104 169)(44 332 105 170)(45 333 106 171)(46 334 107 172)(47 335 108 173)(48 197 272 296)(49 198 273 297)(50 199 274 298)(51 200 275 299)(52 201 276 300)(53 202 277 301)(54 203 278 302)(55 204 279 303)(56 205 280 304)(57 206 281 305)(58 207 282 306)(59 208 236 307)(60 209 237 308)(61 210 238 309)(62 211 239 310)(63 212 240 311)(64 213 241 312)(65 214 242 313)(66 215 243 314)(67 216 244 315)(68 217 245 316)(69 218 246 317)(70 219 247 318)(71 220 248 319)(72 221 249 320)(73 222 250 321)(74 223 251 322)(75 224 252 323)(76 225 253 324)(77 226 254 325)(78 227 255 326)(79 228 256 327)(80 229 257 328)(81 230 258 329)(82 231 259 283)(83 232 260 284)(84 233 261 285)(85 234 262 286)(86 235 263 287)(87 189 264 288)(88 190 265 289)(89 191 266 290)(90 192 267 291)(91 193 268 292)(92 194 269 293)(93 195 270 294)(94 196 271 295)
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), (1,251,109,74)(2,252,110,75)(3,253,111,76)(4,254,112,77)(5,255,113,78)(6,256,114,79)(7,257,115,80)(8,258,116,81)(9,259,117,82)(10,260,118,83)(11,261,119,84)(12,262,120,85)(13,263,121,86)(14,264,122,87)(15,265,123,88)(16,266,124,89)(17,267,125,90)(18,268,126,91)(19,269,127,92)(20,270,128,93)(21,271,129,94)(22,272,130,48)(23,273,131,49)(24,274,132,50)(25,275,133,51)(26,276,134,52)(27,277,135,53)(28,278,136,54)(29,279,137,55)(30,280,138,56)(31,281,139,57)(32,282,140,58)(33,236,141,59)(34,237,95,60)(35,238,96,61)(36,239,97,62)(37,240,98,63)(38,241,99,64)(39,242,100,65)(40,243,101,66)(41,244,102,67)(42,245,103,68)(43,246,104,69)(44,247,105,70)(45,248,106,71)(46,249,107,72)(47,250,108,73)(142,290,351,191)(143,291,352,192)(144,292,353,193)(145,293,354,194)(146,294,355,195)(147,295,356,196)(148,296,357,197)(149,297,358,198)(150,298,359,199)(151,299,360,200)(152,300,361,201)(153,301,362,202)(154,302,363,203)(155,303,364,204)(156,304,365,205)(157,305,366,206)(158,306,367,207)(159,307,368,208)(160,308,369,209)(161,309,370,210)(162,310,371,211)(163,311,372,212)(164,312,373,213)(165,313,374,214)(166,314,375,215)(167,315,376,216)(168,316,330,217)(169,317,331,218)(170,318,332,219)(171,319,333,220)(172,320,334,221)(173,321,335,222)(174,322,336,223)(175,323,337,224)(176,324,338,225)(177,325,339,226)(178,326,340,227)(179,327,341,228)(180,328,342,229)(181,329,343,230)(182,283,344,231)(183,284,345,232)(184,285,346,233)(185,286,347,234)(186,287,348,235)(187,288,349,189)(188,289,350,190), (1,336,109,174)(2,337,110,175)(3,338,111,176)(4,339,112,177)(5,340,113,178)(6,341,114,179)(7,342,115,180)(8,343,116,181)(9,344,117,182)(10,345,118,183)(11,346,119,184)(12,347,120,185)(13,348,121,186)(14,349,122,187)(15,350,123,188)(16,351,124,142)(17,352,125,143)(18,353,126,144)(19,354,127,145)(20,355,128,146)(21,356,129,147)(22,357,130,148)(23,358,131,149)(24,359,132,150)(25,360,133,151)(26,361,134,152)(27,362,135,153)(28,363,136,154)(29,364,137,155)(30,365,138,156)(31,366,139,157)(32,367,140,158)(33,368,141,159)(34,369,95,160)(35,370,96,161)(36,371,97,162)(37,372,98,163)(38,373,99,164)(39,374,100,165)(40,375,101,166)(41,376,102,167)(42,330,103,168)(43,331,104,169)(44,332,105,170)(45,333,106,171)(46,334,107,172)(47,335,108,173)(48,197,272,296)(49,198,273,297)(50,199,274,298)(51,200,275,299)(52,201,276,300)(53,202,277,301)(54,203,278,302)(55,204,279,303)(56,205,280,304)(57,206,281,305)(58,207,282,306)(59,208,236,307)(60,209,237,308)(61,210,238,309)(62,211,239,310)(63,212,240,311)(64,213,241,312)(65,214,242,313)(66,215,243,314)(67,216,244,315)(68,217,245,316)(69,218,246,317)(70,219,247,318)(71,220,248,319)(72,221,249,320)(73,222,250,321)(74,223,251,322)(75,224,252,323)(76,225,253,324)(77,226,254,325)(78,227,255,326)(79,228,256,327)(80,229,257,328)(81,230,258,329)(82,231,259,283)(83,232,260,284)(84,233,261,285)(85,234,262,286)(86,235,263,287)(87,189,264,288)(88,190,265,289)(89,191,266,290)(90,192,267,291)(91,193,268,292)(92,194,269,293)(93,195,270,294)(94,196,271,295)>;
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), (1,251,109,74)(2,252,110,75)(3,253,111,76)(4,254,112,77)(5,255,113,78)(6,256,114,79)(7,257,115,80)(8,258,116,81)(9,259,117,82)(10,260,118,83)(11,261,119,84)(12,262,120,85)(13,263,121,86)(14,264,122,87)(15,265,123,88)(16,266,124,89)(17,267,125,90)(18,268,126,91)(19,269,127,92)(20,270,128,93)(21,271,129,94)(22,272,130,48)(23,273,131,49)(24,274,132,50)(25,275,133,51)(26,276,134,52)(27,277,135,53)(28,278,136,54)(29,279,137,55)(30,280,138,56)(31,281,139,57)(32,282,140,58)(33,236,141,59)(34,237,95,60)(35,238,96,61)(36,239,97,62)(37,240,98,63)(38,241,99,64)(39,242,100,65)(40,243,101,66)(41,244,102,67)(42,245,103,68)(43,246,104,69)(44,247,105,70)(45,248,106,71)(46,249,107,72)(47,250,108,73)(142,290,351,191)(143,291,352,192)(144,292,353,193)(145,293,354,194)(146,294,355,195)(147,295,356,196)(148,296,357,197)(149,297,358,198)(150,298,359,199)(151,299,360,200)(152,300,361,201)(153,301,362,202)(154,302,363,203)(155,303,364,204)(156,304,365,205)(157,305,366,206)(158,306,367,207)(159,307,368,208)(160,308,369,209)(161,309,370,210)(162,310,371,211)(163,311,372,212)(164,312,373,213)(165,313,374,214)(166,314,375,215)(167,315,376,216)(168,316,330,217)(169,317,331,218)(170,318,332,219)(171,319,333,220)(172,320,334,221)(173,321,335,222)(174,322,336,223)(175,323,337,224)(176,324,338,225)(177,325,339,226)(178,326,340,227)(179,327,341,228)(180,328,342,229)(181,329,343,230)(182,283,344,231)(183,284,345,232)(184,285,346,233)(185,286,347,234)(186,287,348,235)(187,288,349,189)(188,289,350,190), (1,336,109,174)(2,337,110,175)(3,338,111,176)(4,339,112,177)(5,340,113,178)(6,341,114,179)(7,342,115,180)(8,343,116,181)(9,344,117,182)(10,345,118,183)(11,346,119,184)(12,347,120,185)(13,348,121,186)(14,349,122,187)(15,350,123,188)(16,351,124,142)(17,352,125,143)(18,353,126,144)(19,354,127,145)(20,355,128,146)(21,356,129,147)(22,357,130,148)(23,358,131,149)(24,359,132,150)(25,360,133,151)(26,361,134,152)(27,362,135,153)(28,363,136,154)(29,364,137,155)(30,365,138,156)(31,366,139,157)(32,367,140,158)(33,368,141,159)(34,369,95,160)(35,370,96,161)(36,371,97,162)(37,372,98,163)(38,373,99,164)(39,374,100,165)(40,375,101,166)(41,376,102,167)(42,330,103,168)(43,331,104,169)(44,332,105,170)(45,333,106,171)(46,334,107,172)(47,335,108,173)(48,197,272,296)(49,198,273,297)(50,199,274,298)(51,200,275,299)(52,201,276,300)(53,202,277,301)(54,203,278,302)(55,204,279,303)(56,205,280,304)(57,206,281,305)(58,207,282,306)(59,208,236,307)(60,209,237,308)(61,210,238,309)(62,211,239,310)(63,212,240,311)(64,213,241,312)(65,214,242,313)(66,215,243,314)(67,216,244,315)(68,217,245,316)(69,218,246,317)(70,219,247,318)(71,220,248,319)(72,221,249,320)(73,222,250,321)(74,223,251,322)(75,224,252,323)(76,225,253,324)(77,226,254,325)(78,227,255,326)(79,228,256,327)(80,229,257,328)(81,230,258,329)(82,231,259,283)(83,232,260,284)(84,233,261,285)(85,234,262,286)(86,235,263,287)(87,189,264,288)(88,190,265,289)(89,191,266,290)(90,192,267,291)(91,193,268,292)(92,194,269,293)(93,195,270,294)(94,196,271,295) );
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)], [(1,251,109,74),(2,252,110,75),(3,253,111,76),(4,254,112,77),(5,255,113,78),(6,256,114,79),(7,257,115,80),(8,258,116,81),(9,259,117,82),(10,260,118,83),(11,261,119,84),(12,262,120,85),(13,263,121,86),(14,264,122,87),(15,265,123,88),(16,266,124,89),(17,267,125,90),(18,268,126,91),(19,269,127,92),(20,270,128,93),(21,271,129,94),(22,272,130,48),(23,273,131,49),(24,274,132,50),(25,275,133,51),(26,276,134,52),(27,277,135,53),(28,278,136,54),(29,279,137,55),(30,280,138,56),(31,281,139,57),(32,282,140,58),(33,236,141,59),(34,237,95,60),(35,238,96,61),(36,239,97,62),(37,240,98,63),(38,241,99,64),(39,242,100,65),(40,243,101,66),(41,244,102,67),(42,245,103,68),(43,246,104,69),(44,247,105,70),(45,248,106,71),(46,249,107,72),(47,250,108,73),(142,290,351,191),(143,291,352,192),(144,292,353,193),(145,293,354,194),(146,294,355,195),(147,295,356,196),(148,296,357,197),(149,297,358,198),(150,298,359,199),(151,299,360,200),(152,300,361,201),(153,301,362,202),(154,302,363,203),(155,303,364,204),(156,304,365,205),(157,305,366,206),(158,306,367,207),(159,307,368,208),(160,308,369,209),(161,309,370,210),(162,310,371,211),(163,311,372,212),(164,312,373,213),(165,313,374,214),(166,314,375,215),(167,315,376,216),(168,316,330,217),(169,317,331,218),(170,318,332,219),(171,319,333,220),(172,320,334,221),(173,321,335,222),(174,322,336,223),(175,323,337,224),(176,324,338,225),(177,325,339,226),(178,326,340,227),(179,327,341,228),(180,328,342,229),(181,329,343,230),(182,283,344,231),(183,284,345,232),(184,285,346,233),(185,286,347,234),(186,287,348,235),(187,288,349,189),(188,289,350,190)], [(1,336,109,174),(2,337,110,175),(3,338,111,176),(4,339,112,177),(5,340,113,178),(6,341,114,179),(7,342,115,180),(8,343,116,181),(9,344,117,182),(10,345,118,183),(11,346,119,184),(12,347,120,185),(13,348,121,186),(14,349,122,187),(15,350,123,188),(16,351,124,142),(17,352,125,143),(18,353,126,144),(19,354,127,145),(20,355,128,146),(21,356,129,147),(22,357,130,148),(23,358,131,149),(24,359,132,150),(25,360,133,151),(26,361,134,152),(27,362,135,153),(28,363,136,154),(29,364,137,155),(30,365,138,156),(31,366,139,157),(32,367,140,158),(33,368,141,159),(34,369,95,160),(35,370,96,161),(36,371,97,162),(37,372,98,163),(38,373,99,164),(39,374,100,165),(40,375,101,166),(41,376,102,167),(42,330,103,168),(43,331,104,169),(44,332,105,170),(45,333,106,171),(46,334,107,172),(47,335,108,173),(48,197,272,296),(49,198,273,297),(50,199,274,298),(51,200,275,299),(52,201,276,300),(53,202,277,301),(54,203,278,302),(55,204,279,303),(56,205,280,304),(57,206,281,305),(58,207,282,306),(59,208,236,307),(60,209,237,308),(61,210,238,309),(62,211,239,310),(63,212,240,311),(64,213,241,312),(65,214,242,313),(66,215,243,314),(67,216,244,315),(68,217,245,316),(69,218,246,317),(70,219,247,318),(71,220,248,319),(72,221,249,320),(73,222,250,321),(74,223,251,322),(75,224,252,323),(76,225,253,324),(77,226,254,325),(78,227,255,326),(79,228,256,327),(80,229,257,328),(81,230,258,329),(82,231,259,283),(83,232,260,284),(84,233,261,285),(85,234,262,286),(86,235,263,287),(87,189,264,288),(88,190,265,289),(89,191,266,290),(90,192,267,291),(91,193,268,292),(92,194,269,293),(93,195,270,294),(94,196,271,295)]])
235 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 47A | ··· | 47AT | 94A | ··· | 94AT | 188A | ··· | 188EH |
| order | 1 | 2 | 4 | 4 | 4 | 47 | ··· | 47 | 94 | ··· | 94 | 188 | ··· | 188 |
| size | 1 | 1 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 |
235 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 |
| type | + | + | - | |||
| image | C1 | C2 | C47 | C94 | Q8 | Q8×C47 |
| kernel | Q8×C47 | C188 | Q8 | C4 | C47 | C1 |
| # reps | 1 | 3 | 46 | 138 | 1 | 46 |
Matrix representation of Q8×C47 ►in GL2(𝔽941) generated by
| 630 | 0 |
| 0 | 630 |
| 361 | 939 |
| 232 | 580 |
| 730 | 498 |
| 417 | 211 |
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