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## G = Q8×C46order 368 = 24·23

### Direct product of C46 and Q8

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

Aliases: Q8×C46, C92.20C22, C46.12C23, (C2×C92).9C2, (C2×C4).3C46, C4.4(C2×C46), C2.2(C22×C46), C22.4(C2×C46), (C2×C46).15C22, SmallGroup(368,39)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2 — Q8×C46
 Chief series C1 — C2 — C46 — C92 — Q8×C23 — Q8×C46
 Lower central C1 — C2 — Q8×C46
 Upper central C1 — C2×C46 — Q8×C46

Generators and relations for Q8×C46
G = < a,b,c | a46=b4=1, c2=b2, ab=ba, ac=ca, cbc-1=b-1 >

Smallest permutation representation of Q8×C46
Regular action on 368 points
Generators in S368
(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)
(1 72 245 314)(2 73 246 315)(3 74 247 316)(4 75 248 317)(5 76 249 318)(6 77 250 319)(7 78 251 320)(8 79 252 321)(9 80 253 322)(10 81 254 277)(11 82 255 278)(12 83 256 279)(13 84 257 280)(14 85 258 281)(15 86 259 282)(16 87 260 283)(17 88 261 284)(18 89 262 285)(19 90 263 286)(20 91 264 287)(21 92 265 288)(22 47 266 289)(23 48 267 290)(24 49 268 291)(25 50 269 292)(26 51 270 293)(27 52 271 294)(28 53 272 295)(29 54 273 296)(30 55 274 297)(31 56 275 298)(32 57 276 299)(33 58 231 300)(34 59 232 301)(35 60 233 302)(36 61 234 303)(37 62 235 304)(38 63 236 305)(39 64 237 306)(40 65 238 307)(41 66 239 308)(42 67 240 309)(43 68 241 310)(44 69 242 311)(45 70 243 312)(46 71 244 313)(93 179 347 216)(94 180 348 217)(95 181 349 218)(96 182 350 219)(97 183 351 220)(98 184 352 221)(99 139 353 222)(100 140 354 223)(101 141 355 224)(102 142 356 225)(103 143 357 226)(104 144 358 227)(105 145 359 228)(106 146 360 229)(107 147 361 230)(108 148 362 185)(109 149 363 186)(110 150 364 187)(111 151 365 188)(112 152 366 189)(113 153 367 190)(114 154 368 191)(115 155 323 192)(116 156 324 193)(117 157 325 194)(118 158 326 195)(119 159 327 196)(120 160 328 197)(121 161 329 198)(122 162 330 199)(123 163 331 200)(124 164 332 201)(125 165 333 202)(126 166 334 203)(127 167 335 204)(128 168 336 205)(129 169 337 206)(130 170 338 207)(131 171 339 208)(132 172 340 209)(133 173 341 210)(134 174 342 211)(135 175 343 212)(136 176 344 213)(137 177 345 214)(138 178 346 215)
(1 199 245 162)(2 200 246 163)(3 201 247 164)(4 202 248 165)(5 203 249 166)(6 204 250 167)(7 205 251 168)(8 206 252 169)(9 207 253 170)(10 208 254 171)(11 209 255 172)(12 210 256 173)(13 211 257 174)(14 212 258 175)(15 213 259 176)(16 214 260 177)(17 215 261 178)(18 216 262 179)(19 217 263 180)(20 218 264 181)(21 219 265 182)(22 220 266 183)(23 221 267 184)(24 222 268 139)(25 223 269 140)(26 224 270 141)(27 225 271 142)(28 226 272 143)(29 227 273 144)(30 228 274 145)(31 229 275 146)(32 230 276 147)(33 185 231 148)(34 186 232 149)(35 187 233 150)(36 188 234 151)(37 189 235 152)(38 190 236 153)(39 191 237 154)(40 192 238 155)(41 193 239 156)(42 194 240 157)(43 195 241 158)(44 196 242 159)(45 197 243 160)(46 198 244 161)(47 351 289 97)(48 352 290 98)(49 353 291 99)(50 354 292 100)(51 355 293 101)(52 356 294 102)(53 357 295 103)(54 358 296 104)(55 359 297 105)(56 360 298 106)(57 361 299 107)(58 362 300 108)(59 363 301 109)(60 364 302 110)(61 365 303 111)(62 366 304 112)(63 367 305 113)(64 368 306 114)(65 323 307 115)(66 324 308 116)(67 325 309 117)(68 326 310 118)(69 327 311 119)(70 328 312 120)(71 329 313 121)(72 330 314 122)(73 331 315 123)(74 332 316 124)(75 333 317 125)(76 334 318 126)(77 335 319 127)(78 336 320 128)(79 337 321 129)(80 338 322 130)(81 339 277 131)(82 340 278 132)(83 341 279 133)(84 342 280 134)(85 343 281 135)(86 344 282 136)(87 345 283 137)(88 346 284 138)(89 347 285 93)(90 348 286 94)(91 349 287 95)(92 350 288 96)

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

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

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

230 conjugacy classes

 class 1 2A 2B 2C 4A ··· 4F 23A ··· 23V 46A ··· 46BN 92A ··· 92EB order 1 2 2 2 4 ··· 4 23 ··· 23 46 ··· 46 92 ··· 92 size 1 1 1 1 2 ··· 2 1 ··· 1 1 ··· 1 2 ··· 2

230 irreducible representations

 dim 1 1 1 1 1 1 2 2 type + + + - image C1 C2 C2 C23 C46 C46 Q8 Q8×C23 kernel Q8×C46 C2×C92 Q8×C23 C2×Q8 C2×C4 Q8 C46 C2 # reps 1 3 4 22 66 88 2 44

Matrix representation of Q8×C46 in GL3(𝔽277) generated by

 276 0 0 0 247 0 0 0 247
,
 1 0 0 0 54 275 0 212 223
,
 1 0 0 0 13 162 0 146 264
G:=sub<GL(3,GF(277))| [276,0,0,0,247,0,0,0,247],[1,0,0,0,54,212,0,275,223],[1,0,0,0,13,146,0,162,264] >;

Q8×C46 in GAP, Magma, Sage, TeX

Q_8\times C_{46}
% in TeX

G:=Group("Q8xC46");
// GroupNames label

G:=SmallGroup(368,39);
// by ID

G=gap.SmallGroup(368,39);
# by ID

G:=PCGroup([5,-2,-2,-2,-23,-2,920,1861,926]);
// Polycyclic

G:=Group<a,b,c|a^46=b^4=1,c^2=b^2,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

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