direct product, metacyclic, nilpotent (class 2), monomial, 2-elementary
Aliases: C11×C4⋊C8, C4⋊C88, C44⋊3C8, C44.67D4, C44.12Q8, C42.2C22, C22.9M4(2), (C2×C4).4C44, (C4×C44).8C2, C2.2(C2×C88), (C2×C8).2C22, (C2×C88).4C2, C4.4(Q8×C11), (C2×C44).13C4, C22.12(C2×C8), C4.18(D4×C11), C22.11(C4⋊C4), C22.10(C2×C44), C2.3(C11×M4(2)), (C2×C44).136C22, C2.2(C11×C4⋊C4), (C2×C4).32(C2×C22), (C2×C22).39(C2×C4), SmallGroup(352,54)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C11×C4⋊C8
G = < a,b,c | a11=b4=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C11×C4⋊C8
►Regular action on 352 points
Generators in S352
(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)
(1 218 158 237)(2 219 159 238)(3 220 160 239)(4 210 161 240)(5 211 162 241)(6 212 163 242)(7 213 164 232)(8 214 165 233)(9 215 155 234)(10 216 156 235)(11 217 157 236)(12 317 342 271)(13 318 343 272)(14 319 344 273)(15 309 345 274)(16 310 346 275)(17 311 347 265)(18 312 348 266)(19 313 349 267)(20 314 350 268)(21 315 351 269)(22 316 352 270)(23 300 76 330)(24 301 77 320)(25 302 67 321)(26 303 68 322)(27 304 69 323)(28 305 70 324)(29 306 71 325)(30 307 72 326)(31 308 73 327)(32 298 74 328)(33 299 75 329)(34 294 64 336)(35 295 65 337)(36 296 66 338)(37 297 56 339)(38 287 57 340)(39 288 58 341)(40 289 59 331)(41 290 60 332)(42 291 61 333)(43 292 62 334)(44 293 63 335)(45 277 82 256)(46 278 83 257)(47 279 84 258)(48 280 85 259)(49 281 86 260)(50 282 87 261)(51 283 88 262)(52 284 78 263)(53 285 79 264)(54 286 80 254)(55 276 81 255)(89 171 135 192)(90 172 136 193)(91 173 137 194)(92 174 138 195)(93 175 139 196)(94 176 140 197)(95 166 141 198)(96 167 142 188)(97 168 143 189)(98 169 133 190)(99 170 134 191)(100 230 132 184)(101 231 122 185)(102 221 123 186)(103 222 124 187)(104 223 125 177)(105 224 126 178)(106 225 127 179)(107 226 128 180)(108 227 129 181)(109 228 130 182)(110 229 131 183)(111 205 150 247)(112 206 151 248)(113 207 152 249)(114 208 153 250)(115 209 154 251)(116 199 144 252)(117 200 145 253)(118 201 146 243)(119 202 147 244)(120 203 148 245)(121 204 149 246)
(1 317 141 325 149 254 131 292)(2 318 142 326 150 255 132 293)(3 319 143 327 151 256 122 294)(4 309 133 328 152 257 123 295)(5 310 134 329 153 258 124 296)(6 311 135 330 154 259 125 297)(7 312 136 320 144 260 126 287)(8 313 137 321 145 261 127 288)(9 314 138 322 146 262 128 289)(10 315 139 323 147 263 129 290)(11 316 140 324 148 264 130 291)(12 198 71 246 80 183 43 218)(13 188 72 247 81 184 44 219)(14 189 73 248 82 185 34 220)(15 190 74 249 83 186 35 210)(16 191 75 250 84 187 36 211)(17 192 76 251 85 177 37 212)(18 193 77 252 86 178 38 213)(19 194 67 253 87 179 39 214)(20 195 68 243 88 180 40 215)(21 196 69 244 78 181 41 216)(22 197 70 245 79 182 42 217)(23 209 48 223 56 242 347 171)(24 199 49 224 57 232 348 172)(25 200 50 225 58 233 349 173)(26 201 51 226 59 234 350 174)(27 202 52 227 60 235 351 175)(28 203 53 228 61 236 352 176)(29 204 54 229 62 237 342 166)(30 205 55 230 63 238 343 167)(31 206 45 231 64 239 344 168)(32 207 46 221 65 240 345 169)(33 208 47 222 66 241 346 170)(89 300 115 280 104 339 163 265)(90 301 116 281 105 340 164 266)(91 302 117 282 106 341 165 267)(92 303 118 283 107 331 155 268)(93 304 119 284 108 332 156 269)(94 305 120 285 109 333 157 270)(95 306 121 286 110 334 158 271)(96 307 111 276 100 335 159 272)(97 308 112 277 101 336 160 273)(98 298 113 278 102 337 161 274)(99 299 114 279 103 338 162 275)
G:=sub<Sym(352)| (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), (1,218,158,237)(2,219,159,238)(3,220,160,239)(4,210,161,240)(5,211,162,241)(6,212,163,242)(7,213,164,232)(8,214,165,233)(9,215,155,234)(10,216,156,235)(11,217,157,236)(12,317,342,271)(13,318,343,272)(14,319,344,273)(15,309,345,274)(16,310,346,275)(17,311,347,265)(18,312,348,266)(19,313,349,267)(20,314,350,268)(21,315,351,269)(22,316,352,270)(23,300,76,330)(24,301,77,320)(25,302,67,321)(26,303,68,322)(27,304,69,323)(28,305,70,324)(29,306,71,325)(30,307,72,326)(31,308,73,327)(32,298,74,328)(33,299,75,329)(34,294,64,336)(35,295,65,337)(36,296,66,338)(37,297,56,339)(38,287,57,340)(39,288,58,341)(40,289,59,331)(41,290,60,332)(42,291,61,333)(43,292,62,334)(44,293,63,335)(45,277,82,256)(46,278,83,257)(47,279,84,258)(48,280,85,259)(49,281,86,260)(50,282,87,261)(51,283,88,262)(52,284,78,263)(53,285,79,264)(54,286,80,254)(55,276,81,255)(89,171,135,192)(90,172,136,193)(91,173,137,194)(92,174,138,195)(93,175,139,196)(94,176,140,197)(95,166,141,198)(96,167,142,188)(97,168,143,189)(98,169,133,190)(99,170,134,191)(100,230,132,184)(101,231,122,185)(102,221,123,186)(103,222,124,187)(104,223,125,177)(105,224,126,178)(106,225,127,179)(107,226,128,180)(108,227,129,181)(109,228,130,182)(110,229,131,183)(111,205,150,247)(112,206,151,248)(113,207,152,249)(114,208,153,250)(115,209,154,251)(116,199,144,252)(117,200,145,253)(118,201,146,243)(119,202,147,244)(120,203,148,245)(121,204,149,246), (1,317,141,325,149,254,131,292)(2,318,142,326,150,255,132,293)(3,319,143,327,151,256,122,294)(4,309,133,328,152,257,123,295)(5,310,134,329,153,258,124,296)(6,311,135,330,154,259,125,297)(7,312,136,320,144,260,126,287)(8,313,137,321,145,261,127,288)(9,314,138,322,146,262,128,289)(10,315,139,323,147,263,129,290)(11,316,140,324,148,264,130,291)(12,198,71,246,80,183,43,218)(13,188,72,247,81,184,44,219)(14,189,73,248,82,185,34,220)(15,190,74,249,83,186,35,210)(16,191,75,250,84,187,36,211)(17,192,76,251,85,177,37,212)(18,193,77,252,86,178,38,213)(19,194,67,253,87,179,39,214)(20,195,68,243,88,180,40,215)(21,196,69,244,78,181,41,216)(22,197,70,245,79,182,42,217)(23,209,48,223,56,242,347,171)(24,199,49,224,57,232,348,172)(25,200,50,225,58,233,349,173)(26,201,51,226,59,234,350,174)(27,202,52,227,60,235,351,175)(28,203,53,228,61,236,352,176)(29,204,54,229,62,237,342,166)(30,205,55,230,63,238,343,167)(31,206,45,231,64,239,344,168)(32,207,46,221,65,240,345,169)(33,208,47,222,66,241,346,170)(89,300,115,280,104,339,163,265)(90,301,116,281,105,340,164,266)(91,302,117,282,106,341,165,267)(92,303,118,283,107,331,155,268)(93,304,119,284,108,332,156,269)(94,305,120,285,109,333,157,270)(95,306,121,286,110,334,158,271)(96,307,111,276,100,335,159,272)(97,308,112,277,101,336,160,273)(98,298,113,278,102,337,161,274)(99,299,114,279,103,338,162,275)>;
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), (1,218,158,237)(2,219,159,238)(3,220,160,239)(4,210,161,240)(5,211,162,241)(6,212,163,242)(7,213,164,232)(8,214,165,233)(9,215,155,234)(10,216,156,235)(11,217,157,236)(12,317,342,271)(13,318,343,272)(14,319,344,273)(15,309,345,274)(16,310,346,275)(17,311,347,265)(18,312,348,266)(19,313,349,267)(20,314,350,268)(21,315,351,269)(22,316,352,270)(23,300,76,330)(24,301,77,320)(25,302,67,321)(26,303,68,322)(27,304,69,323)(28,305,70,324)(29,306,71,325)(30,307,72,326)(31,308,73,327)(32,298,74,328)(33,299,75,329)(34,294,64,336)(35,295,65,337)(36,296,66,338)(37,297,56,339)(38,287,57,340)(39,288,58,341)(40,289,59,331)(41,290,60,332)(42,291,61,333)(43,292,62,334)(44,293,63,335)(45,277,82,256)(46,278,83,257)(47,279,84,258)(48,280,85,259)(49,281,86,260)(50,282,87,261)(51,283,88,262)(52,284,78,263)(53,285,79,264)(54,286,80,254)(55,276,81,255)(89,171,135,192)(90,172,136,193)(91,173,137,194)(92,174,138,195)(93,175,139,196)(94,176,140,197)(95,166,141,198)(96,167,142,188)(97,168,143,189)(98,169,133,190)(99,170,134,191)(100,230,132,184)(101,231,122,185)(102,221,123,186)(103,222,124,187)(104,223,125,177)(105,224,126,178)(106,225,127,179)(107,226,128,180)(108,227,129,181)(109,228,130,182)(110,229,131,183)(111,205,150,247)(112,206,151,248)(113,207,152,249)(114,208,153,250)(115,209,154,251)(116,199,144,252)(117,200,145,253)(118,201,146,243)(119,202,147,244)(120,203,148,245)(121,204,149,246), (1,317,141,325,149,254,131,292)(2,318,142,326,150,255,132,293)(3,319,143,327,151,256,122,294)(4,309,133,328,152,257,123,295)(5,310,134,329,153,258,124,296)(6,311,135,330,154,259,125,297)(7,312,136,320,144,260,126,287)(8,313,137,321,145,261,127,288)(9,314,138,322,146,262,128,289)(10,315,139,323,147,263,129,290)(11,316,140,324,148,264,130,291)(12,198,71,246,80,183,43,218)(13,188,72,247,81,184,44,219)(14,189,73,248,82,185,34,220)(15,190,74,249,83,186,35,210)(16,191,75,250,84,187,36,211)(17,192,76,251,85,177,37,212)(18,193,77,252,86,178,38,213)(19,194,67,253,87,179,39,214)(20,195,68,243,88,180,40,215)(21,196,69,244,78,181,41,216)(22,197,70,245,79,182,42,217)(23,209,48,223,56,242,347,171)(24,199,49,224,57,232,348,172)(25,200,50,225,58,233,349,173)(26,201,51,226,59,234,350,174)(27,202,52,227,60,235,351,175)(28,203,53,228,61,236,352,176)(29,204,54,229,62,237,342,166)(30,205,55,230,63,238,343,167)(31,206,45,231,64,239,344,168)(32,207,46,221,65,240,345,169)(33,208,47,222,66,241,346,170)(89,300,115,280,104,339,163,265)(90,301,116,281,105,340,164,266)(91,302,117,282,106,341,165,267)(92,303,118,283,107,331,155,268)(93,304,119,284,108,332,156,269)(94,305,120,285,109,333,157,270)(95,306,121,286,110,334,158,271)(96,307,111,276,100,335,159,272)(97,308,112,277,101,336,160,273)(98,298,113,278,102,337,161,274)(99,299,114,279,103,338,162,275) );
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)], [(1,218,158,237),(2,219,159,238),(3,220,160,239),(4,210,161,240),(5,211,162,241),(6,212,163,242),(7,213,164,232),(8,214,165,233),(9,215,155,234),(10,216,156,235),(11,217,157,236),(12,317,342,271),(13,318,343,272),(14,319,344,273),(15,309,345,274),(16,310,346,275),(17,311,347,265),(18,312,348,266),(19,313,349,267),(20,314,350,268),(21,315,351,269),(22,316,352,270),(23,300,76,330),(24,301,77,320),(25,302,67,321),(26,303,68,322),(27,304,69,323),(28,305,70,324),(29,306,71,325),(30,307,72,326),(31,308,73,327),(32,298,74,328),(33,299,75,329),(34,294,64,336),(35,295,65,337),(36,296,66,338),(37,297,56,339),(38,287,57,340),(39,288,58,341),(40,289,59,331),(41,290,60,332),(42,291,61,333),(43,292,62,334),(44,293,63,335),(45,277,82,256),(46,278,83,257),(47,279,84,258),(48,280,85,259),(49,281,86,260),(50,282,87,261),(51,283,88,262),(52,284,78,263),(53,285,79,264),(54,286,80,254),(55,276,81,255),(89,171,135,192),(90,172,136,193),(91,173,137,194),(92,174,138,195),(93,175,139,196),(94,176,140,197),(95,166,141,198),(96,167,142,188),(97,168,143,189),(98,169,133,190),(99,170,134,191),(100,230,132,184),(101,231,122,185),(102,221,123,186),(103,222,124,187),(104,223,125,177),(105,224,126,178),(106,225,127,179),(107,226,128,180),(108,227,129,181),(109,228,130,182),(110,229,131,183),(111,205,150,247),(112,206,151,248),(113,207,152,249),(114,208,153,250),(115,209,154,251),(116,199,144,252),(117,200,145,253),(118,201,146,243),(119,202,147,244),(120,203,148,245),(121,204,149,246)], [(1,317,141,325,149,254,131,292),(2,318,142,326,150,255,132,293),(3,319,143,327,151,256,122,294),(4,309,133,328,152,257,123,295),(5,310,134,329,153,258,124,296),(6,311,135,330,154,259,125,297),(7,312,136,320,144,260,126,287),(8,313,137,321,145,261,127,288),(9,314,138,322,146,262,128,289),(10,315,139,323,147,263,129,290),(11,316,140,324,148,264,130,291),(12,198,71,246,80,183,43,218),(13,188,72,247,81,184,44,219),(14,189,73,248,82,185,34,220),(15,190,74,249,83,186,35,210),(16,191,75,250,84,187,36,211),(17,192,76,251,85,177,37,212),(18,193,77,252,86,178,38,213),(19,194,67,253,87,179,39,214),(20,195,68,243,88,180,40,215),(21,196,69,244,78,181,41,216),(22,197,70,245,79,182,42,217),(23,209,48,223,56,242,347,171),(24,199,49,224,57,232,348,172),(25,200,50,225,58,233,349,173),(26,201,51,226,59,234,350,174),(27,202,52,227,60,235,351,175),(28,203,53,228,61,236,352,176),(29,204,54,229,62,237,342,166),(30,205,55,230,63,238,343,167),(31,206,45,231,64,239,344,168),(32,207,46,221,65,240,345,169),(33,208,47,222,66,241,346,170),(89,300,115,280,104,339,163,265),(90,301,116,281,105,340,164,266),(91,302,117,282,106,341,165,267),(92,303,118,283,107,331,155,268),(93,304,119,284,108,332,156,269),(94,305,120,285,109,333,157,270),(95,306,121,286,110,334,158,271),(96,307,111,276,100,335,159,272),(97,308,112,277,101,336,160,273),(98,298,113,278,102,337,161,274),(99,299,114,279,103,338,162,275)]])
220 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 8A | ··· | 8H | 11A | ··· | 11J | 22A | ··· | 22AD | 44A | ··· | 44AN | 44AO | ··· | 44CB | 88A | ··· | 88CB |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 |
220 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | |||||||||||
| image | C1 | C2 | C2 | C4 | C8 | C11 | C22 | C22 | C44 | C88 | D4 | Q8 | M4(2) | D4×C11 | Q8×C11 | C11×M4(2) |
| kernel | C11×C4⋊C8 | C4×C44 | C2×C88 | C2×C44 | C44 | C4⋊C8 | C42 | C2×C8 | C2×C4 | C4 | C44 | C44 | C22 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 4 | 8 | 10 | 10 | 20 | 40 | 80 | 1 | 1 | 2 | 10 | 10 | 20 |
Matrix representation of C11×C4⋊C8 ►in GL3(𝔽89) generated by
| 1 | 0 | 0 |
| 0 | 67 | 0 |
| 0 | 0 | 67 |
| 88 | 0 | 0 |
| 0 | 34 | 0 |
| 0 | 0 | 55 |
| 37 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
G:=sub<GL(3,GF(89))| [1,0,0,0,67,0,0,0,67],[88,0,0,0,34,0,0,0,55],[37,0,0,0,0,1,0,1,0] >;
C11×C4⋊C8 in GAP, Magma, Sage, TeX
C_{11}\times C_4\rtimes C_8 % in TeX
G:=Group("C11xC4:C8"); // GroupNames label
G:=SmallGroup(352,54);
// by ID
G=gap.SmallGroup(352,54);
# by ID
G:=PCGroup([6,-2,-2,-11,-2,-2,-2,528,553,271,88]);
// Polycyclic
G:=Group<a,b,c|a^11=b^4=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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