metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22.5C42, C23.27D22, C22.11D44, C22.3Dic22, (C2×C44)⋊3C4, C22.9(C4⋊C4), (C2×C22).4Q8, (C2×C4)⋊2Dic11, (C2×C22).32D4, C2.2(D22⋊C4), (C2×Dic11)⋊2C4, C11⋊(C2.C42), (C22×C44).1C2, C2.5(C4×Dic11), C2.2(C44⋊C4), (C22×C4).2D11, C22.12(C4×D11), C22.11(C22⋊C4), C2.2(Dic11⋊C4), C2.2(C23.D11), C22.16(C11⋊D4), (C22×C22).31C22, (C22×Dic11).1C2, C22.10(C2×Dic11), (C2×C22).13(C2×C4), SmallGroup(352,37)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22.C42
G = < a,b,c | a22=b4=c4=1, bab-1=a-1, ac=ca, cbc-1=a11b >
Subgroups: 330 in 76 conjugacy classes, 45 normal (19 characteristic)
C1, C2, C2, C4, C22, C22, C2×C4, C2×C4, C23, C11, C22×C4, C22×C4, C22, C22, C2.C42, Dic11, C44, C2×C22, C2×C22, C2×Dic11, C2×Dic11, C2×C44, C2×C44, C22×C22, C22×Dic11, C22×C44, C22.C42
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C42, C22⋊C4, C4⋊C4, D11, C2.C42, Dic11, D22, Dic22, C4×D11, D44, C2×Dic11, C11⋊D4, C4×Dic11, Dic11⋊C4, C44⋊C4, D22⋊C4, C23.D11, C22.C42
►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)
(1 233 45 196)(2 232 46 195)(3 231 47 194)(4 230 48 193)(5 229 49 192)(6 228 50 191)(7 227 51 190)(8 226 52 189)(9 225 53 188)(10 224 54 187)(11 223 55 186)(12 222 56 185)(13 221 57 184)(14 242 58 183)(15 241 59 182)(16 240 60 181)(17 239 61 180)(18 238 62 179)(19 237 63 178)(20 236 64 177)(21 235 65 198)(22 234 66 197)(23 260 72 217)(24 259 73 216)(25 258 74 215)(26 257 75 214)(27 256 76 213)(28 255 77 212)(29 254 78 211)(30 253 79 210)(31 252 80 209)(32 251 81 208)(33 250 82 207)(34 249 83 206)(35 248 84 205)(36 247 85 204)(37 246 86 203)(38 245 87 202)(39 244 88 201)(40 243 67 200)(41 264 68 199)(42 263 69 220)(43 262 70 219)(44 261 71 218)(89 325 142 276)(90 324 143 275)(91 323 144 274)(92 322 145 273)(93 321 146 272)(94 320 147 271)(95 319 148 270)(96 318 149 269)(97 317 150 268)(98 316 151 267)(99 315 152 266)(100 314 153 265)(101 313 154 286)(102 312 133 285)(103 311 134 284)(104 310 135 283)(105 309 136 282)(106 330 137 281)(107 329 138 280)(108 328 139 279)(109 327 140 278)(110 326 141 277)(111 352 161 307)(112 351 162 306)(113 350 163 305)(114 349 164 304)(115 348 165 303)(116 347 166 302)(117 346 167 301)(118 345 168 300)(119 344 169 299)(120 343 170 298)(121 342 171 297)(122 341 172 296)(123 340 173 295)(124 339 174 294)(125 338 175 293)(126 337 176 292)(127 336 155 291)(128 335 156 290)(129 334 157 289)(130 333 158 288)(131 332 159 287)(132 331 160 308)
(1 117 26 107)(2 118 27 108)(3 119 28 109)(4 120 29 110)(5 121 30 89)(6 122 31 90)(7 123 32 91)(8 124 33 92)(9 125 34 93)(10 126 35 94)(11 127 36 95)(12 128 37 96)(13 129 38 97)(14 130 39 98)(15 131 40 99)(16 132 41 100)(17 111 42 101)(18 112 43 102)(19 113 44 103)(20 114 23 104)(21 115 24 105)(22 116 25 106)(45 167 75 138)(46 168 76 139)(47 169 77 140)(48 170 78 141)(49 171 79 142)(50 172 80 143)(51 173 81 144)(52 174 82 145)(53 175 83 146)(54 176 84 147)(55 155 85 148)(56 156 86 149)(57 157 87 150)(58 158 88 151)(59 159 67 152)(60 160 68 153)(61 161 69 154)(62 162 70 133)(63 163 71 134)(64 164 72 135)(65 165 73 136)(66 166 74 137)(177 293 217 272)(178 294 218 273)(179 295 219 274)(180 296 220 275)(181 297 199 276)(182 298 200 277)(183 299 201 278)(184 300 202 279)(185 301 203 280)(186 302 204 281)(187 303 205 282)(188 304 206 283)(189 305 207 284)(190 306 208 285)(191 307 209 286)(192 308 210 265)(193 287 211 266)(194 288 212 267)(195 289 213 268)(196 290 214 269)(197 291 215 270)(198 292 216 271)(221 345 245 328)(222 346 246 329)(223 347 247 330)(224 348 248 309)(225 349 249 310)(226 350 250 311)(227 351 251 312)(228 352 252 313)(229 331 253 314)(230 332 254 315)(231 333 255 316)(232 334 256 317)(233 335 257 318)(234 336 258 319)(235 337 259 320)(236 338 260 321)(237 339 261 322)(238 340 262 323)(239 341 263 324)(240 342 264 325)(241 343 243 326)(242 344 244 327)
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), (1,233,45,196)(2,232,46,195)(3,231,47,194)(4,230,48,193)(5,229,49,192)(6,228,50,191)(7,227,51,190)(8,226,52,189)(9,225,53,188)(10,224,54,187)(11,223,55,186)(12,222,56,185)(13,221,57,184)(14,242,58,183)(15,241,59,182)(16,240,60,181)(17,239,61,180)(18,238,62,179)(19,237,63,178)(20,236,64,177)(21,235,65,198)(22,234,66,197)(23,260,72,217)(24,259,73,216)(25,258,74,215)(26,257,75,214)(27,256,76,213)(28,255,77,212)(29,254,78,211)(30,253,79,210)(31,252,80,209)(32,251,81,208)(33,250,82,207)(34,249,83,206)(35,248,84,205)(36,247,85,204)(37,246,86,203)(38,245,87,202)(39,244,88,201)(40,243,67,200)(41,264,68,199)(42,263,69,220)(43,262,70,219)(44,261,71,218)(89,325,142,276)(90,324,143,275)(91,323,144,274)(92,322,145,273)(93,321,146,272)(94,320,147,271)(95,319,148,270)(96,318,149,269)(97,317,150,268)(98,316,151,267)(99,315,152,266)(100,314,153,265)(101,313,154,286)(102,312,133,285)(103,311,134,284)(104,310,135,283)(105,309,136,282)(106,330,137,281)(107,329,138,280)(108,328,139,279)(109,327,140,278)(110,326,141,277)(111,352,161,307)(112,351,162,306)(113,350,163,305)(114,349,164,304)(115,348,165,303)(116,347,166,302)(117,346,167,301)(118,345,168,300)(119,344,169,299)(120,343,170,298)(121,342,171,297)(122,341,172,296)(123,340,173,295)(124,339,174,294)(125,338,175,293)(126,337,176,292)(127,336,155,291)(128,335,156,290)(129,334,157,289)(130,333,158,288)(131,332,159,287)(132,331,160,308), (1,117,26,107)(2,118,27,108)(3,119,28,109)(4,120,29,110)(5,121,30,89)(6,122,31,90)(7,123,32,91)(8,124,33,92)(9,125,34,93)(10,126,35,94)(11,127,36,95)(12,128,37,96)(13,129,38,97)(14,130,39,98)(15,131,40,99)(16,132,41,100)(17,111,42,101)(18,112,43,102)(19,113,44,103)(20,114,23,104)(21,115,24,105)(22,116,25,106)(45,167,75,138)(46,168,76,139)(47,169,77,140)(48,170,78,141)(49,171,79,142)(50,172,80,143)(51,173,81,144)(52,174,82,145)(53,175,83,146)(54,176,84,147)(55,155,85,148)(56,156,86,149)(57,157,87,150)(58,158,88,151)(59,159,67,152)(60,160,68,153)(61,161,69,154)(62,162,70,133)(63,163,71,134)(64,164,72,135)(65,165,73,136)(66,166,74,137)(177,293,217,272)(178,294,218,273)(179,295,219,274)(180,296,220,275)(181,297,199,276)(182,298,200,277)(183,299,201,278)(184,300,202,279)(185,301,203,280)(186,302,204,281)(187,303,205,282)(188,304,206,283)(189,305,207,284)(190,306,208,285)(191,307,209,286)(192,308,210,265)(193,287,211,266)(194,288,212,267)(195,289,213,268)(196,290,214,269)(197,291,215,270)(198,292,216,271)(221,345,245,328)(222,346,246,329)(223,347,247,330)(224,348,248,309)(225,349,249,310)(226,350,250,311)(227,351,251,312)(228,352,252,313)(229,331,253,314)(230,332,254,315)(231,333,255,316)(232,334,256,317)(233,335,257,318)(234,336,258,319)(235,337,259,320)(236,338,260,321)(237,339,261,322)(238,340,262,323)(239,341,263,324)(240,342,264,325)(241,343,243,326)(242,344,244,327)>;
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), (1,233,45,196)(2,232,46,195)(3,231,47,194)(4,230,48,193)(5,229,49,192)(6,228,50,191)(7,227,51,190)(8,226,52,189)(9,225,53,188)(10,224,54,187)(11,223,55,186)(12,222,56,185)(13,221,57,184)(14,242,58,183)(15,241,59,182)(16,240,60,181)(17,239,61,180)(18,238,62,179)(19,237,63,178)(20,236,64,177)(21,235,65,198)(22,234,66,197)(23,260,72,217)(24,259,73,216)(25,258,74,215)(26,257,75,214)(27,256,76,213)(28,255,77,212)(29,254,78,211)(30,253,79,210)(31,252,80,209)(32,251,81,208)(33,250,82,207)(34,249,83,206)(35,248,84,205)(36,247,85,204)(37,246,86,203)(38,245,87,202)(39,244,88,201)(40,243,67,200)(41,264,68,199)(42,263,69,220)(43,262,70,219)(44,261,71,218)(89,325,142,276)(90,324,143,275)(91,323,144,274)(92,322,145,273)(93,321,146,272)(94,320,147,271)(95,319,148,270)(96,318,149,269)(97,317,150,268)(98,316,151,267)(99,315,152,266)(100,314,153,265)(101,313,154,286)(102,312,133,285)(103,311,134,284)(104,310,135,283)(105,309,136,282)(106,330,137,281)(107,329,138,280)(108,328,139,279)(109,327,140,278)(110,326,141,277)(111,352,161,307)(112,351,162,306)(113,350,163,305)(114,349,164,304)(115,348,165,303)(116,347,166,302)(117,346,167,301)(118,345,168,300)(119,344,169,299)(120,343,170,298)(121,342,171,297)(122,341,172,296)(123,340,173,295)(124,339,174,294)(125,338,175,293)(126,337,176,292)(127,336,155,291)(128,335,156,290)(129,334,157,289)(130,333,158,288)(131,332,159,287)(132,331,160,308), (1,117,26,107)(2,118,27,108)(3,119,28,109)(4,120,29,110)(5,121,30,89)(6,122,31,90)(7,123,32,91)(8,124,33,92)(9,125,34,93)(10,126,35,94)(11,127,36,95)(12,128,37,96)(13,129,38,97)(14,130,39,98)(15,131,40,99)(16,132,41,100)(17,111,42,101)(18,112,43,102)(19,113,44,103)(20,114,23,104)(21,115,24,105)(22,116,25,106)(45,167,75,138)(46,168,76,139)(47,169,77,140)(48,170,78,141)(49,171,79,142)(50,172,80,143)(51,173,81,144)(52,174,82,145)(53,175,83,146)(54,176,84,147)(55,155,85,148)(56,156,86,149)(57,157,87,150)(58,158,88,151)(59,159,67,152)(60,160,68,153)(61,161,69,154)(62,162,70,133)(63,163,71,134)(64,164,72,135)(65,165,73,136)(66,166,74,137)(177,293,217,272)(178,294,218,273)(179,295,219,274)(180,296,220,275)(181,297,199,276)(182,298,200,277)(183,299,201,278)(184,300,202,279)(185,301,203,280)(186,302,204,281)(187,303,205,282)(188,304,206,283)(189,305,207,284)(190,306,208,285)(191,307,209,286)(192,308,210,265)(193,287,211,266)(194,288,212,267)(195,289,213,268)(196,290,214,269)(197,291,215,270)(198,292,216,271)(221,345,245,328)(222,346,246,329)(223,347,247,330)(224,348,248,309)(225,349,249,310)(226,350,250,311)(227,351,251,312)(228,352,252,313)(229,331,253,314)(230,332,254,315)(231,333,255,316)(232,334,256,317)(233,335,257,318)(234,336,258,319)(235,337,259,320)(236,338,260,321)(237,339,261,322)(238,340,262,323)(239,341,263,324)(240,342,264,325)(241,343,243,326)(242,344,244,327) );
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)], [(1,233,45,196),(2,232,46,195),(3,231,47,194),(4,230,48,193),(5,229,49,192),(6,228,50,191),(7,227,51,190),(8,226,52,189),(9,225,53,188),(10,224,54,187),(11,223,55,186),(12,222,56,185),(13,221,57,184),(14,242,58,183),(15,241,59,182),(16,240,60,181),(17,239,61,180),(18,238,62,179),(19,237,63,178),(20,236,64,177),(21,235,65,198),(22,234,66,197),(23,260,72,217),(24,259,73,216),(25,258,74,215),(26,257,75,214),(27,256,76,213),(28,255,77,212),(29,254,78,211),(30,253,79,210),(31,252,80,209),(32,251,81,208),(33,250,82,207),(34,249,83,206),(35,248,84,205),(36,247,85,204),(37,246,86,203),(38,245,87,202),(39,244,88,201),(40,243,67,200),(41,264,68,199),(42,263,69,220),(43,262,70,219),(44,261,71,218),(89,325,142,276),(90,324,143,275),(91,323,144,274),(92,322,145,273),(93,321,146,272),(94,320,147,271),(95,319,148,270),(96,318,149,269),(97,317,150,268),(98,316,151,267),(99,315,152,266),(100,314,153,265),(101,313,154,286),(102,312,133,285),(103,311,134,284),(104,310,135,283),(105,309,136,282),(106,330,137,281),(107,329,138,280),(108,328,139,279),(109,327,140,278),(110,326,141,277),(111,352,161,307),(112,351,162,306),(113,350,163,305),(114,349,164,304),(115,348,165,303),(116,347,166,302),(117,346,167,301),(118,345,168,300),(119,344,169,299),(120,343,170,298),(121,342,171,297),(122,341,172,296),(123,340,173,295),(124,339,174,294),(125,338,175,293),(126,337,176,292),(127,336,155,291),(128,335,156,290),(129,334,157,289),(130,333,158,288),(131,332,159,287),(132,331,160,308)], [(1,117,26,107),(2,118,27,108),(3,119,28,109),(4,120,29,110),(5,121,30,89),(6,122,31,90),(7,123,32,91),(8,124,33,92),(9,125,34,93),(10,126,35,94),(11,127,36,95),(12,128,37,96),(13,129,38,97),(14,130,39,98),(15,131,40,99),(16,132,41,100),(17,111,42,101),(18,112,43,102),(19,113,44,103),(20,114,23,104),(21,115,24,105),(22,116,25,106),(45,167,75,138),(46,168,76,139),(47,169,77,140),(48,170,78,141),(49,171,79,142),(50,172,80,143),(51,173,81,144),(52,174,82,145),(53,175,83,146),(54,176,84,147),(55,155,85,148),(56,156,86,149),(57,157,87,150),(58,158,88,151),(59,159,67,152),(60,160,68,153),(61,161,69,154),(62,162,70,133),(63,163,71,134),(64,164,72,135),(65,165,73,136),(66,166,74,137),(177,293,217,272),(178,294,218,273),(179,295,219,274),(180,296,220,275),(181,297,199,276),(182,298,200,277),(183,299,201,278),(184,300,202,279),(185,301,203,280),(186,302,204,281),(187,303,205,282),(188,304,206,283),(189,305,207,284),(190,306,208,285),(191,307,209,286),(192,308,210,265),(193,287,211,266),(194,288,212,267),(195,289,213,268),(196,290,214,269),(197,291,215,270),(198,292,216,271),(221,345,245,328),(222,346,246,329),(223,347,247,330),(224,348,248,309),(225,349,249,310),(226,350,250,311),(227,351,251,312),(228,352,252,313),(229,331,253,314),(230,332,254,315),(231,333,255,316),(232,334,256,317),(233,335,257,318),(234,336,258,319),(235,337,259,320),(236,338,260,321),(237,339,261,322),(238,340,262,323),(239,341,263,324),(240,342,264,325),(241,343,243,326),(242,344,244,327)]])
100 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 11A | ··· | 11E | 22A | ··· | 22AI | 44A | ··· | 44AN |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 22 | ··· | 22 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | + | - | + | ||||
| image | C1 | C2 | C2 | C4 | C4 | D4 | Q8 | D11 | Dic11 | D22 | Dic22 | C4×D11 | D44 | C11⋊D4 |
| kernel | C22.C42 | C22×Dic11 | C22×C44 | C2×Dic11 | C2×C44 | C2×C22 | C2×C22 | C22×C4 | C2×C4 | C23 | C22 | C22 | C22 | C22 |
| # reps | 1 | 2 | 1 | 8 | 4 | 3 | 1 | 5 | 10 | 5 | 10 | 20 | 10 | 20 |
Matrix representation of C22.C42 ►in GL4(𝔽89) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 5 | 5 |
| 0 | 0 | 84 | 13 |
| 55 | 0 | 0 | 0 |
| 0 | 34 | 0 | 0 |
| 0 | 0 | 9 | 54 |
| 0 | 0 | 15 | 80 |
| 1 | 0 | 0 | 0 |
| 0 | 34 | 0 | 0 |
| 0 | 0 | 31 | 28 |
| 0 | 0 | 61 | 58 |
G:=sub<GL(4,GF(89))| [1,0,0,0,0,1,0,0,0,0,5,84,0,0,5,13],[55,0,0,0,0,34,0,0,0,0,9,15,0,0,54,80],[1,0,0,0,0,34,0,0,0,0,31,61,0,0,28,58] >;
C22.C42 in GAP, Magma, Sage, TeX
C_{22}.C_4^2 % in TeX
G:=Group("C22.C4^2"); // GroupNames label
G:=SmallGroup(352,37);
// by ID
G=gap.SmallGroup(352,37);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,24,217,55,11525]);
// Polycyclic
G:=Group<a,b,c|a^22=b^4=c^4=1,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^11*b>;
// generators/relations