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## G = C4⋊C4×C22order 352 = 25·11

### Direct product of C22 and C4⋊C4

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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2 — C4⋊C4×C22
 Chief series C1 — C2 — C22 — C2×C22 — C2×C44 — C11×C4⋊C4 — C4⋊C4×C22
 Lower central C1 — C2 — C4⋊C4×C22
 Upper central C1 — C22×C22 — C4⋊C4×C22

Generators and relations for C4⋊C4×C22
G = < a,b,c | a22=b4=c4=1, ab=ba, ac=ca, cbc-1=b-1 >

Subgroups: 108 in 92 conjugacy classes, 76 normal (16 characteristic)
C1, C2, C2, C4, C4, C22, C22, C2×C4, C2×C4, C23, C11, C4⋊C4, C22×C4, C22×C4, C22, C22, C2×C4⋊C4, C44, C44, C2×C22, C2×C22, C2×C44, C2×C44, C22×C22, C11×C4⋊C4, C22×C44, C22×C44, C4⋊C4×C22
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, C11, C4⋊C4, C22×C4, C2×D4, C2×Q8, C22, C2×C4⋊C4, C44, C2×C22, C2×C44, D4×C11, Q8×C11, C22×C22, C11×C4⋊C4, C22×C44, D4×C22, Q8×C22, C4⋊C4×C22

Smallest permutation representation of C4⋊C4×C22
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)
(1 227 208 308)(2 228 209 287)(3 229 210 288)(4 230 211 289)(5 231 212 290)(6 232 213 291)(7 233 214 292)(8 234 215 293)(9 235 216 294)(10 236 217 295)(11 237 218 296)(12 238 219 297)(13 239 220 298)(14 240 199 299)(15 241 200 300)(16 242 201 301)(17 221 202 302)(18 222 203 303)(19 223 204 304)(20 224 205 305)(21 225 206 306)(22 226 207 307)(23 338 112 266)(24 339 113 267)(25 340 114 268)(26 341 115 269)(27 342 116 270)(28 343 117 271)(29 344 118 272)(30 345 119 273)(31 346 120 274)(32 347 121 275)(33 348 122 276)(34 349 123 277)(35 350 124 278)(36 351 125 279)(37 352 126 280)(38 331 127 281)(39 332 128 282)(40 333 129 283)(41 334 130 284)(42 335 131 285)(43 336 132 286)(44 337 111 265)(45 245 144 189)(46 246 145 190)(47 247 146 191)(48 248 147 192)(49 249 148 193)(50 250 149 194)(51 251 150 195)(52 252 151 196)(53 253 152 197)(54 254 153 198)(55 255 154 177)(56 256 133 178)(57 257 134 179)(58 258 135 180)(59 259 136 181)(60 260 137 182)(61 261 138 183)(62 262 139 184)(63 263 140 185)(64 264 141 186)(65 243 142 187)(66 244 143 188)(67 324 175 101)(68 325 176 102)(69 326 155 103)(70 327 156 104)(71 328 157 105)(72 329 158 106)(73 330 159 107)(74 309 160 108)(75 310 161 109)(76 311 162 110)(77 312 163 89)(78 313 164 90)(79 314 165 91)(80 315 166 92)(81 316 167 93)(82 317 168 94)(83 318 169 95)(84 319 170 96)(85 320 171 97)(86 321 172 98)(87 322 173 99)(88 323 174 100)
(1 93 28 187)(2 94 29 188)(3 95 30 189)(4 96 31 190)(5 97 32 191)(6 98 33 192)(7 99 34 193)(8 100 35 194)(9 101 36 195)(10 102 37 196)(11 103 38 197)(12 104 39 198)(13 105 40 177)(14 106 41 178)(15 107 42 179)(16 108 43 180)(17 109 44 181)(18 110 23 182)(19 89 24 183)(20 90 25 184)(21 91 26 185)(22 92 27 186)(45 288 83 273)(46 289 84 274)(47 290 85 275)(48 291 86 276)(49 292 87 277)(50 293 88 278)(51 294 67 279)(52 295 68 280)(53 296 69 281)(54 297 70 282)(55 298 71 283)(56 299 72 284)(57 300 73 285)(58 301 74 286)(59 302 75 265)(60 303 76 266)(61 304 77 267)(62 305 78 268)(63 306 79 269)(64 307 80 270)(65 308 81 271)(66 287 82 272)(111 259 202 310)(112 260 203 311)(113 261 204 312)(114 262 205 313)(115 263 206 314)(116 264 207 315)(117 243 208 316)(118 244 209 317)(119 245 210 318)(120 246 211 319)(121 247 212 320)(122 248 213 321)(123 249 214 322)(124 250 215 323)(125 251 216 324)(126 252 217 325)(127 253 218 326)(128 254 219 327)(129 255 220 328)(130 256 199 329)(131 257 200 330)(132 258 201 309)(133 240 158 334)(134 241 159 335)(135 242 160 336)(136 221 161 337)(137 222 162 338)(138 223 163 339)(139 224 164 340)(140 225 165 341)(141 226 166 342)(142 227 167 343)(143 228 168 344)(144 229 169 345)(145 230 170 346)(146 231 171 347)(147 232 172 348)(148 233 173 349)(149 234 174 350)(150 235 175 351)(151 236 176 352)(152 237 155 331)(153 238 156 332)(154 239 157 333)

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

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

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

220 conjugacy classes

 class 1 2A ··· 2G 4A ··· 4L 11A ··· 11J 22A ··· 22BR 44A ··· 44DP order 1 2 ··· 2 4 ··· 4 11 ··· 11 22 ··· 22 44 ··· 44 size 1 1 ··· 1 2 ··· 2 1 ··· 1 1 ··· 1 2 ··· 2

220 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 type + + + + - image C1 C2 C2 C4 C11 C22 C22 C44 D4 Q8 D4×C11 Q8×C11 kernel C4⋊C4×C22 C11×C4⋊C4 C22×C44 C2×C44 C2×C4⋊C4 C4⋊C4 C22×C4 C2×C4 C2×C22 C2×C22 C22 C22 # reps 1 4 3 8 10 40 30 80 2 2 20 20

Matrix representation of C4⋊C4×C22 in GL4(𝔽89) generated by

 88 0 0 0 0 88 0 0 0 0 64 0 0 0 0 64
,
 88 0 0 0 0 88 0 0 0 0 0 88 0 0 1 0
,
 55 0 0 0 0 88 0 0 0 0 38 54 0 0 54 51
G:=sub<GL(4,GF(89))| [88,0,0,0,0,88,0,0,0,0,64,0,0,0,0,64],[88,0,0,0,0,88,0,0,0,0,0,1,0,0,88,0],[55,0,0,0,0,88,0,0,0,0,38,54,0,0,54,51] >;

C4⋊C4×C22 in GAP, Magma, Sage, TeX

C_4\rtimes C_4\times C_{22}
% in TeX

G:=Group("C4:C4xC22");
// GroupNames label

G:=SmallGroup(352,151);
// by ID

G=gap.SmallGroup(352,151);
# by ID

G:=PCGroup([6,-2,-2,-2,-11,-2,-2,1056,1081,535]);
// Polycyclic

G:=Group<a,b,c|a^22=b^4=c^4=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

׿
×
𝔽