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## G = C4×Dic22order 352 = 25·11

### Direct product of C4 and Dic22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C4×Dic22
 Chief series C1 — C11 — C22 — C2×C22 — C2×Dic11 — C2×Dic22 — C4×Dic22
 Lower central C11 — C22 — C4×Dic22
 Upper central C1 — C2×C4 — C42

Generators and relations for C4×Dic22
G = < a,b,c | a4=b44=1, c2=b22, ab=ba, ac=ca, cbc-1=b-1 >

Subgroups: 306 in 70 conjugacy classes, 45 normal (21 characteristic)
C1, C2, C4, C4, C22, C2×C4, C2×C4, Q8, C11, C42, C42, C4⋊C4, C2×Q8, C22, C4×Q8, Dic11, Dic11, C44, C44, C2×C22, Dic22, C2×Dic11, C2×C44, C4×Dic11, Dic11⋊C4, C44⋊C4, C4×C44, C2×Dic22, C4×Dic22
Quotients: C1, C2, C4, C22, C2×C4, Q8, C23, C22×C4, C2×Q8, C4○D4, D11, C4×Q8, D22, Dic22, C4×D11, C22×D11, C2×Dic22, C2×C4×D11, D445C2, C4×Dic22

Smallest permutation representation of C4×Dic22
Regular action on 352 points
Generators in S352
(1 73 242 124)(2 74 243 125)(3 75 244 126)(4 76 245 127)(5 77 246 128)(6 78 247 129)(7 79 248 130)(8 80 249 131)(9 81 250 132)(10 82 251 89)(11 83 252 90)(12 84 253 91)(13 85 254 92)(14 86 255 93)(15 87 256 94)(16 88 257 95)(17 45 258 96)(18 46 259 97)(19 47 260 98)(20 48 261 99)(21 49 262 100)(22 50 263 101)(23 51 264 102)(24 52 221 103)(25 53 222 104)(26 54 223 105)(27 55 224 106)(28 56 225 107)(29 57 226 108)(30 58 227 109)(31 59 228 110)(32 60 229 111)(33 61 230 112)(34 62 231 113)(35 63 232 114)(36 64 233 115)(37 65 234 116)(38 66 235 117)(39 67 236 118)(40 68 237 119)(41 69 238 120)(42 70 239 121)(43 71 240 122)(44 72 241 123)(133 206 338 269)(134 207 339 270)(135 208 340 271)(136 209 341 272)(137 210 342 273)(138 211 343 274)(139 212 344 275)(140 213 345 276)(141 214 346 277)(142 215 347 278)(143 216 348 279)(144 217 349 280)(145 218 350 281)(146 219 351 282)(147 220 352 283)(148 177 309 284)(149 178 310 285)(150 179 311 286)(151 180 312 287)(152 181 313 288)(153 182 314 289)(154 183 315 290)(155 184 316 291)(156 185 317 292)(157 186 318 293)(158 187 319 294)(159 188 320 295)(160 189 321 296)(161 190 322 297)(162 191 323 298)(163 192 324 299)(164 193 325 300)(165 194 326 301)(166 195 327 302)(167 196 328 303)(168 197 329 304)(169 198 330 305)(170 199 331 306)(171 200 332 307)(172 201 333 308)(173 202 334 265)(174 203 335 266)(175 204 336 267)(176 205 337 268)
(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)
(1 147 23 169)(2 146 24 168)(3 145 25 167)(4 144 26 166)(5 143 27 165)(6 142 28 164)(7 141 29 163)(8 140 30 162)(9 139 31 161)(10 138 32 160)(11 137 33 159)(12 136 34 158)(13 135 35 157)(14 134 36 156)(15 133 37 155)(16 176 38 154)(17 175 39 153)(18 174 40 152)(19 173 41 151)(20 172 42 150)(21 171 43 149)(22 170 44 148)(45 204 67 182)(46 203 68 181)(47 202 69 180)(48 201 70 179)(49 200 71 178)(50 199 72 177)(51 198 73 220)(52 197 74 219)(53 196 75 218)(54 195 76 217)(55 194 77 216)(56 193 78 215)(57 192 79 214)(58 191 80 213)(59 190 81 212)(60 189 82 211)(61 188 83 210)(62 187 84 209)(63 186 85 208)(64 185 86 207)(65 184 87 206)(66 183 88 205)(89 274 111 296)(90 273 112 295)(91 272 113 294)(92 271 114 293)(93 270 115 292)(94 269 116 291)(95 268 117 290)(96 267 118 289)(97 266 119 288)(98 265 120 287)(99 308 121 286)(100 307 122 285)(101 306 123 284)(102 305 124 283)(103 304 125 282)(104 303 126 281)(105 302 127 280)(106 301 128 279)(107 300 129 278)(108 299 130 277)(109 298 131 276)(110 297 132 275)(221 329 243 351)(222 328 244 350)(223 327 245 349)(224 326 246 348)(225 325 247 347)(226 324 248 346)(227 323 249 345)(228 322 250 344)(229 321 251 343)(230 320 252 342)(231 319 253 341)(232 318 254 340)(233 317 255 339)(234 316 256 338)(235 315 257 337)(236 314 258 336)(237 313 259 335)(238 312 260 334)(239 311 261 333)(240 310 262 332)(241 309 263 331)(242 352 264 330)

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

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

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

100 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 4G 4H 4I ··· 4P 11A ··· 11E 22A ··· 22O 44A ··· 44BH order 1 2 2 2 4 4 4 4 4 4 4 4 4 ··· 4 11 ··· 11 22 ··· 22 44 ··· 44 size 1 1 1 1 1 1 1 1 2 2 2 2 22 ··· 22 2 ··· 2 2 ··· 2 2 ··· 2

100 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 2 2 type + + + + + + - + + - image C1 C2 C2 C2 C2 C2 C4 Q8 C4○D4 D11 D22 Dic22 C4×D11 D44⋊5C2 kernel C4×Dic22 C4×Dic11 Dic11⋊C4 C44⋊C4 C4×C44 C2×Dic22 Dic22 C44 C22 C42 C2×C4 C4 C4 C2 # reps 1 2 2 1 1 1 8 2 2 5 15 20 20 20

Matrix representation of C4×Dic22 in GL4(𝔽89) generated by

 34 0 0 0 0 34 0 0 0 0 88 0 0 0 0 88
,
 0 1 0 0 88 7 0 0 0 0 80 76 0 0 13 78
,
 24 47 0 0 37 65 0 0 0 0 80 27 0 0 53 9
G:=sub<GL(4,GF(89))| [34,0,0,0,0,34,0,0,0,0,88,0,0,0,0,88],[0,88,0,0,1,7,0,0,0,0,80,13,0,0,76,78],[24,37,0,0,47,65,0,0,0,0,80,53,0,0,27,9] >;

C4×Dic22 in GAP, Magma, Sage, TeX

C_4\times {\rm Dic}_{22}
% in TeX

G:=Group("C4xDic22");
// GroupNames label

G:=SmallGroup(352,63);
// by ID

G=gap.SmallGroup(352,63);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-11,96,217,103,50,11525]);
// Polycyclic

G:=Group<a,b,c|a^4=b^44=1,c^2=b^22,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

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