metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C88⋊1C4, C2.1D88, C22.4D8, C44.5Q8, C8⋊1Dic11, C22.2Q16, C2.2Dic44, C4.5Dic22, C22.9D44, (C2×C88).5C2, (C2×C8).3D11, C11⋊2(C2.D8), C22.6(C4⋊C4), C44.34(C2×C4), (C2×C4).69D22, (C2×C22).14D4, C44⋊C4.3C2, C4.7(C2×Dic11), C2.4(C44⋊C4), (C2×C44).82C22, SmallGroup(352,24)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C44.5Q8
G = < a,b,c | a44=1, b4=a22, c2=a33b2, ab=ba, cac-1=a-1, cbc-1=a22b3 >
Smallest permutation representation of C44.5Q8
►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)
(1 151 284 237 23 173 306 259)(2 152 285 238 24 174 307 260)(3 153 286 239 25 175 308 261)(4 154 287 240 26 176 265 262)(5 155 288 241 27 133 266 263)(6 156 289 242 28 134 267 264)(7 157 290 243 29 135 268 221)(8 158 291 244 30 136 269 222)(9 159 292 245 31 137 270 223)(10 160 293 246 32 138 271 224)(11 161 294 247 33 139 272 225)(12 162 295 248 34 140 273 226)(13 163 296 249 35 141 274 227)(14 164 297 250 36 142 275 228)(15 165 298 251 37 143 276 229)(16 166 299 252 38 144 277 230)(17 167 300 253 39 145 278 231)(18 168 301 254 40 146 279 232)(19 169 302 255 41 147 280 233)(20 170 303 256 42 148 281 234)(21 171 304 257 43 149 282 235)(22 172 305 258 44 150 283 236)(45 94 340 178 67 116 318 200)(46 95 341 179 68 117 319 201)(47 96 342 180 69 118 320 202)(48 97 343 181 70 119 321 203)(49 98 344 182 71 120 322 204)(50 99 345 183 72 121 323 205)(51 100 346 184 73 122 324 206)(52 101 347 185 74 123 325 207)(53 102 348 186 75 124 326 208)(54 103 349 187 76 125 327 209)(55 104 350 188 77 126 328 210)(56 105 351 189 78 127 329 211)(57 106 352 190 79 128 330 212)(58 107 309 191 80 129 331 213)(59 108 310 192 81 130 332 214)(60 109 311 193 82 131 333 215)(61 110 312 194 83 132 334 216)(62 111 313 195 84 89 335 217)(63 112 314 196 85 90 336 218)(64 113 315 197 86 91 337 219)(65 114 316 198 87 92 338 220)(66 115 317 199 88 93 339 177)
(1 309 273 69)(2 352 274 68)(3 351 275 67)(4 350 276 66)(5 349 277 65)(6 348 278 64)(7 347 279 63)(8 346 280 62)(9 345 281 61)(10 344 282 60)(11 343 283 59)(12 342 284 58)(13 341 285 57)(14 340 286 56)(15 339 287 55)(16 338 288 54)(17 337 289 53)(18 336 290 52)(19 335 291 51)(20 334 292 50)(21 333 293 49)(22 332 294 48)(23 331 295 47)(24 330 296 46)(25 329 297 45)(26 328 298 88)(27 327 299 87)(28 326 300 86)(29 325 301 85)(30 324 302 84)(31 323 303 83)(32 322 304 82)(33 321 305 81)(34 320 306 80)(35 319 307 79)(36 318 308 78)(37 317 265 77)(38 316 266 76)(39 315 267 75)(40 314 268 74)(41 313 269 73)(42 312 270 72)(43 311 271 71)(44 310 272 70)(89 244 206 169)(90 243 207 168)(91 242 208 167)(92 241 209 166)(93 240 210 165)(94 239 211 164)(95 238 212 163)(96 237 213 162)(97 236 214 161)(98 235 215 160)(99 234 216 159)(100 233 217 158)(101 232 218 157)(102 231 219 156)(103 230 220 155)(104 229 177 154)(105 228 178 153)(106 227 179 152)(107 226 180 151)(108 225 181 150)(109 224 182 149)(110 223 183 148)(111 222 184 147)(112 221 185 146)(113 264 186 145)(114 263 187 144)(115 262 188 143)(116 261 189 142)(117 260 190 141)(118 259 191 140)(119 258 192 139)(120 257 193 138)(121 256 194 137)(122 255 195 136)(123 254 196 135)(124 253 197 134)(125 252 198 133)(126 251 199 176)(127 250 200 175)(128 249 201 174)(129 248 202 173)(130 247 203 172)(131 246 204 171)(132 245 205 170)
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), (1,151,284,237,23,173,306,259)(2,152,285,238,24,174,307,260)(3,153,286,239,25,175,308,261)(4,154,287,240,26,176,265,262)(5,155,288,241,27,133,266,263)(6,156,289,242,28,134,267,264)(7,157,290,243,29,135,268,221)(8,158,291,244,30,136,269,222)(9,159,292,245,31,137,270,223)(10,160,293,246,32,138,271,224)(11,161,294,247,33,139,272,225)(12,162,295,248,34,140,273,226)(13,163,296,249,35,141,274,227)(14,164,297,250,36,142,275,228)(15,165,298,251,37,143,276,229)(16,166,299,252,38,144,277,230)(17,167,300,253,39,145,278,231)(18,168,301,254,40,146,279,232)(19,169,302,255,41,147,280,233)(20,170,303,256,42,148,281,234)(21,171,304,257,43,149,282,235)(22,172,305,258,44,150,283,236)(45,94,340,178,67,116,318,200)(46,95,341,179,68,117,319,201)(47,96,342,180,69,118,320,202)(48,97,343,181,70,119,321,203)(49,98,344,182,71,120,322,204)(50,99,345,183,72,121,323,205)(51,100,346,184,73,122,324,206)(52,101,347,185,74,123,325,207)(53,102,348,186,75,124,326,208)(54,103,349,187,76,125,327,209)(55,104,350,188,77,126,328,210)(56,105,351,189,78,127,329,211)(57,106,352,190,79,128,330,212)(58,107,309,191,80,129,331,213)(59,108,310,192,81,130,332,214)(60,109,311,193,82,131,333,215)(61,110,312,194,83,132,334,216)(62,111,313,195,84,89,335,217)(63,112,314,196,85,90,336,218)(64,113,315,197,86,91,337,219)(65,114,316,198,87,92,338,220)(66,115,317,199,88,93,339,177), (1,309,273,69)(2,352,274,68)(3,351,275,67)(4,350,276,66)(5,349,277,65)(6,348,278,64)(7,347,279,63)(8,346,280,62)(9,345,281,61)(10,344,282,60)(11,343,283,59)(12,342,284,58)(13,341,285,57)(14,340,286,56)(15,339,287,55)(16,338,288,54)(17,337,289,53)(18,336,290,52)(19,335,291,51)(20,334,292,50)(21,333,293,49)(22,332,294,48)(23,331,295,47)(24,330,296,46)(25,329,297,45)(26,328,298,88)(27,327,299,87)(28,326,300,86)(29,325,301,85)(30,324,302,84)(31,323,303,83)(32,322,304,82)(33,321,305,81)(34,320,306,80)(35,319,307,79)(36,318,308,78)(37,317,265,77)(38,316,266,76)(39,315,267,75)(40,314,268,74)(41,313,269,73)(42,312,270,72)(43,311,271,71)(44,310,272,70)(89,244,206,169)(90,243,207,168)(91,242,208,167)(92,241,209,166)(93,240,210,165)(94,239,211,164)(95,238,212,163)(96,237,213,162)(97,236,214,161)(98,235,215,160)(99,234,216,159)(100,233,217,158)(101,232,218,157)(102,231,219,156)(103,230,220,155)(104,229,177,154)(105,228,178,153)(106,227,179,152)(107,226,180,151)(108,225,181,150)(109,224,182,149)(110,223,183,148)(111,222,184,147)(112,221,185,146)(113,264,186,145)(114,263,187,144)(115,262,188,143)(116,261,189,142)(117,260,190,141)(118,259,191,140)(119,258,192,139)(120,257,193,138)(121,256,194,137)(122,255,195,136)(123,254,196,135)(124,253,197,134)(125,252,198,133)(126,251,199,176)(127,250,200,175)(128,249,201,174)(129,248,202,173)(130,247,203,172)(131,246,204,171)(132,245,205,170)>;
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), (1,151,284,237,23,173,306,259)(2,152,285,238,24,174,307,260)(3,153,286,239,25,175,308,261)(4,154,287,240,26,176,265,262)(5,155,288,241,27,133,266,263)(6,156,289,242,28,134,267,264)(7,157,290,243,29,135,268,221)(8,158,291,244,30,136,269,222)(9,159,292,245,31,137,270,223)(10,160,293,246,32,138,271,224)(11,161,294,247,33,139,272,225)(12,162,295,248,34,140,273,226)(13,163,296,249,35,141,274,227)(14,164,297,250,36,142,275,228)(15,165,298,251,37,143,276,229)(16,166,299,252,38,144,277,230)(17,167,300,253,39,145,278,231)(18,168,301,254,40,146,279,232)(19,169,302,255,41,147,280,233)(20,170,303,256,42,148,281,234)(21,171,304,257,43,149,282,235)(22,172,305,258,44,150,283,236)(45,94,340,178,67,116,318,200)(46,95,341,179,68,117,319,201)(47,96,342,180,69,118,320,202)(48,97,343,181,70,119,321,203)(49,98,344,182,71,120,322,204)(50,99,345,183,72,121,323,205)(51,100,346,184,73,122,324,206)(52,101,347,185,74,123,325,207)(53,102,348,186,75,124,326,208)(54,103,349,187,76,125,327,209)(55,104,350,188,77,126,328,210)(56,105,351,189,78,127,329,211)(57,106,352,190,79,128,330,212)(58,107,309,191,80,129,331,213)(59,108,310,192,81,130,332,214)(60,109,311,193,82,131,333,215)(61,110,312,194,83,132,334,216)(62,111,313,195,84,89,335,217)(63,112,314,196,85,90,336,218)(64,113,315,197,86,91,337,219)(65,114,316,198,87,92,338,220)(66,115,317,199,88,93,339,177), (1,309,273,69)(2,352,274,68)(3,351,275,67)(4,350,276,66)(5,349,277,65)(6,348,278,64)(7,347,279,63)(8,346,280,62)(9,345,281,61)(10,344,282,60)(11,343,283,59)(12,342,284,58)(13,341,285,57)(14,340,286,56)(15,339,287,55)(16,338,288,54)(17,337,289,53)(18,336,290,52)(19,335,291,51)(20,334,292,50)(21,333,293,49)(22,332,294,48)(23,331,295,47)(24,330,296,46)(25,329,297,45)(26,328,298,88)(27,327,299,87)(28,326,300,86)(29,325,301,85)(30,324,302,84)(31,323,303,83)(32,322,304,82)(33,321,305,81)(34,320,306,80)(35,319,307,79)(36,318,308,78)(37,317,265,77)(38,316,266,76)(39,315,267,75)(40,314,268,74)(41,313,269,73)(42,312,270,72)(43,311,271,71)(44,310,272,70)(89,244,206,169)(90,243,207,168)(91,242,208,167)(92,241,209,166)(93,240,210,165)(94,239,211,164)(95,238,212,163)(96,237,213,162)(97,236,214,161)(98,235,215,160)(99,234,216,159)(100,233,217,158)(101,232,218,157)(102,231,219,156)(103,230,220,155)(104,229,177,154)(105,228,178,153)(106,227,179,152)(107,226,180,151)(108,225,181,150)(109,224,182,149)(110,223,183,148)(111,222,184,147)(112,221,185,146)(113,264,186,145)(114,263,187,144)(115,262,188,143)(116,261,189,142)(117,260,190,141)(118,259,191,140)(119,258,192,139)(120,257,193,138)(121,256,194,137)(122,255,195,136)(123,254,196,135)(124,253,197,134)(125,252,198,133)(126,251,199,176)(127,250,200,175)(128,249,201,174)(129,248,202,173)(130,247,203,172)(131,246,204,171)(132,245,205,170) );
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)], [(1,151,284,237,23,173,306,259),(2,152,285,238,24,174,307,260),(3,153,286,239,25,175,308,261),(4,154,287,240,26,176,265,262),(5,155,288,241,27,133,266,263),(6,156,289,242,28,134,267,264),(7,157,290,243,29,135,268,221),(8,158,291,244,30,136,269,222),(9,159,292,245,31,137,270,223),(10,160,293,246,32,138,271,224),(11,161,294,247,33,139,272,225),(12,162,295,248,34,140,273,226),(13,163,296,249,35,141,274,227),(14,164,297,250,36,142,275,228),(15,165,298,251,37,143,276,229),(16,166,299,252,38,144,277,230),(17,167,300,253,39,145,278,231),(18,168,301,254,40,146,279,232),(19,169,302,255,41,147,280,233),(20,170,303,256,42,148,281,234),(21,171,304,257,43,149,282,235),(22,172,305,258,44,150,283,236),(45,94,340,178,67,116,318,200),(46,95,341,179,68,117,319,201),(47,96,342,180,69,118,320,202),(48,97,343,181,70,119,321,203),(49,98,344,182,71,120,322,204),(50,99,345,183,72,121,323,205),(51,100,346,184,73,122,324,206),(52,101,347,185,74,123,325,207),(53,102,348,186,75,124,326,208),(54,103,349,187,76,125,327,209),(55,104,350,188,77,126,328,210),(56,105,351,189,78,127,329,211),(57,106,352,190,79,128,330,212),(58,107,309,191,80,129,331,213),(59,108,310,192,81,130,332,214),(60,109,311,193,82,131,333,215),(61,110,312,194,83,132,334,216),(62,111,313,195,84,89,335,217),(63,112,314,196,85,90,336,218),(64,113,315,197,86,91,337,219),(65,114,316,198,87,92,338,220),(66,115,317,199,88,93,339,177)], [(1,309,273,69),(2,352,274,68),(3,351,275,67),(4,350,276,66),(5,349,277,65),(6,348,278,64),(7,347,279,63),(8,346,280,62),(9,345,281,61),(10,344,282,60),(11,343,283,59),(12,342,284,58),(13,341,285,57),(14,340,286,56),(15,339,287,55),(16,338,288,54),(17,337,289,53),(18,336,290,52),(19,335,291,51),(20,334,292,50),(21,333,293,49),(22,332,294,48),(23,331,295,47),(24,330,296,46),(25,329,297,45),(26,328,298,88),(27,327,299,87),(28,326,300,86),(29,325,301,85),(30,324,302,84),(31,323,303,83),(32,322,304,82),(33,321,305,81),(34,320,306,80),(35,319,307,79),(36,318,308,78),(37,317,265,77),(38,316,266,76),(39,315,267,75),(40,314,268,74),(41,313,269,73),(42,312,270,72),(43,311,271,71),(44,310,272,70),(89,244,206,169),(90,243,207,168),(91,242,208,167),(92,241,209,166),(93,240,210,165),(94,239,211,164),(95,238,212,163),(96,237,213,162),(97,236,214,161),(98,235,215,160),(99,234,216,159),(100,233,217,158),(101,232,218,157),(102,231,219,156),(103,230,220,155),(104,229,177,154),(105,228,178,153),(106,227,179,152),(107,226,180,151),(108,225,181,150),(109,224,182,149),(110,223,183,148),(111,222,184,147),(112,221,185,146),(113,264,186,145),(114,263,187,144),(115,262,188,143),(116,261,189,142),(117,260,190,141),(118,259,191,140),(119,258,192,139),(120,257,193,138),(121,256,194,137),(122,255,195,136),(123,254,196,135),(124,253,197,134),(125,252,198,133),(126,251,199,176),(127,250,200,175),(128,249,201,174),(129,248,202,173),(130,247,203,172),(131,246,204,171),(132,245,205,170)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44T | 88A | ··· | 88AN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 44 | 44 | 44 | 44 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | + | - | + | - | + | - | + | + | - | |
| image | C1 | C2 | C2 | C4 | Q8 | D4 | D8 | Q16 | D11 | Dic11 | D22 | Dic22 | D44 | D88 | Dic44 |
| kernel | C44.5Q8 | C44⋊C4 | C2×C88 | C88 | C44 | C2×C22 | C22 | C22 | C2×C8 | C8 | C2×C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 1 | 1 | 2 | 2 | 5 | 10 | 5 | 10 | 10 | 20 | 20 |
Matrix representation of C44.5Q8 ►in GL4(𝔽89) generated by
| 86 | 81 | 0 | 0 |
| 8 | 21 | 0 | 0 |
| 0 | 0 | 65 | 73 |
| 0 | 0 | 45 | 4 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 7 | 70 |
| 0 | 0 | 59 | 18 |
| 13 | 5 | 0 | 0 |
| 55 | 76 | 0 | 0 |
| 0 | 0 | 72 | 43 |
| 0 | 0 | 45 | 17 |
G:=sub<GL(4,GF(89))| [86,8,0,0,81,21,0,0,0,0,65,45,0,0,73,4],[88,0,0,0,0,88,0,0,0,0,7,59,0,0,70,18],[13,55,0,0,5,76,0,0,0,0,72,45,0,0,43,17] >;
C44.5Q8 in GAP, Magma, Sage, TeX
C_{44}._5Q_8 % in TeX
G:=Group("C44.5Q8"); // GroupNames label
G:=SmallGroup(352,24);
// by ID
G=gap.SmallGroup(352,24);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,24,121,151,579,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^44=1,b^4=a^22,c^2=a^33*b^2,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=a^22*b^3>;
// generators/relations
Export