metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C44.2D4, C4.10D44, C22.4Q16, Dic22⋊3C4, C22.5SD16, C44.4(C2×C4), C4⋊C4.3D11, C4.2(C4×D11), (C2×C4).36D22, (C2×C22).31D4, C2.6(D22⋊C4), C11⋊1(Q8⋊C4), C22.4(C22⋊C4), (C2×C44).11C22, C2.2(D4.D11), (C2×Dic22).5C2, C2.2(C11⋊Q16), C22.15(C11⋊D4), (C2×C11⋊C8).3C2, (C11×C4⋊C4).3C2, SmallGroup(352,16)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22.Q16
G = < a,b,c | a22=b8=1, c2=a11b4, bab-1=a-1, ac=ca, cbc-1=a11b-1 >
Smallest permutation representation of C22.Q16
►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)
(1 287 260 123 330 29 239 190)(2 308 261 122 309 28 240 189)(3 307 262 121 310 27 241 188)(4 306 263 120 311 26 242 187)(5 305 264 119 312 25 221 186)(6 304 243 118 313 24 222 185)(7 303 244 117 314 23 223 184)(8 302 245 116 315 44 224 183)(9 301 246 115 316 43 225 182)(10 300 247 114 317 42 226 181)(11 299 248 113 318 41 227 180)(12 298 249 112 319 40 228 179)(13 297 250 111 320 39 229 178)(14 296 251 132 321 38 230 177)(15 295 252 131 322 37 231 198)(16 294 253 130 323 36 232 197)(17 293 254 129 324 35 233 196)(18 292 255 128 325 34 234 195)(19 291 256 127 326 33 235 194)(20 290 257 126 327 32 236 193)(21 289 258 125 328 31 237 192)(22 288 259 124 329 30 238 191)(45 97 266 164 334 72 146 202)(46 96 267 163 335 71 147 201)(47 95 268 162 336 70 148 200)(48 94 269 161 337 69 149 199)(49 93 270 160 338 68 150 220)(50 92 271 159 339 67 151 219)(51 91 272 158 340 88 152 218)(52 90 273 157 341 87 153 217)(53 89 274 156 342 86 154 216)(54 110 275 155 343 85 133 215)(55 109 276 176 344 84 134 214)(56 108 277 175 345 83 135 213)(57 107 278 174 346 82 136 212)(58 106 279 173 347 81 137 211)(59 105 280 172 348 80 138 210)(60 104 281 171 349 79 139 209)(61 103 282 170 350 78 140 208)(62 102 283 169 351 77 141 207)(63 101 284 168 352 76 142 206)(64 100 285 167 331 75 143 205)(65 99 286 166 332 74 144 204)(66 98 265 165 333 73 145 203)
(1 87 319 101)(2 88 320 102)(3 67 321 103)(4 68 322 104)(5 69 323 105)(6 70 324 106)(7 71 325 107)(8 72 326 108)(9 73 327 109)(10 74 328 110)(11 75 329 89)(12 76 330 90)(13 77 309 91)(14 78 310 92)(15 79 311 93)(16 80 312 94)(17 81 313 95)(18 82 314 96)(19 83 315 97)(20 84 316 98)(21 85 317 99)(22 86 318 100)(23 57 292 335)(24 58 293 336)(25 59 294 337)(26 60 295 338)(27 61 296 339)(28 62 297 340)(29 63 298 341)(30 64 299 342)(31 65 300 343)(32 66 301 344)(33 45 302 345)(34 46 303 346)(35 47 304 347)(36 48 305 348)(37 49 306 349)(38 50 307 350)(39 51 308 351)(40 52 287 352)(41 53 288 331)(42 54 289 332)(43 55 290 333)(44 56 291 334)(111 272 189 141)(112 273 190 142)(113 274 191 143)(114 275 192 144)(115 276 193 145)(116 277 194 146)(117 278 195 147)(118 279 196 148)(119 280 197 149)(120 281 198 150)(121 282 177 151)(122 283 178 152)(123 284 179 153)(124 285 180 154)(125 286 181 133)(126 265 182 134)(127 266 183 135)(128 267 184 136)(129 268 185 137)(130 269 186 138)(131 270 187 139)(132 271 188 140)(155 226 204 258)(156 227 205 259)(157 228 206 260)(158 229 207 261)(159 230 208 262)(160 231 209 263)(161 232 210 264)(162 233 211 243)(163 234 212 244)(164 235 213 245)(165 236 214 246)(166 237 215 247)(167 238 216 248)(168 239 217 249)(169 240 218 250)(170 241 219 251)(171 242 220 252)(172 221 199 253)(173 222 200 254)(174 223 201 255)(175 224 202 256)(176 225 203 257)
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), (1,287,260,123,330,29,239,190)(2,308,261,122,309,28,240,189)(3,307,262,121,310,27,241,188)(4,306,263,120,311,26,242,187)(5,305,264,119,312,25,221,186)(6,304,243,118,313,24,222,185)(7,303,244,117,314,23,223,184)(8,302,245,116,315,44,224,183)(9,301,246,115,316,43,225,182)(10,300,247,114,317,42,226,181)(11,299,248,113,318,41,227,180)(12,298,249,112,319,40,228,179)(13,297,250,111,320,39,229,178)(14,296,251,132,321,38,230,177)(15,295,252,131,322,37,231,198)(16,294,253,130,323,36,232,197)(17,293,254,129,324,35,233,196)(18,292,255,128,325,34,234,195)(19,291,256,127,326,33,235,194)(20,290,257,126,327,32,236,193)(21,289,258,125,328,31,237,192)(22,288,259,124,329,30,238,191)(45,97,266,164,334,72,146,202)(46,96,267,163,335,71,147,201)(47,95,268,162,336,70,148,200)(48,94,269,161,337,69,149,199)(49,93,270,160,338,68,150,220)(50,92,271,159,339,67,151,219)(51,91,272,158,340,88,152,218)(52,90,273,157,341,87,153,217)(53,89,274,156,342,86,154,216)(54,110,275,155,343,85,133,215)(55,109,276,176,344,84,134,214)(56,108,277,175,345,83,135,213)(57,107,278,174,346,82,136,212)(58,106,279,173,347,81,137,211)(59,105,280,172,348,80,138,210)(60,104,281,171,349,79,139,209)(61,103,282,170,350,78,140,208)(62,102,283,169,351,77,141,207)(63,101,284,168,352,76,142,206)(64,100,285,167,331,75,143,205)(65,99,286,166,332,74,144,204)(66,98,265,165,333,73,145,203), (1,87,319,101)(2,88,320,102)(3,67,321,103)(4,68,322,104)(5,69,323,105)(6,70,324,106)(7,71,325,107)(8,72,326,108)(9,73,327,109)(10,74,328,110)(11,75,329,89)(12,76,330,90)(13,77,309,91)(14,78,310,92)(15,79,311,93)(16,80,312,94)(17,81,313,95)(18,82,314,96)(19,83,315,97)(20,84,316,98)(21,85,317,99)(22,86,318,100)(23,57,292,335)(24,58,293,336)(25,59,294,337)(26,60,295,338)(27,61,296,339)(28,62,297,340)(29,63,298,341)(30,64,299,342)(31,65,300,343)(32,66,301,344)(33,45,302,345)(34,46,303,346)(35,47,304,347)(36,48,305,348)(37,49,306,349)(38,50,307,350)(39,51,308,351)(40,52,287,352)(41,53,288,331)(42,54,289,332)(43,55,290,333)(44,56,291,334)(111,272,189,141)(112,273,190,142)(113,274,191,143)(114,275,192,144)(115,276,193,145)(116,277,194,146)(117,278,195,147)(118,279,196,148)(119,280,197,149)(120,281,198,150)(121,282,177,151)(122,283,178,152)(123,284,179,153)(124,285,180,154)(125,286,181,133)(126,265,182,134)(127,266,183,135)(128,267,184,136)(129,268,185,137)(130,269,186,138)(131,270,187,139)(132,271,188,140)(155,226,204,258)(156,227,205,259)(157,228,206,260)(158,229,207,261)(159,230,208,262)(160,231,209,263)(161,232,210,264)(162,233,211,243)(163,234,212,244)(164,235,213,245)(165,236,214,246)(166,237,215,247)(167,238,216,248)(168,239,217,249)(169,240,218,250)(170,241,219,251)(171,242,220,252)(172,221,199,253)(173,222,200,254)(174,223,201,255)(175,224,202,256)(176,225,203,257)>;
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), (1,287,260,123,330,29,239,190)(2,308,261,122,309,28,240,189)(3,307,262,121,310,27,241,188)(4,306,263,120,311,26,242,187)(5,305,264,119,312,25,221,186)(6,304,243,118,313,24,222,185)(7,303,244,117,314,23,223,184)(8,302,245,116,315,44,224,183)(9,301,246,115,316,43,225,182)(10,300,247,114,317,42,226,181)(11,299,248,113,318,41,227,180)(12,298,249,112,319,40,228,179)(13,297,250,111,320,39,229,178)(14,296,251,132,321,38,230,177)(15,295,252,131,322,37,231,198)(16,294,253,130,323,36,232,197)(17,293,254,129,324,35,233,196)(18,292,255,128,325,34,234,195)(19,291,256,127,326,33,235,194)(20,290,257,126,327,32,236,193)(21,289,258,125,328,31,237,192)(22,288,259,124,329,30,238,191)(45,97,266,164,334,72,146,202)(46,96,267,163,335,71,147,201)(47,95,268,162,336,70,148,200)(48,94,269,161,337,69,149,199)(49,93,270,160,338,68,150,220)(50,92,271,159,339,67,151,219)(51,91,272,158,340,88,152,218)(52,90,273,157,341,87,153,217)(53,89,274,156,342,86,154,216)(54,110,275,155,343,85,133,215)(55,109,276,176,344,84,134,214)(56,108,277,175,345,83,135,213)(57,107,278,174,346,82,136,212)(58,106,279,173,347,81,137,211)(59,105,280,172,348,80,138,210)(60,104,281,171,349,79,139,209)(61,103,282,170,350,78,140,208)(62,102,283,169,351,77,141,207)(63,101,284,168,352,76,142,206)(64,100,285,167,331,75,143,205)(65,99,286,166,332,74,144,204)(66,98,265,165,333,73,145,203), (1,87,319,101)(2,88,320,102)(3,67,321,103)(4,68,322,104)(5,69,323,105)(6,70,324,106)(7,71,325,107)(8,72,326,108)(9,73,327,109)(10,74,328,110)(11,75,329,89)(12,76,330,90)(13,77,309,91)(14,78,310,92)(15,79,311,93)(16,80,312,94)(17,81,313,95)(18,82,314,96)(19,83,315,97)(20,84,316,98)(21,85,317,99)(22,86,318,100)(23,57,292,335)(24,58,293,336)(25,59,294,337)(26,60,295,338)(27,61,296,339)(28,62,297,340)(29,63,298,341)(30,64,299,342)(31,65,300,343)(32,66,301,344)(33,45,302,345)(34,46,303,346)(35,47,304,347)(36,48,305,348)(37,49,306,349)(38,50,307,350)(39,51,308,351)(40,52,287,352)(41,53,288,331)(42,54,289,332)(43,55,290,333)(44,56,291,334)(111,272,189,141)(112,273,190,142)(113,274,191,143)(114,275,192,144)(115,276,193,145)(116,277,194,146)(117,278,195,147)(118,279,196,148)(119,280,197,149)(120,281,198,150)(121,282,177,151)(122,283,178,152)(123,284,179,153)(124,285,180,154)(125,286,181,133)(126,265,182,134)(127,266,183,135)(128,267,184,136)(129,268,185,137)(130,269,186,138)(131,270,187,139)(132,271,188,140)(155,226,204,258)(156,227,205,259)(157,228,206,260)(158,229,207,261)(159,230,208,262)(160,231,209,263)(161,232,210,264)(162,233,211,243)(163,234,212,244)(164,235,213,245)(165,236,214,246)(166,237,215,247)(167,238,216,248)(168,239,217,249)(169,240,218,250)(170,241,219,251)(171,242,220,252)(172,221,199,253)(173,222,200,254)(174,223,201,255)(175,224,202,256)(176,225,203,257) );
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)], [(1,287,260,123,330,29,239,190),(2,308,261,122,309,28,240,189),(3,307,262,121,310,27,241,188),(4,306,263,120,311,26,242,187),(5,305,264,119,312,25,221,186),(6,304,243,118,313,24,222,185),(7,303,244,117,314,23,223,184),(8,302,245,116,315,44,224,183),(9,301,246,115,316,43,225,182),(10,300,247,114,317,42,226,181),(11,299,248,113,318,41,227,180),(12,298,249,112,319,40,228,179),(13,297,250,111,320,39,229,178),(14,296,251,132,321,38,230,177),(15,295,252,131,322,37,231,198),(16,294,253,130,323,36,232,197),(17,293,254,129,324,35,233,196),(18,292,255,128,325,34,234,195),(19,291,256,127,326,33,235,194),(20,290,257,126,327,32,236,193),(21,289,258,125,328,31,237,192),(22,288,259,124,329,30,238,191),(45,97,266,164,334,72,146,202),(46,96,267,163,335,71,147,201),(47,95,268,162,336,70,148,200),(48,94,269,161,337,69,149,199),(49,93,270,160,338,68,150,220),(50,92,271,159,339,67,151,219),(51,91,272,158,340,88,152,218),(52,90,273,157,341,87,153,217),(53,89,274,156,342,86,154,216),(54,110,275,155,343,85,133,215),(55,109,276,176,344,84,134,214),(56,108,277,175,345,83,135,213),(57,107,278,174,346,82,136,212),(58,106,279,173,347,81,137,211),(59,105,280,172,348,80,138,210),(60,104,281,171,349,79,139,209),(61,103,282,170,350,78,140,208),(62,102,283,169,351,77,141,207),(63,101,284,168,352,76,142,206),(64,100,285,167,331,75,143,205),(65,99,286,166,332,74,144,204),(66,98,265,165,333,73,145,203)], [(1,87,319,101),(2,88,320,102),(3,67,321,103),(4,68,322,104),(5,69,323,105),(6,70,324,106),(7,71,325,107),(8,72,326,108),(9,73,327,109),(10,74,328,110),(11,75,329,89),(12,76,330,90),(13,77,309,91),(14,78,310,92),(15,79,311,93),(16,80,312,94),(17,81,313,95),(18,82,314,96),(19,83,315,97),(20,84,316,98),(21,85,317,99),(22,86,318,100),(23,57,292,335),(24,58,293,336),(25,59,294,337),(26,60,295,338),(27,61,296,339),(28,62,297,340),(29,63,298,341),(30,64,299,342),(31,65,300,343),(32,66,301,344),(33,45,302,345),(34,46,303,346),(35,47,304,347),(36,48,305,348),(37,49,306,349),(38,50,307,350),(39,51,308,351),(40,52,287,352),(41,53,288,331),(42,54,289,332),(43,55,290,333),(44,56,291,334),(111,272,189,141),(112,273,190,142),(113,274,191,143),(114,275,192,144),(115,276,193,145),(116,277,194,146),(117,278,195,147),(118,279,196,148),(119,280,197,149),(120,281,198,150),(121,282,177,151),(122,283,178,152),(123,284,179,153),(124,285,180,154),(125,286,181,133),(126,265,182,134),(127,266,183,135),(128,267,184,136),(129,268,185,137),(130,269,186,138),(131,270,187,139),(132,271,188,140),(155,226,204,258),(156,227,205,259),(157,228,206,260),(158,229,207,261),(159,230,208,262),(160,231,209,263),(161,232,210,264),(162,233,211,243),(163,234,212,244),(164,235,213,245),(165,236,214,246),(166,237,215,247),(167,238,216,248),(168,239,217,249),(169,240,218,250),(170,241,219,251),(171,242,220,252),(172,221,199,253),(173,222,200,254),(174,223,201,255),(175,224,202,256),(176,225,203,257)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44AD |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 44 | 44 | 22 | 22 | 22 | 22 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C4 | D4 | D4 | SD16 | Q16 | D11 | D22 | C4×D11 | D44 | C11⋊D4 | D4.D11 | C11⋊Q16 |
| kernel | C22.Q16 | C2×C11⋊C8 | C11×C4⋊C4 | C2×Dic22 | Dic22 | C44 | C2×C22 | C22 | C22 | C4⋊C4 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 2 | 2 | 5 | 5 | 10 | 10 | 10 | 5 | 5 |
Matrix representation of C22.Q16 ►in GL4(𝔽89) generated by
| 6 | 5 | 0 | 0 |
| 32 | 12 | 0 | 0 |
| 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 88 |
| 7 | 29 | 0 | 0 |
| 72 | 82 | 0 | 0 |
| 0 | 0 | 0 | 78 |
| 0 | 0 | 8 | 49 |
| 1 | 28 | 0 | 0 |
| 19 | 88 | 0 | 0 |
| 0 | 0 | 69 | 43 |
| 0 | 0 | 88 | 20 |
G:=sub<GL(4,GF(89))| [6,32,0,0,5,12,0,0,0,0,88,0,0,0,0,88],[7,72,0,0,29,82,0,0,0,0,0,8,0,0,78,49],[1,19,0,0,28,88,0,0,0,0,69,88,0,0,43,20] >;
C22.Q16 in GAP, Magma, Sage, TeX
C_{22}.Q_{16} % in TeX
G:=Group("C22.Q16"); // GroupNames label
G:=SmallGroup(352,16);
// by ID
G=gap.SmallGroup(352,16);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,96,121,31,579,297,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^22=b^8=1,c^2=a^11*b^4,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^11*b^-1>;
// generators/relations
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