direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: Q16×C22, C44.43D4, C44.46C23, C88.27C22, (C2×C8).4C22, C8.5(C2×C22), C4.8(D4×C11), (C2×C88).14C2, C22.76(C2×D4), C2.13(D4×C22), (C2×C22).54D4, (C2×Q8).4C22, Q8.1(C2×C22), (Q8×C22).9C2, C4.3(C22×C22), C22.16(D4×C11), (C2×C44).131C22, (Q8×C11).12C22, (C2×C4).27(C2×C22), SmallGroup(352,169)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Q16×C22
G = < a,b,c | a22=b8=1, c2=b4, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 76 in 60 conjugacy classes, 44 normal (16 characteristic)
C1, C2, C2, C4, C4, C22, C8, C2×C4, C2×C4, Q8, Q8, C11, C2×C8, Q16, C2×Q8, C22, C22, C2×Q16, C44, C44, C2×C22, C88, C2×C44, C2×C44, Q8×C11, Q8×C11, C2×C88, C11×Q16, Q8×C22, Q16×C22
Quotients: C1, C2, C22, D4, C23, C11, Q16, C2×D4, C22, C2×Q16, C2×C22, D4×C11, C22×C22, C11×Q16, D4×C22, Q16×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)
(1 312 125 337 29 177 158 285)(2 313 126 338 30 178 159 286)(3 314 127 339 31 179 160 265)(4 315 128 340 32 180 161 266)(5 316 129 341 33 181 162 267)(6 317 130 342 34 182 163 268)(7 318 131 343 35 183 164 269)(8 319 132 344 36 184 165 270)(9 320 111 345 37 185 166 271)(10 321 112 346 38 186 167 272)(11 322 113 347 39 187 168 273)(12 323 114 348 40 188 169 274)(13 324 115 349 41 189 170 275)(14 325 116 350 42 190 171 276)(15 326 117 351 43 191 172 277)(16 327 118 352 44 192 173 278)(17 328 119 331 23 193 174 279)(18 329 120 332 24 194 175 280)(19 330 121 333 25 195 176 281)(20 309 122 334 26 196 155 282)(21 310 123 335 27 197 156 283)(22 311 124 336 28 198 157 284)(45 206 81 228 293 101 251 136)(46 207 82 229 294 102 252 137)(47 208 83 230 295 103 253 138)(48 209 84 231 296 104 254 139)(49 210 85 232 297 105 255 140)(50 211 86 233 298 106 256 141)(51 212 87 234 299 107 257 142)(52 213 88 235 300 108 258 143)(53 214 67 236 301 109 259 144)(54 215 68 237 302 110 260 145)(55 216 69 238 303 89 261 146)(56 217 70 239 304 90 262 147)(57 218 71 240 305 91 263 148)(58 219 72 241 306 92 264 149)(59 220 73 242 307 93 243 150)(60 199 74 221 308 94 244 151)(61 200 75 222 287 95 245 152)(62 201 76 223 288 96 246 153)(63 202 77 224 289 97 247 154)(64 203 78 225 290 98 248 133)(65 204 79 226 291 99 249 134)(66 205 80 227 292 100 250 135)
(1 292 29 66)(2 293 30 45)(3 294 31 46)(4 295 32 47)(5 296 33 48)(6 297 34 49)(7 298 35 50)(8 299 36 51)(9 300 37 52)(10 301 38 53)(11 302 39 54)(12 303 40 55)(13 304 41 56)(14 305 42 57)(15 306 43 58)(16 307 44 59)(17 308 23 60)(18 287 24 61)(19 288 25 62)(20 289 26 63)(21 290 27 64)(22 291 28 65)(67 167 259 112)(68 168 260 113)(69 169 261 114)(70 170 262 115)(71 171 263 116)(72 172 264 117)(73 173 243 118)(74 174 244 119)(75 175 245 120)(76 176 246 121)(77 155 247 122)(78 156 248 123)(79 157 249 124)(80 158 250 125)(81 159 251 126)(82 160 252 127)(83 161 253 128)(84 162 254 129)(85 163 255 130)(86 164 256 131)(87 165 257 132)(88 166 258 111)(89 348 216 274)(90 349 217 275)(91 350 218 276)(92 351 219 277)(93 352 220 278)(94 331 199 279)(95 332 200 280)(96 333 201 281)(97 334 202 282)(98 335 203 283)(99 336 204 284)(100 337 205 285)(101 338 206 286)(102 339 207 265)(103 340 208 266)(104 341 209 267)(105 342 210 268)(106 343 211 269)(107 344 212 270)(108 345 213 271)(109 346 214 272)(110 347 215 273)(133 310 225 197)(134 311 226 198)(135 312 227 177)(136 313 228 178)(137 314 229 179)(138 315 230 180)(139 316 231 181)(140 317 232 182)(141 318 233 183)(142 319 234 184)(143 320 235 185)(144 321 236 186)(145 322 237 187)(146 323 238 188)(147 324 239 189)(148 325 240 190)(149 326 241 191)(150 327 242 192)(151 328 221 193)(152 329 222 194)(153 330 223 195)(154 309 224 196)
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), (1,312,125,337,29,177,158,285)(2,313,126,338,30,178,159,286)(3,314,127,339,31,179,160,265)(4,315,128,340,32,180,161,266)(5,316,129,341,33,181,162,267)(6,317,130,342,34,182,163,268)(7,318,131,343,35,183,164,269)(8,319,132,344,36,184,165,270)(9,320,111,345,37,185,166,271)(10,321,112,346,38,186,167,272)(11,322,113,347,39,187,168,273)(12,323,114,348,40,188,169,274)(13,324,115,349,41,189,170,275)(14,325,116,350,42,190,171,276)(15,326,117,351,43,191,172,277)(16,327,118,352,44,192,173,278)(17,328,119,331,23,193,174,279)(18,329,120,332,24,194,175,280)(19,330,121,333,25,195,176,281)(20,309,122,334,26,196,155,282)(21,310,123,335,27,197,156,283)(22,311,124,336,28,198,157,284)(45,206,81,228,293,101,251,136)(46,207,82,229,294,102,252,137)(47,208,83,230,295,103,253,138)(48,209,84,231,296,104,254,139)(49,210,85,232,297,105,255,140)(50,211,86,233,298,106,256,141)(51,212,87,234,299,107,257,142)(52,213,88,235,300,108,258,143)(53,214,67,236,301,109,259,144)(54,215,68,237,302,110,260,145)(55,216,69,238,303,89,261,146)(56,217,70,239,304,90,262,147)(57,218,71,240,305,91,263,148)(58,219,72,241,306,92,264,149)(59,220,73,242,307,93,243,150)(60,199,74,221,308,94,244,151)(61,200,75,222,287,95,245,152)(62,201,76,223,288,96,246,153)(63,202,77,224,289,97,247,154)(64,203,78,225,290,98,248,133)(65,204,79,226,291,99,249,134)(66,205,80,227,292,100,250,135), (1,292,29,66)(2,293,30,45)(3,294,31,46)(4,295,32,47)(5,296,33,48)(6,297,34,49)(7,298,35,50)(8,299,36,51)(9,300,37,52)(10,301,38,53)(11,302,39,54)(12,303,40,55)(13,304,41,56)(14,305,42,57)(15,306,43,58)(16,307,44,59)(17,308,23,60)(18,287,24,61)(19,288,25,62)(20,289,26,63)(21,290,27,64)(22,291,28,65)(67,167,259,112)(68,168,260,113)(69,169,261,114)(70,170,262,115)(71,171,263,116)(72,172,264,117)(73,173,243,118)(74,174,244,119)(75,175,245,120)(76,176,246,121)(77,155,247,122)(78,156,248,123)(79,157,249,124)(80,158,250,125)(81,159,251,126)(82,160,252,127)(83,161,253,128)(84,162,254,129)(85,163,255,130)(86,164,256,131)(87,165,257,132)(88,166,258,111)(89,348,216,274)(90,349,217,275)(91,350,218,276)(92,351,219,277)(93,352,220,278)(94,331,199,279)(95,332,200,280)(96,333,201,281)(97,334,202,282)(98,335,203,283)(99,336,204,284)(100,337,205,285)(101,338,206,286)(102,339,207,265)(103,340,208,266)(104,341,209,267)(105,342,210,268)(106,343,211,269)(107,344,212,270)(108,345,213,271)(109,346,214,272)(110,347,215,273)(133,310,225,197)(134,311,226,198)(135,312,227,177)(136,313,228,178)(137,314,229,179)(138,315,230,180)(139,316,231,181)(140,317,232,182)(141,318,233,183)(142,319,234,184)(143,320,235,185)(144,321,236,186)(145,322,237,187)(146,323,238,188)(147,324,239,189)(148,325,240,190)(149,326,241,191)(150,327,242,192)(151,328,221,193)(152,329,222,194)(153,330,223,195)(154,309,224,196)>;
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), (1,312,125,337,29,177,158,285)(2,313,126,338,30,178,159,286)(3,314,127,339,31,179,160,265)(4,315,128,340,32,180,161,266)(5,316,129,341,33,181,162,267)(6,317,130,342,34,182,163,268)(7,318,131,343,35,183,164,269)(8,319,132,344,36,184,165,270)(9,320,111,345,37,185,166,271)(10,321,112,346,38,186,167,272)(11,322,113,347,39,187,168,273)(12,323,114,348,40,188,169,274)(13,324,115,349,41,189,170,275)(14,325,116,350,42,190,171,276)(15,326,117,351,43,191,172,277)(16,327,118,352,44,192,173,278)(17,328,119,331,23,193,174,279)(18,329,120,332,24,194,175,280)(19,330,121,333,25,195,176,281)(20,309,122,334,26,196,155,282)(21,310,123,335,27,197,156,283)(22,311,124,336,28,198,157,284)(45,206,81,228,293,101,251,136)(46,207,82,229,294,102,252,137)(47,208,83,230,295,103,253,138)(48,209,84,231,296,104,254,139)(49,210,85,232,297,105,255,140)(50,211,86,233,298,106,256,141)(51,212,87,234,299,107,257,142)(52,213,88,235,300,108,258,143)(53,214,67,236,301,109,259,144)(54,215,68,237,302,110,260,145)(55,216,69,238,303,89,261,146)(56,217,70,239,304,90,262,147)(57,218,71,240,305,91,263,148)(58,219,72,241,306,92,264,149)(59,220,73,242,307,93,243,150)(60,199,74,221,308,94,244,151)(61,200,75,222,287,95,245,152)(62,201,76,223,288,96,246,153)(63,202,77,224,289,97,247,154)(64,203,78,225,290,98,248,133)(65,204,79,226,291,99,249,134)(66,205,80,227,292,100,250,135), (1,292,29,66)(2,293,30,45)(3,294,31,46)(4,295,32,47)(5,296,33,48)(6,297,34,49)(7,298,35,50)(8,299,36,51)(9,300,37,52)(10,301,38,53)(11,302,39,54)(12,303,40,55)(13,304,41,56)(14,305,42,57)(15,306,43,58)(16,307,44,59)(17,308,23,60)(18,287,24,61)(19,288,25,62)(20,289,26,63)(21,290,27,64)(22,291,28,65)(67,167,259,112)(68,168,260,113)(69,169,261,114)(70,170,262,115)(71,171,263,116)(72,172,264,117)(73,173,243,118)(74,174,244,119)(75,175,245,120)(76,176,246,121)(77,155,247,122)(78,156,248,123)(79,157,249,124)(80,158,250,125)(81,159,251,126)(82,160,252,127)(83,161,253,128)(84,162,254,129)(85,163,255,130)(86,164,256,131)(87,165,257,132)(88,166,258,111)(89,348,216,274)(90,349,217,275)(91,350,218,276)(92,351,219,277)(93,352,220,278)(94,331,199,279)(95,332,200,280)(96,333,201,281)(97,334,202,282)(98,335,203,283)(99,336,204,284)(100,337,205,285)(101,338,206,286)(102,339,207,265)(103,340,208,266)(104,341,209,267)(105,342,210,268)(106,343,211,269)(107,344,212,270)(108,345,213,271)(109,346,214,272)(110,347,215,273)(133,310,225,197)(134,311,226,198)(135,312,227,177)(136,313,228,178)(137,314,229,179)(138,315,230,180)(139,316,231,181)(140,317,232,182)(141,318,233,183)(142,319,234,184)(143,320,235,185)(144,321,236,186)(145,322,237,187)(146,323,238,188)(147,324,239,189)(148,325,240,190)(149,326,241,191)(150,327,242,192)(151,328,221,193)(152,329,222,194)(153,330,223,195)(154,309,224,196) );
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)], [(1,312,125,337,29,177,158,285),(2,313,126,338,30,178,159,286),(3,314,127,339,31,179,160,265),(4,315,128,340,32,180,161,266),(5,316,129,341,33,181,162,267),(6,317,130,342,34,182,163,268),(7,318,131,343,35,183,164,269),(8,319,132,344,36,184,165,270),(9,320,111,345,37,185,166,271),(10,321,112,346,38,186,167,272),(11,322,113,347,39,187,168,273),(12,323,114,348,40,188,169,274),(13,324,115,349,41,189,170,275),(14,325,116,350,42,190,171,276),(15,326,117,351,43,191,172,277),(16,327,118,352,44,192,173,278),(17,328,119,331,23,193,174,279),(18,329,120,332,24,194,175,280),(19,330,121,333,25,195,176,281),(20,309,122,334,26,196,155,282),(21,310,123,335,27,197,156,283),(22,311,124,336,28,198,157,284),(45,206,81,228,293,101,251,136),(46,207,82,229,294,102,252,137),(47,208,83,230,295,103,253,138),(48,209,84,231,296,104,254,139),(49,210,85,232,297,105,255,140),(50,211,86,233,298,106,256,141),(51,212,87,234,299,107,257,142),(52,213,88,235,300,108,258,143),(53,214,67,236,301,109,259,144),(54,215,68,237,302,110,260,145),(55,216,69,238,303,89,261,146),(56,217,70,239,304,90,262,147),(57,218,71,240,305,91,263,148),(58,219,72,241,306,92,264,149),(59,220,73,242,307,93,243,150),(60,199,74,221,308,94,244,151),(61,200,75,222,287,95,245,152),(62,201,76,223,288,96,246,153),(63,202,77,224,289,97,247,154),(64,203,78,225,290,98,248,133),(65,204,79,226,291,99,249,134),(66,205,80,227,292,100,250,135)], [(1,292,29,66),(2,293,30,45),(3,294,31,46),(4,295,32,47),(5,296,33,48),(6,297,34,49),(7,298,35,50),(8,299,36,51),(9,300,37,52),(10,301,38,53),(11,302,39,54),(12,303,40,55),(13,304,41,56),(14,305,42,57),(15,306,43,58),(16,307,44,59),(17,308,23,60),(18,287,24,61),(19,288,25,62),(20,289,26,63),(21,290,27,64),(22,291,28,65),(67,167,259,112),(68,168,260,113),(69,169,261,114),(70,170,262,115),(71,171,263,116),(72,172,264,117),(73,173,243,118),(74,174,244,119),(75,175,245,120),(76,176,246,121),(77,155,247,122),(78,156,248,123),(79,157,249,124),(80,158,250,125),(81,159,251,126),(82,160,252,127),(83,161,253,128),(84,162,254,129),(85,163,255,130),(86,164,256,131),(87,165,257,132),(88,166,258,111),(89,348,216,274),(90,349,217,275),(91,350,218,276),(92,351,219,277),(93,352,220,278),(94,331,199,279),(95,332,200,280),(96,333,201,281),(97,334,202,282),(98,335,203,283),(99,336,204,284),(100,337,205,285),(101,338,206,286),(102,339,207,265),(103,340,208,266),(104,341,209,267),(105,342,210,268),(106,343,211,269),(107,344,212,270),(108,345,213,271),(109,346,214,272),(110,347,215,273),(133,310,225,197),(134,311,226,198),(135,312,227,177),(136,313,228,178),(137,314,229,179),(138,315,230,180),(139,316,231,181),(140,317,232,182),(141,318,233,183),(142,319,234,184),(143,320,235,185),(144,321,236,186),(145,322,237,187),(146,323,238,188),(147,324,239,189),(148,325,240,190),(149,326,241,191),(150,327,242,192),(151,328,221,193),(152,329,222,194),(153,330,223,195),(154,309,224,196)]])
154 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 11A | ··· | 11J | 22A | ··· | 22AD | 44A | ··· | 44T | 44U | ··· | 44BH | 88A | ··· | 88AN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 |
154 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | |||||||
| image | C1 | C2 | C2 | C2 | C11 | C22 | C22 | C22 | D4 | D4 | Q16 | D4×C11 | D4×C11 | C11×Q16 |
| kernel | Q16×C22 | C2×C88 | C11×Q16 | Q8×C22 | C2×Q16 | C2×C8 | Q16 | C2×Q8 | C44 | C2×C22 | C22 | C4 | C22 | C2 |
| # reps | 1 | 1 | 4 | 2 | 10 | 10 | 40 | 20 | 1 | 1 | 4 | 10 | 10 | 40 |
Matrix representation of Q16×C22 ►in GL3(𝔽89) generated by
| 88 | 0 | 0 |
| 0 | 22 | 0 |
| 0 | 0 | 22 |
| 1 | 0 | 0 |
| 0 | 25 | 25 |
| 0 | 32 | 0 |
| 1 | 0 | 0 |
| 0 | 77 | 66 |
| 0 | 45 | 12 |
G:=sub<GL(3,GF(89))| [88,0,0,0,22,0,0,0,22],[1,0,0,0,25,32,0,25,0],[1,0,0,0,77,45,0,66,12] >;
Q16×C22 in GAP, Magma, Sage, TeX
Q_{16}\times C_{22} % in TeX
G:=Group("Q16xC22"); // GroupNames label
G:=SmallGroup(352,169);
// by ID
G=gap.SmallGroup(352,169);
# by ID
G:=PCGroup([6,-2,-2,-2,-11,-2,-2,1056,1081,1063,7924,3970,88]);
// Polycyclic
G:=Group<a,b,c|a^22=b^8=1,c^2=b^4,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations