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G = Q16×C23order 368 = 24·23

Direct product of C23 and Q16

direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary

Aliases: Q16×C23, C8.C46, Q8.C46, C184.3C2, C46.16D4, C92.19C22, C4.3(C2×C46), C2.5(D4×C23), (Q8×C23).2C2, SmallGroup(368,26)

Series: Derived Chief Lower central Upper central

C1C4 — Q16×C23
C1C2C4C92Q8×C23 — Q16×C23
C1C2C4 — Q16×C23
C1C46C92 — Q16×C23

Generators and relations for Q16×C23
 G = < a,b,c | a23=b8=1, c2=b4, ab=ba, ac=ca, cbc-1=b-1 >

2C4
2C4
2C92
2C92

Smallest permutation representation of Q16×C23
Regular action on 368 points
Generators in S368
(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)(346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368)
(1 221 266 283 356 68 141 115)(2 222 267 284 357 69 142 93)(3 223 268 285 358 47 143 94)(4 224 269 286 359 48 144 95)(5 225 270 287 360 49 145 96)(6 226 271 288 361 50 146 97)(7 227 272 289 362 51 147 98)(8 228 273 290 363 52 148 99)(9 229 274 291 364 53 149 100)(10 230 275 292 365 54 150 101)(11 208 276 293 366 55 151 102)(12 209 254 294 367 56 152 103)(13 210 255 295 368 57 153 104)(14 211 256 296 346 58 154 105)(15 212 257 297 347 59 155 106)(16 213 258 298 348 60 156 107)(17 214 259 299 349 61 157 108)(18 215 260 277 350 62 158 109)(19 216 261 278 351 63 159 110)(20 217 262 279 352 64 160 111)(21 218 263 280 353 65 161 112)(22 219 264 281 354 66 139 113)(23 220 265 282 355 67 140 114)(24 137 166 306 233 198 325 78)(25 138 167 307 234 199 326 79)(26 116 168 308 235 200 327 80)(27 117 169 309 236 201 328 81)(28 118 170 310 237 202 329 82)(29 119 171 311 238 203 330 83)(30 120 172 312 239 204 331 84)(31 121 173 313 240 205 332 85)(32 122 174 314 241 206 333 86)(33 123 175 315 242 207 334 87)(34 124 176 316 243 185 335 88)(35 125 177 317 244 186 336 89)(36 126 178 318 245 187 337 90)(37 127 179 319 246 188 338 91)(38 128 180 320 247 189 339 92)(39 129 181 321 248 190 340 70)(40 130 182 322 249 191 341 71)(41 131 183 300 250 192 342 72)(42 132 184 301 251 193 343 73)(43 133 162 302 252 194 344 74)(44 134 163 303 253 195 345 75)(45 135 164 304 231 196 323 76)(46 136 165 305 232 197 324 77)
(1 75 356 303)(2 76 357 304)(3 77 358 305)(4 78 359 306)(5 79 360 307)(6 80 361 308)(7 81 362 309)(8 82 363 310)(9 83 364 311)(10 84 365 312)(11 85 366 313)(12 86 367 314)(13 87 368 315)(14 88 346 316)(15 89 347 317)(16 90 348 318)(17 91 349 319)(18 92 350 320)(19 70 351 321)(20 71 352 322)(21 72 353 300)(22 73 354 301)(23 74 355 302)(24 286 233 95)(25 287 234 96)(26 288 235 97)(27 289 236 98)(28 290 237 99)(29 291 238 100)(30 292 239 101)(31 293 240 102)(32 294 241 103)(33 295 242 104)(34 296 243 105)(35 297 244 106)(36 298 245 107)(37 299 246 108)(38 277 247 109)(39 278 248 110)(40 279 249 111)(41 280 250 112)(42 281 251 113)(43 282 252 114)(44 283 253 115)(45 284 231 93)(46 285 232 94)(47 165 223 324)(48 166 224 325)(49 167 225 326)(50 168 226 327)(51 169 227 328)(52 170 228 329)(53 171 229 330)(54 172 230 331)(55 173 208 332)(56 174 209 333)(57 175 210 334)(58 176 211 335)(59 177 212 336)(60 178 213 337)(61 179 214 338)(62 180 215 339)(63 181 216 340)(64 182 217 341)(65 183 218 342)(66 184 219 343)(67 162 220 344)(68 163 221 345)(69 164 222 323)(116 271 200 146)(117 272 201 147)(118 273 202 148)(119 274 203 149)(120 275 204 150)(121 276 205 151)(122 254 206 152)(123 255 207 153)(124 256 185 154)(125 257 186 155)(126 258 187 156)(127 259 188 157)(128 260 189 158)(129 261 190 159)(130 262 191 160)(131 263 192 161)(132 264 193 139)(133 265 194 140)(134 266 195 141)(135 267 196 142)(136 268 197 143)(137 269 198 144)(138 270 199 145)

G:=sub<Sym(368)| (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)(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368), (1,221,266,283,356,68,141,115)(2,222,267,284,357,69,142,93)(3,223,268,285,358,47,143,94)(4,224,269,286,359,48,144,95)(5,225,270,287,360,49,145,96)(6,226,271,288,361,50,146,97)(7,227,272,289,362,51,147,98)(8,228,273,290,363,52,148,99)(9,229,274,291,364,53,149,100)(10,230,275,292,365,54,150,101)(11,208,276,293,366,55,151,102)(12,209,254,294,367,56,152,103)(13,210,255,295,368,57,153,104)(14,211,256,296,346,58,154,105)(15,212,257,297,347,59,155,106)(16,213,258,298,348,60,156,107)(17,214,259,299,349,61,157,108)(18,215,260,277,350,62,158,109)(19,216,261,278,351,63,159,110)(20,217,262,279,352,64,160,111)(21,218,263,280,353,65,161,112)(22,219,264,281,354,66,139,113)(23,220,265,282,355,67,140,114)(24,137,166,306,233,198,325,78)(25,138,167,307,234,199,326,79)(26,116,168,308,235,200,327,80)(27,117,169,309,236,201,328,81)(28,118,170,310,237,202,329,82)(29,119,171,311,238,203,330,83)(30,120,172,312,239,204,331,84)(31,121,173,313,240,205,332,85)(32,122,174,314,241,206,333,86)(33,123,175,315,242,207,334,87)(34,124,176,316,243,185,335,88)(35,125,177,317,244,186,336,89)(36,126,178,318,245,187,337,90)(37,127,179,319,246,188,338,91)(38,128,180,320,247,189,339,92)(39,129,181,321,248,190,340,70)(40,130,182,322,249,191,341,71)(41,131,183,300,250,192,342,72)(42,132,184,301,251,193,343,73)(43,133,162,302,252,194,344,74)(44,134,163,303,253,195,345,75)(45,135,164,304,231,196,323,76)(46,136,165,305,232,197,324,77), (1,75,356,303)(2,76,357,304)(3,77,358,305)(4,78,359,306)(5,79,360,307)(6,80,361,308)(7,81,362,309)(8,82,363,310)(9,83,364,311)(10,84,365,312)(11,85,366,313)(12,86,367,314)(13,87,368,315)(14,88,346,316)(15,89,347,317)(16,90,348,318)(17,91,349,319)(18,92,350,320)(19,70,351,321)(20,71,352,322)(21,72,353,300)(22,73,354,301)(23,74,355,302)(24,286,233,95)(25,287,234,96)(26,288,235,97)(27,289,236,98)(28,290,237,99)(29,291,238,100)(30,292,239,101)(31,293,240,102)(32,294,241,103)(33,295,242,104)(34,296,243,105)(35,297,244,106)(36,298,245,107)(37,299,246,108)(38,277,247,109)(39,278,248,110)(40,279,249,111)(41,280,250,112)(42,281,251,113)(43,282,252,114)(44,283,253,115)(45,284,231,93)(46,285,232,94)(47,165,223,324)(48,166,224,325)(49,167,225,326)(50,168,226,327)(51,169,227,328)(52,170,228,329)(53,171,229,330)(54,172,230,331)(55,173,208,332)(56,174,209,333)(57,175,210,334)(58,176,211,335)(59,177,212,336)(60,178,213,337)(61,179,214,338)(62,180,215,339)(63,181,216,340)(64,182,217,341)(65,183,218,342)(66,184,219,343)(67,162,220,344)(68,163,221,345)(69,164,222,323)(116,271,200,146)(117,272,201,147)(118,273,202,148)(119,274,203,149)(120,275,204,150)(121,276,205,151)(122,254,206,152)(123,255,207,153)(124,256,185,154)(125,257,186,155)(126,258,187,156)(127,259,188,157)(128,260,189,158)(129,261,190,159)(130,262,191,160)(131,263,192,161)(132,264,193,139)(133,265,194,140)(134,266,195,141)(135,267,196,142)(136,268,197,143)(137,269,198,144)(138,270,199,145)>;

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)(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368), (1,221,266,283,356,68,141,115)(2,222,267,284,357,69,142,93)(3,223,268,285,358,47,143,94)(4,224,269,286,359,48,144,95)(5,225,270,287,360,49,145,96)(6,226,271,288,361,50,146,97)(7,227,272,289,362,51,147,98)(8,228,273,290,363,52,148,99)(9,229,274,291,364,53,149,100)(10,230,275,292,365,54,150,101)(11,208,276,293,366,55,151,102)(12,209,254,294,367,56,152,103)(13,210,255,295,368,57,153,104)(14,211,256,296,346,58,154,105)(15,212,257,297,347,59,155,106)(16,213,258,298,348,60,156,107)(17,214,259,299,349,61,157,108)(18,215,260,277,350,62,158,109)(19,216,261,278,351,63,159,110)(20,217,262,279,352,64,160,111)(21,218,263,280,353,65,161,112)(22,219,264,281,354,66,139,113)(23,220,265,282,355,67,140,114)(24,137,166,306,233,198,325,78)(25,138,167,307,234,199,326,79)(26,116,168,308,235,200,327,80)(27,117,169,309,236,201,328,81)(28,118,170,310,237,202,329,82)(29,119,171,311,238,203,330,83)(30,120,172,312,239,204,331,84)(31,121,173,313,240,205,332,85)(32,122,174,314,241,206,333,86)(33,123,175,315,242,207,334,87)(34,124,176,316,243,185,335,88)(35,125,177,317,244,186,336,89)(36,126,178,318,245,187,337,90)(37,127,179,319,246,188,338,91)(38,128,180,320,247,189,339,92)(39,129,181,321,248,190,340,70)(40,130,182,322,249,191,341,71)(41,131,183,300,250,192,342,72)(42,132,184,301,251,193,343,73)(43,133,162,302,252,194,344,74)(44,134,163,303,253,195,345,75)(45,135,164,304,231,196,323,76)(46,136,165,305,232,197,324,77), (1,75,356,303)(2,76,357,304)(3,77,358,305)(4,78,359,306)(5,79,360,307)(6,80,361,308)(7,81,362,309)(8,82,363,310)(9,83,364,311)(10,84,365,312)(11,85,366,313)(12,86,367,314)(13,87,368,315)(14,88,346,316)(15,89,347,317)(16,90,348,318)(17,91,349,319)(18,92,350,320)(19,70,351,321)(20,71,352,322)(21,72,353,300)(22,73,354,301)(23,74,355,302)(24,286,233,95)(25,287,234,96)(26,288,235,97)(27,289,236,98)(28,290,237,99)(29,291,238,100)(30,292,239,101)(31,293,240,102)(32,294,241,103)(33,295,242,104)(34,296,243,105)(35,297,244,106)(36,298,245,107)(37,299,246,108)(38,277,247,109)(39,278,248,110)(40,279,249,111)(41,280,250,112)(42,281,251,113)(43,282,252,114)(44,283,253,115)(45,284,231,93)(46,285,232,94)(47,165,223,324)(48,166,224,325)(49,167,225,326)(50,168,226,327)(51,169,227,328)(52,170,228,329)(53,171,229,330)(54,172,230,331)(55,173,208,332)(56,174,209,333)(57,175,210,334)(58,176,211,335)(59,177,212,336)(60,178,213,337)(61,179,214,338)(62,180,215,339)(63,181,216,340)(64,182,217,341)(65,183,218,342)(66,184,219,343)(67,162,220,344)(68,163,221,345)(69,164,222,323)(116,271,200,146)(117,272,201,147)(118,273,202,148)(119,274,203,149)(120,275,204,150)(121,276,205,151)(122,254,206,152)(123,255,207,153)(124,256,185,154)(125,257,186,155)(126,258,187,156)(127,259,188,157)(128,260,189,158)(129,261,190,159)(130,262,191,160)(131,263,192,161)(132,264,193,139)(133,265,194,140)(134,266,195,141)(135,267,196,142)(136,268,197,143)(137,269,198,144)(138,270,199,145) );

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),(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)], [(1,221,266,283,356,68,141,115),(2,222,267,284,357,69,142,93),(3,223,268,285,358,47,143,94),(4,224,269,286,359,48,144,95),(5,225,270,287,360,49,145,96),(6,226,271,288,361,50,146,97),(7,227,272,289,362,51,147,98),(8,228,273,290,363,52,148,99),(9,229,274,291,364,53,149,100),(10,230,275,292,365,54,150,101),(11,208,276,293,366,55,151,102),(12,209,254,294,367,56,152,103),(13,210,255,295,368,57,153,104),(14,211,256,296,346,58,154,105),(15,212,257,297,347,59,155,106),(16,213,258,298,348,60,156,107),(17,214,259,299,349,61,157,108),(18,215,260,277,350,62,158,109),(19,216,261,278,351,63,159,110),(20,217,262,279,352,64,160,111),(21,218,263,280,353,65,161,112),(22,219,264,281,354,66,139,113),(23,220,265,282,355,67,140,114),(24,137,166,306,233,198,325,78),(25,138,167,307,234,199,326,79),(26,116,168,308,235,200,327,80),(27,117,169,309,236,201,328,81),(28,118,170,310,237,202,329,82),(29,119,171,311,238,203,330,83),(30,120,172,312,239,204,331,84),(31,121,173,313,240,205,332,85),(32,122,174,314,241,206,333,86),(33,123,175,315,242,207,334,87),(34,124,176,316,243,185,335,88),(35,125,177,317,244,186,336,89),(36,126,178,318,245,187,337,90),(37,127,179,319,246,188,338,91),(38,128,180,320,247,189,339,92),(39,129,181,321,248,190,340,70),(40,130,182,322,249,191,341,71),(41,131,183,300,250,192,342,72),(42,132,184,301,251,193,343,73),(43,133,162,302,252,194,344,74),(44,134,163,303,253,195,345,75),(45,135,164,304,231,196,323,76),(46,136,165,305,232,197,324,77)], [(1,75,356,303),(2,76,357,304),(3,77,358,305),(4,78,359,306),(5,79,360,307),(6,80,361,308),(7,81,362,309),(8,82,363,310),(9,83,364,311),(10,84,365,312),(11,85,366,313),(12,86,367,314),(13,87,368,315),(14,88,346,316),(15,89,347,317),(16,90,348,318),(17,91,349,319),(18,92,350,320),(19,70,351,321),(20,71,352,322),(21,72,353,300),(22,73,354,301),(23,74,355,302),(24,286,233,95),(25,287,234,96),(26,288,235,97),(27,289,236,98),(28,290,237,99),(29,291,238,100),(30,292,239,101),(31,293,240,102),(32,294,241,103),(33,295,242,104),(34,296,243,105),(35,297,244,106),(36,298,245,107),(37,299,246,108),(38,277,247,109),(39,278,248,110),(40,279,249,111),(41,280,250,112),(42,281,251,113),(43,282,252,114),(44,283,253,115),(45,284,231,93),(46,285,232,94),(47,165,223,324),(48,166,224,325),(49,167,225,326),(50,168,226,327),(51,169,227,328),(52,170,228,329),(53,171,229,330),(54,172,230,331),(55,173,208,332),(56,174,209,333),(57,175,210,334),(58,176,211,335),(59,177,212,336),(60,178,213,337),(61,179,214,338),(62,180,215,339),(63,181,216,340),(64,182,217,341),(65,183,218,342),(66,184,219,343),(67,162,220,344),(68,163,221,345),(69,164,222,323),(116,271,200,146),(117,272,201,147),(118,273,202,148),(119,274,203,149),(120,275,204,150),(121,276,205,151),(122,254,206,152),(123,255,207,153),(124,256,185,154),(125,257,186,155),(126,258,187,156),(127,259,188,157),(128,260,189,158),(129,261,190,159),(130,262,191,160),(131,263,192,161),(132,264,193,139),(133,265,194,140),(134,266,195,141),(135,267,196,142),(136,268,197,143),(137,269,198,144),(138,270,199,145)])

161 conjugacy classes

class 1  2 4A4B4C8A8B23A···23V46A···46V92A···92V92W···92BN184A···184AR
order124448823···2346···4692···9292···92184···184
size11244221···11···12···24···42···2

161 irreducible representations

dim1111112222
type++++-
imageC1C2C2C23C46C46D4Q16D4×C23Q16×C23
kernelQ16×C23C184Q8×C23Q16C8Q8C46C23C2C1
# reps112222244122244

Matrix representation of Q16×C23 in GL2(𝔽47) generated by

280
028
,
034
297
,
3916
408
G:=sub<GL(2,GF(47))| [28,0,0,28],[0,29,34,7],[39,40,16,8] >;

Q16×C23 in GAP, Magma, Sage, TeX

Q_{16}\times C_{23}
% in TeX

G:=Group("Q16xC23");
// GroupNames label

G:=SmallGroup(368,26);
// by ID

G=gap.SmallGroup(368,26);
# by ID

G:=PCGroup([5,-2,-2,-23,-2,-2,920,941,926,5523,2768,58]);
// Polycyclic

G:=Group<a,b,c|a^23=b^8=1,c^2=b^4,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of Q16×C23 in TeX

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