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G = Q8×C45order 360 = 23·32·5

Direct product of C45 and Q8

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

Aliases: Q8×C45, C4.C90, C36.3C10, C180.7C2, C60.12C6, C12.4C30, C20.3C18, C90.24C22, C3.(Q8×C15), C2.2(C2×C90), C6.7(C2×C30), C15.2(C3×Q8), C30.30(C2×C6), C10.7(C2×C18), C18.7(C2×C10), (Q8×C15).2C3, (C3×Q8).2C15, SmallGroup(360,32)

Series: Derived Chief Lower central Upper central

C1C2 — Q8×C45
C1C3C6C30C90C180 — Q8×C45
C1C2 — Q8×C45
C1C90 — Q8×C45

Generators and relations for Q8×C45
 G = < a,b,c | a45=b4=1, c2=b2, ab=ba, ac=ca, cbc-1=b-1 >


Smallest permutation representation of Q8×C45
Regular action on 360 points
Generators in S360
(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)
(1 125 163 296)(2 126 164 297)(3 127 165 298)(4 128 166 299)(5 129 167 300)(6 130 168 301)(7 131 169 302)(8 132 170 303)(9 133 171 304)(10 134 172 305)(11 135 173 306)(12 91 174 307)(13 92 175 308)(14 93 176 309)(15 94 177 310)(16 95 178 311)(17 96 179 312)(18 97 180 313)(19 98 136 314)(20 99 137 315)(21 100 138 271)(22 101 139 272)(23 102 140 273)(24 103 141 274)(25 104 142 275)(26 105 143 276)(27 106 144 277)(28 107 145 278)(29 108 146 279)(30 109 147 280)(31 110 148 281)(32 111 149 282)(33 112 150 283)(34 113 151 284)(35 114 152 285)(36 115 153 286)(37 116 154 287)(38 117 155 288)(39 118 156 289)(40 119 157 290)(41 120 158 291)(42 121 159 292)(43 122 160 293)(44 123 161 294)(45 124 162 295)(46 246 217 326)(47 247 218 327)(48 248 219 328)(49 249 220 329)(50 250 221 330)(51 251 222 331)(52 252 223 332)(53 253 224 333)(54 254 225 334)(55 255 181 335)(56 256 182 336)(57 257 183 337)(58 258 184 338)(59 259 185 339)(60 260 186 340)(61 261 187 341)(62 262 188 342)(63 263 189 343)(64 264 190 344)(65 265 191 345)(66 266 192 346)(67 267 193 347)(68 268 194 348)(69 269 195 349)(70 270 196 350)(71 226 197 351)(72 227 198 352)(73 228 199 353)(74 229 200 354)(75 230 201 355)(76 231 202 356)(77 232 203 357)(78 233 204 358)(79 234 205 359)(80 235 206 360)(81 236 207 316)(82 237 208 317)(83 238 209 318)(84 239 210 319)(85 240 211 320)(86 241 212 321)(87 242 213 322)(88 243 214 323)(89 244 215 324)(90 245 216 325)
(1 53 163 224)(2 54 164 225)(3 55 165 181)(4 56 166 182)(5 57 167 183)(6 58 168 184)(7 59 169 185)(8 60 170 186)(9 61 171 187)(10 62 172 188)(11 63 173 189)(12 64 174 190)(13 65 175 191)(14 66 176 192)(15 67 177 193)(16 68 178 194)(17 69 179 195)(18 70 180 196)(19 71 136 197)(20 72 137 198)(21 73 138 199)(22 74 139 200)(23 75 140 201)(24 76 141 202)(25 77 142 203)(26 78 143 204)(27 79 144 205)(28 80 145 206)(29 81 146 207)(30 82 147 208)(31 83 148 209)(32 84 149 210)(33 85 150 211)(34 86 151 212)(35 87 152 213)(36 88 153 214)(37 89 154 215)(38 90 155 216)(39 46 156 217)(40 47 157 218)(41 48 158 219)(42 49 159 220)(43 50 160 221)(44 51 161 222)(45 52 162 223)(91 344 307 264)(92 345 308 265)(93 346 309 266)(94 347 310 267)(95 348 311 268)(96 349 312 269)(97 350 313 270)(98 351 314 226)(99 352 315 227)(100 353 271 228)(101 354 272 229)(102 355 273 230)(103 356 274 231)(104 357 275 232)(105 358 276 233)(106 359 277 234)(107 360 278 235)(108 316 279 236)(109 317 280 237)(110 318 281 238)(111 319 282 239)(112 320 283 240)(113 321 284 241)(114 322 285 242)(115 323 286 243)(116 324 287 244)(117 325 288 245)(118 326 289 246)(119 327 290 247)(120 328 291 248)(121 329 292 249)(122 330 293 250)(123 331 294 251)(124 332 295 252)(125 333 296 253)(126 334 297 254)(127 335 298 255)(128 336 299 256)(129 337 300 257)(130 338 301 258)(131 339 302 259)(132 340 303 260)(133 341 304 261)(134 342 305 262)(135 343 306 263)

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

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

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

225 conjugacy classes

class 1  2 3A3B4A4B4C5A5B5C5D6A6B9A···9F10A10B10C10D12A···12F15A···15H18A···18F20A···20L30A···30H36A···36R45A···45X60A···60X90A···90X180A···180BT
order12334445555669···91010101012···1215···1518···1820···2030···3036···3645···4560···6090···90180···180
size11112221111111···111112···21···11···12···21···12···21···12···21···12···2

225 irreducible representations

dim111111111111222222
type++-
imageC1C2C3C5C6C9C10C15C18C30C45C90Q8C3×Q8C5×Q8Q8×C9Q8×C15Q8×C45
kernelQ8×C45C180Q8×C15Q8×C9C60C5×Q8C36C3×Q8C20C12Q8C4C45C15C9C5C3C1
# reps132466128182424721246824

Matrix representation of Q8×C45 in GL3(𝔽181) generated by

7300
050
005
,
100
01179
01180
,
18000
011066
014371
G:=sub<GL(3,GF(181))| [73,0,0,0,5,0,0,0,5],[1,0,0,0,1,1,0,179,180],[180,0,0,0,110,143,0,66,71] >;

Q8×C45 in GAP, Magma, Sage, TeX

Q_8\times C_{45}
% in TeX

G:=Group("Q8xC45");
// GroupNames label

G:=SmallGroup(360,32);
// by ID

G=gap.SmallGroup(360,32);
# by ID

G:=PCGroup([6,-2,-2,-3,-5,-2,-3,360,745,367,554]);
// Polycyclic

G:=Group<a,b,c|a^45=b^4=1,c^2=b^2,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of Q8×C45 in TeX

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