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G = C45⋊Q8order 360 = 23·32·5

The semidirect product of C45 and Q8 acting via Q8/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C45⋊Q8, C30.1D6, C51Dic18, C91Dic10, Dic9.D5, C15.Dic6, C18.1D10, C10.1D18, C90.1C22, Dic5.1D9, Dic45.2C2, C3.(C15⋊Q8), C6.8(S3×D5), C2.4(D5×D9), (C5×Dic9).1C2, (C3×Dic5).1S3, (C9×Dic5).1C2, SmallGroup(360,7)

Series: Derived Chief Lower central Upper central

C1C90 — C45⋊Q8
C1C3C15C45C90C9×Dic5 — C45⋊Q8
C45C90 — C45⋊Q8
C1C2

Generators and relations for C45⋊Q8
 G = < a,b,c | a45=b4=1, c2=b2, bab-1=a26, cac-1=a19, cbc-1=b-1 >

5C4
9C4
45C4
45Q8
3Dic3
5C12
15Dic3
9Dic5
9C20
15Dic6
5C36
5Dic9
9Dic10
3C5×Dic3
3Dic15
5Dic18
3C15⋊Q8

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

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

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

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

45 conjugacy classes

class 1  2  3 4A4B4C5A5B 6 9A9B9C10A10B12A12B15A15B18A18B18C20A20B20C20D30A30B36A···36F45A···45F90A···90F
order12344455699910101212151518181820202020303036···3645···4590···90
size11210189022222222101044222181818184410···104···44···4

45 irreducible representations

dim111122222222224444
type+++++-++++-+--+-+-
imageC1C2C2C2S3Q8D5D6D9D10Dic6D18Dic10Dic18S3×D5C15⋊Q8D5×D9C45⋊Q8
kernelC45⋊Q8C5×Dic9C9×Dic5Dic45C3×Dic5C45Dic9C30Dic5C18C15C10C9C5C6C3C2C1
# reps111111213223462266

Matrix representation of C45⋊Q8 in GL4(𝔽181) generated by

1418000
1518000
0013154
001274
,
1329100
834900
00144123
008637
,
1082500
47300
0010
0001
G:=sub<GL(4,GF(181))| [14,15,0,0,180,180,0,0,0,0,131,127,0,0,54,4],[132,83,0,0,91,49,0,0,0,0,144,86,0,0,123,37],[108,4,0,0,25,73,0,0,0,0,1,0,0,0,0,1] >;

C45⋊Q8 in GAP, Magma, Sage, TeX

C_{45}\rtimes Q_8
% in TeX

G:=Group("C45:Q8");
// GroupNames label

G:=SmallGroup(360,7);
// by ID

G=gap.SmallGroup(360,7);
# by ID

G:=PCGroup([6,-2,-2,-2,-3,-5,-3,24,73,31,1641,741,2884,4331]);
// Polycyclic

G:=Group<a,b,c|a^45=b^4=1,c^2=b^2,b*a*b^-1=a^26,c*a*c^-1=a^19,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C45⋊Q8 in TeX

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