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## G = C5×C23.63C23order 320 = 26·5

### Direct product of C5 and C23.63C23

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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C5×C23.63C23
 Chief series C1 — C2 — C22 — C23 — C22×C10 — C22×C20 — C10×C4⋊C4 — C5×C23.63C23
 Lower central C1 — C22 — C5×C23.63C23
 Upper central C1 — C22×C10 — C5×C23.63C23

Generators and relations for C5×C23.63C23
G = < a,b,c,d,e,f,g | a5=b2=c2=d2=1, e2=f2=d, g2=b, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bc=cb, bd=db, fef-1=be=eb, bf=fb, bg=gb, cd=dc, geg-1=ce=ec, cf=fc, cg=gc, de=ed, df=fd, dg=gd, fg=gf >

Subgroups: 226 in 154 conjugacy classes, 90 normal (62 characteristic)
C1, C2, C4, C22, C5, C2×C4, C2×C4, C23, C10, C42, C4⋊C4, C4⋊C4, C22×C4, C20, C2×C10, C2.C42, C2×C42, C2×C4⋊C4, C2×C20, C2×C20, C22×C10, C23.63C23, C4×C20, C5×C4⋊C4, C5×C4⋊C4, C22×C20, C5×C2.C42, C2×C4×C20, C10×C4⋊C4, C5×C23.63C23
Quotients:

Smallest permutation representation of C5×C23.63C23
Regular action on 320 points
Generators in S320
(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)
(1 42)(2 43)(3 44)(4 45)(5 41)(6 300)(7 296)(8 297)(9 298)(10 299)(11 53)(12 54)(13 55)(14 51)(15 52)(16 301)(17 302)(18 303)(19 304)(20 305)(21 315)(22 311)(23 312)(24 313)(25 314)(26 69)(27 70)(28 66)(29 67)(30 68)(31 316)(32 317)(33 318)(34 319)(35 320)(36 46)(37 47)(38 48)(39 49)(40 50)(56 81)(57 82)(58 83)(59 84)(60 85)(61 95)(62 91)(63 92)(64 93)(65 94)(71 109)(72 110)(73 106)(74 107)(75 108)(76 86)(77 87)(78 88)(79 89)(80 90)(96 121)(97 122)(98 123)(99 124)(100 125)(101 135)(102 131)(103 132)(104 133)(105 134)(111 149)(112 150)(113 146)(114 147)(115 148)(116 126)(117 127)(118 128)(119 129)(120 130)(136 161)(137 162)(138 163)(139 164)(140 165)(141 175)(142 171)(143 172)(144 173)(145 174)(151 189)(152 190)(153 186)(154 187)(155 188)(156 166)(157 167)(158 168)(159 169)(160 170)(176 201)(177 202)(178 203)(179 204)(180 205)(181 215)(182 211)(183 212)(184 213)(185 214)(191 229)(192 230)(193 226)(194 227)(195 228)(196 206)(197 207)(198 208)(199 209)(200 210)(216 241)(217 242)(218 243)(219 244)(220 245)(221 255)(222 251)(223 252)(224 253)(225 254)(231 269)(232 270)(233 266)(234 267)(235 268)(236 246)(237 247)(238 248)(239 249)(240 250)(256 281)(257 282)(258 283)(259 284)(260 285)(261 295)(262 291)(263 292)(264 293)(265 294)(271 309)(272 310)(273 306)(274 307)(275 308)(276 286)(277 287)(278 288)(279 289)(280 290)
(1 66)(2 67)(3 68)(4 69)(5 70)(6 23)(7 24)(8 25)(9 21)(10 22)(11 36)(12 37)(13 38)(14 39)(15 40)(16 33)(17 34)(18 35)(19 31)(20 32)(26 45)(27 41)(28 42)(29 43)(30 44)(46 53)(47 54)(48 55)(49 51)(50 52)(56 73)(57 74)(58 75)(59 71)(60 72)(61 78)(62 79)(63 80)(64 76)(65 77)(81 106)(82 107)(83 108)(84 109)(85 110)(86 93)(87 94)(88 95)(89 91)(90 92)(96 113)(97 114)(98 115)(99 111)(100 112)(101 118)(102 119)(103 120)(104 116)(105 117)(121 146)(122 147)(123 148)(124 149)(125 150)(126 133)(127 134)(128 135)(129 131)(130 132)(136 153)(137 154)(138 155)(139 151)(140 152)(141 158)(142 159)(143 160)(144 156)(145 157)(161 186)(162 187)(163 188)(164 189)(165 190)(166 173)(167 174)(168 175)(169 171)(170 172)(176 193)(177 194)(178 195)(179 191)(180 192)(181 198)(182 199)(183 200)(184 196)(185 197)(201 226)(202 227)(203 228)(204 229)(205 230)(206 213)(207 214)(208 215)(209 211)(210 212)(216 233)(217 234)(218 235)(219 231)(220 232)(221 238)(222 239)(223 240)(224 236)(225 237)(241 266)(242 267)(243 268)(244 269)(245 270)(246 253)(247 254)(248 255)(249 251)(250 252)(256 273)(257 274)(258 275)(259 271)(260 272)(261 278)(262 279)(263 280)(264 276)(265 277)(281 306)(282 307)(283 308)(284 309)(285 310)(286 293)(287 294)(288 295)(289 291)(290 292)(296 313)(297 314)(298 315)(299 311)(300 312)(301 318)(302 319)(303 320)(304 316)(305 317)
(1 12)(2 13)(3 14)(4 15)(5 11)(6 304)(7 305)(8 301)(9 302)(10 303)(16 297)(17 298)(18 299)(19 300)(20 296)(21 319)(22 320)(23 316)(24 317)(25 318)(26 50)(27 46)(28 47)(29 48)(30 49)(31 312)(32 313)(33 314)(34 315)(35 311)(36 70)(37 66)(38 67)(39 68)(40 69)(41 53)(42 54)(43 55)(44 51)(45 52)(56 94)(57 95)(58 91)(59 92)(60 93)(61 82)(62 83)(63 84)(64 85)(65 81)(71 90)(72 86)(73 87)(74 88)(75 89)(76 110)(77 106)(78 107)(79 108)(80 109)(96 134)(97 135)(98 131)(99 132)(100 133)(101 122)(102 123)(103 124)(104 125)(105 121)(111 130)(112 126)(113 127)(114 128)(115 129)(116 150)(117 146)(118 147)(119 148)(120 149)(136 174)(137 175)(138 171)(139 172)(140 173)(141 162)(142 163)(143 164)(144 165)(145 161)(151 170)(152 166)(153 167)(154 168)(155 169)(156 190)(157 186)(158 187)(159 188)(160 189)(176 214)(177 215)(178 211)(179 212)(180 213)(181 202)(182 203)(183 204)(184 205)(185 201)(191 210)(192 206)(193 207)(194 208)(195 209)(196 230)(197 226)(198 227)(199 228)(200 229)(216 254)(217 255)(218 251)(219 252)(220 253)(221 242)(222 243)(223 244)(224 245)(225 241)(231 250)(232 246)(233 247)(234 248)(235 249)(236 270)(237 266)(238 267)(239 268)(240 269)(256 294)(257 295)(258 291)(259 292)(260 293)(261 282)(262 283)(263 284)(264 285)(265 281)(271 290)(272 286)(273 287)(274 288)(275 289)(276 310)(277 306)(278 307)(279 308)(280 309)
(1 185 12 201)(2 181 13 202)(3 182 14 203)(4 183 15 204)(5 184 11 205)(6 165 304 144)(7 161 305 145)(8 162 301 141)(9 163 302 142)(10 164 303 143)(16 175 297 137)(17 171 298 138)(18 172 299 139)(19 173 300 140)(20 174 296 136)(21 188 319 159)(22 189 320 160)(23 190 316 156)(24 186 317 157)(25 187 318 158)(26 210 50 191)(27 206 46 192)(28 207 47 193)(29 208 48 194)(30 209 49 195)(31 166 312 152)(32 167 313 153)(33 168 314 154)(34 169 315 155)(35 170 311 151)(36 230 70 196)(37 226 66 197)(38 227 67 198)(39 228 68 199)(40 229 69 200)(41 213 53 180)(42 214 54 176)(43 215 55 177)(44 211 51 178)(45 212 52 179)(56 254 94 216)(57 255 95 217)(58 251 91 218)(59 252 92 219)(60 253 93 220)(61 242 82 221)(62 243 83 222)(63 244 84 223)(64 245 85 224)(65 241 81 225)(71 250 90 231)(72 246 86 232)(73 247 87 233)(74 248 88 234)(75 249 89 235)(76 270 110 236)(77 266 106 237)(78 267 107 238)(79 268 108 239)(80 269 109 240)(96 294 134 256)(97 295 135 257)(98 291 131 258)(99 292 132 259)(100 293 133 260)(101 282 122 261)(102 283 123 262)(103 284 124 263)(104 285 125 264)(105 281 121 265)(111 290 130 271)(112 286 126 272)(113 287 127 273)(114 288 128 274)(115 289 129 275)(116 310 150 276)(117 306 146 277)(118 307 147 278)(119 308 148 279)(120 309 149 280)
(1 105 12 121)(2 101 13 122)(3 102 14 123)(4 103 15 124)(5 104 11 125)(6 220 304 253)(7 216 305 254)(8 217 301 255)(9 218 302 251)(10 219 303 252)(16 221 297 242)(17 222 298 243)(18 223 299 244)(19 224 300 245)(20 225 296 241)(21 235 319 249)(22 231 320 250)(23 232 316 246)(24 233 317 247)(25 234 318 248)(26 130 50 111)(27 126 46 112)(28 127 47 113)(29 128 48 114)(30 129 49 115)(31 236 312 270)(32 237 313 266)(33 238 314 267)(34 239 315 268)(35 240 311 269)(36 150 70 116)(37 146 66 117)(38 147 67 118)(39 148 68 119)(40 149 69 120)(41 133 53 100)(42 134 54 96)(43 135 55 97)(44 131 51 98)(45 132 52 99)(56 174 94 136)(57 175 95 137)(58 171 91 138)(59 172 92 139)(60 173 93 140)(61 162 82 141)(62 163 83 142)(63 164 84 143)(64 165 85 144)(65 161 81 145)(71 170 90 151)(72 166 86 152)(73 167 87 153)(74 168 88 154)(75 169 89 155)(76 190 110 156)(77 186 106 157)(78 187 107 158)(79 188 108 159)(80 189 109 160)(176 265 214 281)(177 261 215 282)(178 262 211 283)(179 263 212 284)(180 264 213 285)(181 257 202 295)(182 258 203 291)(183 259 204 292)(184 260 205 293)(185 256 201 294)(191 280 210 309)(192 276 206 310)(193 277 207 306)(194 278 208 307)(195 279 209 308)(196 272 230 286)(197 273 226 287)(198 274 227 288)(199 275 228 289)(200 271 229 290)
(1 56 42 81)(2 57 43 82)(3 58 44 83)(4 59 45 84)(5 60 41 85)(6 310 300 272)(7 306 296 273)(8 307 297 274)(9 308 298 275)(10 309 299 271)(11 93 53 64)(12 94 54 65)(13 95 55 61)(14 91 51 62)(15 92 52 63)(16 288 301 278)(17 289 302 279)(18 290 303 280)(19 286 304 276)(20 287 305 277)(21 283 315 258)(22 284 311 259)(23 285 312 260)(24 281 313 256)(25 282 314 257)(26 109 69 71)(27 110 70 72)(28 106 66 73)(29 107 67 74)(30 108 68 75)(31 293 316 264)(32 294 317 265)(33 295 318 261)(34 291 319 262)(35 292 320 263)(36 86 46 76)(37 87 47 77)(38 88 48 78)(39 89 49 79)(40 90 50 80)(96 161 121 136)(97 162 122 137)(98 163 123 138)(99 164 124 139)(100 165 125 140)(101 175 135 141)(102 171 131 142)(103 172 132 143)(104 173 133 144)(105 174 134 145)(111 189 149 151)(112 190 150 152)(113 186 146 153)(114 187 147 154)(115 188 148 155)(116 166 126 156)(117 167 127 157)(118 168 128 158)(119 169 129 159)(120 170 130 160)(176 266 201 233)(177 267 202 234)(178 268 203 235)(179 269 204 231)(180 270 205 232)(181 248 215 238)(182 249 211 239)(183 250 212 240)(184 246 213 236)(185 247 214 237)(191 244 229 219)(192 245 230 220)(193 241 226 216)(194 242 227 217)(195 243 228 218)(196 253 206 224)(197 254 207 225)(198 255 208 221)(199 251 209 222)(200 252 210 223)

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

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

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

140 conjugacy classes

 class 1 2A ··· 2G 4A ··· 4L 4M ··· 4T 5A 5B 5C 5D 10A ··· 10AB 20A ··· 20AV 20AW ··· 20CB order 1 2 ··· 2 4 ··· 4 4 ··· 4 5 5 5 5 10 ··· 10 20 ··· 20 20 ··· 20 size 1 1 ··· 1 2 ··· 2 4 ··· 4 1 1 1 1 1 ··· 1 2 ··· 2 4 ··· 4

140 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 type + + + + + - image C1 C2 C2 C2 C4 C5 C10 C10 C10 C20 D4 Q8 C4○D4 C5×D4 C5×Q8 C5×C4○D4 kernel C5×C23.63C23 C5×C2.C42 C2×C4×C20 C10×C4⋊C4 C5×C4⋊C4 C23.63C23 C2.C42 C2×C42 C2×C4⋊C4 C4⋊C4 C2×C20 C2×C20 C2×C10 C2×C4 C2×C4 C22 # reps 1 4 1 2 8 4 16 4 8 32 2 2 8 8 8 32

Matrix representation of C5×C23.63C23 in GL5(𝔽41)

 16 0 0 0 0 0 18 0 0 0 0 0 18 0 0 0 0 0 10 0 0 0 0 0 10
,
 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 40 0 0 0 0 0 40
,
 1 0 0 0 0 0 40 0 0 0 0 0 40 0 0 0 0 0 1 0 0 0 0 0 1
,
 40 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
,
 32 0 0 0 0 0 9 25 0 0 0 5 32 0 0 0 0 0 7 1 0 0 0 34 34
,
 9 0 0 0 0 0 40 0 0 0 0 0 40 0 0 0 0 0 40 39 0 0 0 0 1
,
 1 0 0 0 0 0 40 0 0 0 0 4 1 0 0 0 0 0 32 0 0 0 0 0 32

G:=sub<GL(5,GF(41))| [16,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,10,0,0,0,0,0,10],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,1],[40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[32,0,0,0,0,0,9,5,0,0,0,25,32,0,0,0,0,0,7,34,0,0,0,1,34],[9,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,39,1],[1,0,0,0,0,0,40,4,0,0,0,0,1,0,0,0,0,0,32,0,0,0,0,0,32] >;

C5×C23.63C23 in GAP, Magma, Sage, TeX

C_5\times C_2^3._{63}C_2^3
% in TeX

G:=Group("C5xC2^3.63C2^3");
// GroupNames label

G:=SmallGroup(320,888);
// by ID

G=gap.SmallGroup(320,888);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,1120,589,1128,1766,226]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^5=b^2=c^2=d^2=1,e^2=f^2=d,g^2=b,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,b*d=d*b,f*e*f^-1=b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,g*e*g^-1=c*e=e*c,c*f=f*c,c*g=g*c,d*e=e*d,d*f=f*d,d*g=g*d,f*g=g*f>;
// generators/relations

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