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## G = C5×C23.67C23order 320 = 26·5

### Direct product of C5 and C23.67C23

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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C5×C23.67C23
 Chief series C1 — C2 — C22 — C23 — C22×C10 — C22×C20 — C5×C2.C42 — C5×C23.67C23
 Lower central C1 — C22 — C5×C23.67C23
 Upper central C1 — C22×C10 — C5×C23.67C23

Generators and relations for C5×C23.67C23
G = < a,b,c,d,e,f,g | a5=b2=c2=d2=1, e2=d, f2=bcd, g2=c, 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: 274 in 186 conjugacy classes, 106 normal (26 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C2×C4, C2×C4, Q8, C23, C10, C10, C42, C4⋊C4, C22×C4, C22×C4, C2×Q8, C2×Q8, C20, C20, C2×C10, C2×C10, C2.C42, C2×C42, C2×C4⋊C4, C22×Q8, C2×C20, C2×C20, C5×Q8, C22×C10, C23.67C23, C4×C20, C5×C4⋊C4, C22×C20, C22×C20, Q8×C10, Q8×C10, C5×C2.C42, C2×C4×C20, C10×C4⋊C4, Q8×C2×C10, C5×C23.67C23
Quotients:

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

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

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

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

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 1 1 2 2 2 2 2 2 type + + + + + + - image C1 C2 C2 C2 C2 C4 C5 C10 C10 C10 C10 C20 D4 Q8 C4○D4 C5×D4 C5×Q8 C5×C4○D4 kernel C5×C23.67C23 C5×C2.C42 C2×C4×C20 C10×C4⋊C4 Q8×C2×C10 Q8×C10 C23.67C23 C2.C42 C2×C42 C2×C4⋊C4 C22×Q8 C2×Q8 C2×C20 C2×C20 C2×C10 C2×C4 C2×C4 C22 # reps 1 4 1 1 1 8 4 16 4 4 4 32 4 4 4 16 16 16

Matrix representation of C5×C23.67C23 in GL5(𝔽41)

 1 0 0 0 0 0 18 0 0 0 0 0 18 0 0 0 0 0 18 0 0 0 0 0 18
,
 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 40 0 0 0 0 0 40 0 0 0 0 0 40 0 0 0 0 0 40
,
 32 0 0 0 0 0 26 26 0 0 0 26 15 0 0 0 0 0 34 28 0 0 0 7 7
,
 32 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 2 0 0 0 0 40
,
 1 0 0 0 0 0 0 1 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 40

G:=sub<GL(5,GF(41))| [1,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,18],[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],[40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[32,0,0,0,0,0,26,26,0,0,0,26,15,0,0,0,0,0,34,7,0,0,0,28,7],[32,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,2,40],[1,0,0,0,0,0,0,40,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,40] >;

C5×C23.67C23 in GAP, Magma, Sage, TeX

C_5\times C_2^3._{67}C_2^3
% in TeX

G:=Group("C5xC2^3.67C2^3");
// GroupNames label

G:=SmallGroup(320,892);
// by ID

G=gap.SmallGroup(320,892);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,1120,589,1968,1766,436]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^5=b^2=c^2=d^2=1,e^2=d,f^2=b*c*d,g^2=c,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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