Copied to
clipboard

G = C5×C23.67C23order 320 = 26·5

Direct product of C5 and C23.67C23

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

Aliases: C5×C23.67C23, (C2×Q8)⋊3C20, (C2×C20)⋊11Q8, C2.5(Q8×C20), (Q8×C10)⋊23C4, C10.41(C4×Q8), (C2×C20).512D4, C10.37(C4⋊Q8), (C2×C42).11C10, C22.40(D4×C10), (C22×Q8).1C10, C22.15(Q8×C10), C10.86(C22⋊Q8), C20.122(C22⋊C4), C10.66(C4.4D4), C2.C42.7C10, C23.64(C22×C10), C22.40(C22×C20), (C22×C20).577C22, (C22×C10).455C23, (C2×C4)⋊3(C5×Q8), C2.3(C5×C4⋊Q8), (C2×C4×C20).34C2, (C2×C4⋊C4).8C10, (C2×C4).67(C5×D4), C4.7(C5×C22⋊C4), (C10×C4⋊C4).37C2, (Q8×C2×C10).11C2, (C2×C4).17(C2×C20), C2.5(C5×C22⋊Q8), C2.9(C10×C22⋊C4), C2.4(C5×C4.4D4), (C2×C20).439(C2×C4), (C2×C10).607(C2×D4), (C2×C10).107(C2×Q8), C22.25(C5×C4○D4), C10.137(C2×C22⋊C4), (C22×C4).91(C2×C10), (C2×C10).215(C4○D4), (C2×C10).328(C22×C4), (C5×C2.C42).26C2, SmallGroup(320,892)

Series: Derived Chief Lower central Upper central

C1C22 — C5×C23.67C23
C1C2C22C23C22×C10C22×C20C5×C2.C42 — C5×C23.67C23
C1C22 — C5×C23.67C23
C1C22×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 [×3], C2 [×4], C4 [×4], C4 [×10], C22 [×3], C22 [×4], C5, C2×C4 [×14], C2×C4 [×14], Q8 [×8], C23, C10 [×3], C10 [×4], C42 [×2], C4⋊C4 [×2], C22×C4, C22×C4 [×6], C2×Q8 [×4], C2×Q8 [×4], C20 [×4], C20 [×10], C2×C10 [×3], C2×C10 [×4], C2.C42 [×4], C2×C42, C2×C4⋊C4, C22×Q8, C2×C20 [×14], C2×C20 [×14], C5×Q8 [×8], C22×C10, C23.67C23, C4×C20 [×2], C5×C4⋊C4 [×2], C22×C20, C22×C20 [×6], Q8×C10 [×4], Q8×C10 [×4], C5×C2.C42 [×4], C2×C4×C20, C10×C4⋊C4, Q8×C2×C10, C5×C23.67C23
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C5, C2×C4 [×6], D4 [×4], Q8 [×4], C23, C10 [×7], C22⋊C4 [×4], C22×C4, C2×D4 [×2], C2×Q8 [×2], C4○D4 [×2], C20 [×4], C2×C10 [×7], C2×C22⋊C4, C4×Q8 [×2], C22⋊Q8 [×2], C4.4D4, C4⋊Q8, C2×C20 [×6], C5×D4 [×4], C5×Q8 [×4], C22×C10, C23.67C23, C5×C22⋊C4 [×4], C22×C20, D4×C10 [×2], Q8×C10 [×2], C5×C4○D4 [×2], C10×C22⋊C4, Q8×C20 [×2], C5×C22⋊Q8 [×2], C5×C4.4D4, C5×C4⋊Q8, C5×C23.67C23

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

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

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

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

140 conjugacy classes

class 1 2A···2G4A···4L4M···4T5A5B5C5D10A···10AB20A···20AV20AW···20CB
order12···24···44···4555510···1020···2020···20
size11···12···24···411111···12···24···4

140 irreducible representations

dim111111111111222222
type++++++-
imageC1C2C2C2C2C4C5C10C10C10C10C20D4Q8C4○D4C5×D4C5×Q8C5×C4○D4
kernelC5×C23.67C23C5×C2.C42C2×C4×C20C10×C4⋊C4Q8×C2×C10Q8×C10C23.67C23C2.C42C2×C42C2×C4⋊C4C22×Q8C2×Q8C2×C20C2×C20C2×C10C2×C4C2×C4C22
# reps14111841644432444161616

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

10000
018000
001800
000180
000018
,
10000
01000
00100
000400
000040
,
10000
040000
004000
00010
00001
,
400000
040000
004000
000400
000040
,
320000
0262600
0261500
0003428
00077
,
320000
01000
00100
00012
000040
,
10000
00100
040000
000400
000040

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

׿
×
𝔽