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## G = C5×C23.78C23order 320 = 26·5

### Direct product of C5 and C23.78C23

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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C23 — C5×C23.78C23
 Chief series C1 — C2 — C22 — C23 — C22×C10 — C22×C20 — Q8×C2×C10 — C5×C23.78C23
 Lower central C1 — C23 — C5×C23.78C23
 Upper central C1 — C22×C10 — C5×C23.78C23

Generators and relations for C5×C23.78C23
G = < a,b,c,d,e,f,g | a5=b2=c2=d2=1, e2=f2=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, gfg-1=df=fd, dg=gd >

Subgroups: 282 in 182 conjugacy classes, 86 normal (14 characteristic)
C1, C2, C2, C4, C22, C22, C5, C2×C4, C2×C4, Q8, C23, C10, C10, C4⋊C4, C22×C4, C22×C4, C2×Q8, C20, C2×C10, C2×C10, C2.C42, C2×C4⋊C4, C22×Q8, C2×C20, C2×C20, C5×Q8, C22×C10, C23.78C23, C5×C4⋊C4, C22×C20, C22×C20, Q8×C10, C5×C2.C42, C10×C4⋊C4, Q8×C2×C10, C5×C23.78C23
Quotients: C1, C2, C22, C5, D4, Q8, C23, C10, C2×D4, C2×Q8, C4○D4, C2×C10, C22≀C2, C22⋊Q8, C4⋊Q8, C5×D4, C5×Q8, C22×C10, C23.78C23, D4×C10, Q8×C10, C5×C4○D4, C5×C22≀C2, C5×C22⋊Q8, C5×C4⋊Q8, C5×C23.78C23

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

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

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

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

110 conjugacy classes

 class 1 2A ··· 2G 4A ··· 4N 5A 5B 5C 5D 10A ··· 10AB 20A ··· 20BD order 1 2 ··· 2 4 ··· 4 5 5 5 5 10 ··· 10 20 ··· 20 size 1 1 ··· 1 4 ··· 4 1 1 1 1 1 ··· 1 4 ··· 4

110 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 type + + + + + - image C1 C2 C2 C2 C5 C10 C10 C10 D4 Q8 C4○D4 C5×D4 C5×Q8 C5×C4○D4 kernel C5×C23.78C23 C5×C2.C42 C10×C4⋊C4 Q8×C2×C10 C23.78C23 C2.C42 C2×C4⋊C4 C22×Q8 C2×C20 C2×C20 C2×C10 C2×C4 C2×C4 C22 # reps 1 3 3 1 4 12 12 4 6 6 2 24 24 8

Matrix representation of C5×C23.78C23 in GL6(𝔽41)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 18 0 0 0 0 0 0 18 0 0 0 0 0 0 16 0 0 0 0 0 0 16
,
 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 40 0 0 0 0 0 0 40
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40
,
 0 1 0 0 0 0 40 0 0 0 0 0 0 0 0 1 0 0 0 0 40 0 0 0 0 0 0 0 27 34 0 0 0 0 34 14
,
 32 0 0 0 0 0 0 9 0 0 0 0 0 0 3 21 0 0 0 0 21 38 0 0 0 0 0 0 34 14 0 0 0 0 14 7
,
 32 0 0 0 0 0 0 32 0 0 0 0 0 0 0 1 0 0 0 0 40 0 0 0 0 0 0 0 0 1 0 0 0 0 40 0

G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,18,0,0,0,0,0,0,18,0,0,0,0,0,0,16,0,0,0,0,0,0,16],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,27,34,0,0,0,0,34,14],[32,0,0,0,0,0,0,9,0,0,0,0,0,0,3,21,0,0,0,0,21,38,0,0,0,0,0,0,34,14,0,0,0,0,14,7],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0] >;

C5×C23.78C23 in GAP, Magma, Sage, TeX

C_5\times C_2^3._{78}C_2^3
% in TeX

G:=Group("C5xC2^3.78C2^3");
// GroupNames label

G:=SmallGroup(320,896);
// by ID

G=gap.SmallGroup(320,896);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,280,589,288,1766,1731,226]);
// Polycyclic

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

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