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G = C20.6M4(2)  order 320 = 26·5

6th non-split extension by C20 of M4(2) acting via M4(2)/C2=C2×C4

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C20.6M4(2), C5⋊C83Q8, C2.8(Q8×F5), C53(C84Q8), (C2×Q8).6F5, C10.8(C4×Q8), C4⋊Dic5.8C4, (Q8×C10).7C4, C20⋊C8.6C2, C2.9(Q8.F5), C10.24(C8○D4), (Q8×Dic5).16C2, Dic5.32(C2×Q8), C4.3(C22.F5), Dic5⋊C8.3C2, C10.32(C2×M4(2)), Dic5.71(C4○D4), C22.98(C22×F5), C10.C42.2C2, (C4×Dic5).197C22, (C2×Dic5).358C23, (C4×C5⋊C8).5C2, (C2×C4).42(C2×F5), (C2×C20).27(C2×C4), (C2×C5⋊C8).42C22, C2.11(C2×C22.F5), (C2×C10).87(C22×C4), (C2×Dic5).77(C2×C4), SmallGroup(320,1126)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C20.6M4(2)
C1C5C10Dic5C2×Dic5C2×C5⋊C8C4×C5⋊C8 — C20.6M4(2)
C5C2×C10 — C20.6M4(2)
C1C22C2×Q8

Generators and relations for C20.6M4(2)
 G = < a,b,c | a20=b8=1, c2=a10, bab-1=a3, cac-1=a11, cbc-1=b5 >

Subgroups: 266 in 94 conjugacy classes, 48 normal (26 characteristic)
C1, C2 [×3], C4 [×2], C4 [×7], C22, C5, C8 [×5], C2×C4, C2×C4 [×2], C2×C4 [×4], Q8 [×2], C10 [×3], C42 [×3], C4⋊C4 [×3], C2×C8 [×4], C2×Q8, Dic5 [×2], Dic5 [×3], C20 [×2], C20 [×2], C2×C10, C4×C8, C8⋊C4 [×2], C4⋊C8 [×3], C4×Q8, C5⋊C8 [×2], C5⋊C8 [×3], C2×Dic5 [×2], C2×Dic5 [×2], C2×C20, C2×C20 [×2], C5×Q8 [×2], C84Q8, C4×Dic5, C4×Dic5 [×2], C4⋊Dic5, C4⋊Dic5 [×2], C2×C5⋊C8 [×2], C2×C5⋊C8 [×2], Q8×C10, C4×C5⋊C8, C20⋊C8, C10.C42 [×2], Dic5⋊C8 [×2], Q8×Dic5, C20.6M4(2)
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], Q8 [×2], C23, M4(2) [×2], C22×C4, C2×Q8, C4○D4, F5, C4×Q8, C2×M4(2), C8○D4, C2×F5 [×3], C84Q8, C22.F5 [×2], C22×F5, Q8.F5, Q8×F5, C2×C22.F5, C20.6M4(2)

Smallest permutation representation of C20.6M4(2)
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 98 202 163 242 150 187 116)(2 85 211 166 243 157 196 119)(3 92 220 169 244 144 185 102)(4 99 209 172 245 151 194 105)(5 86 218 175 246 158 183 108)(6 93 207 178 247 145 192 111)(7 100 216 161 248 152 181 114)(8 87 205 164 249 159 190 117)(9 94 214 167 250 146 199 120)(10 81 203 170 251 153 188 103)(11 88 212 173 252 160 197 106)(12 95 201 176 253 147 186 109)(13 82 210 179 254 154 195 112)(14 89 219 162 255 141 184 115)(15 96 208 165 256 148 193 118)(16 83 217 168 257 155 182 101)(17 90 206 171 258 142 191 104)(18 97 215 174 259 149 200 107)(19 84 204 177 260 156 189 110)(20 91 213 180 241 143 198 113)(21 276 225 300 49 138 315 79)(22 263 234 283 50 125 304 62)(23 270 223 286 51 132 313 65)(24 277 232 289 52 139 302 68)(25 264 221 292 53 126 311 71)(26 271 230 295 54 133 320 74)(27 278 239 298 55 140 309 77)(28 265 228 281 56 127 318 80)(29 272 237 284 57 134 307 63)(30 279 226 287 58 121 316 66)(31 266 235 290 59 128 305 69)(32 273 224 293 60 135 314 72)(33 280 233 296 41 122 303 75)(34 267 222 299 42 129 312 78)(35 274 231 282 43 136 301 61)(36 261 240 285 44 123 310 64)(37 268 229 288 45 130 319 67)(38 275 238 291 46 137 308 70)(39 262 227 294 47 124 317 73)(40 269 236 297 48 131 306 76)
(1 263 11 273)(2 274 12 264)(3 265 13 275)(4 276 14 266)(5 267 15 277)(6 278 16 268)(7 269 17 279)(8 280 18 270)(9 271 19 261)(10 262 20 272)(21 162 31 172)(22 173 32 163)(23 164 33 174)(24 175 34 165)(25 166 35 176)(26 177 36 167)(27 168 37 178)(28 179 38 169)(29 170 39 180)(30 161 40 171)(41 107 51 117)(42 118 52 108)(43 109 53 119)(44 120 54 110)(45 111 55 101)(46 102 56 112)(47 113 57 103)(48 104 58 114)(49 115 59 105)(50 106 60 116)(61 186 71 196)(62 197 72 187)(63 188 73 198)(64 199 74 189)(65 190 75 200)(66 181 76 191)(67 192 77 182)(68 183 78 193)(69 194 79 184)(70 185 80 195)(81 317 91 307)(82 308 92 318)(83 319 93 309)(84 310 94 320)(85 301 95 311)(86 312 96 302)(87 303 97 313)(88 314 98 304)(89 305 99 315)(90 316 100 306)(121 248 131 258)(122 259 132 249)(123 250 133 260)(124 241 134 251)(125 252 135 242)(126 243 136 253)(127 254 137 244)(128 245 138 255)(129 256 139 246)(130 247 140 257)(141 235 151 225)(142 226 152 236)(143 237 153 227)(144 228 154 238)(145 239 155 229)(146 230 156 240)(147 221 157 231)(148 232 158 222)(149 223 159 233)(150 234 160 224)(201 292 211 282)(202 283 212 293)(203 294 213 284)(204 285 214 295)(205 296 215 286)(206 287 216 297)(207 298 217 288)(208 289 218 299)(209 300 219 290)(210 291 220 281)

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

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

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

38 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J4K4L 5 8A···8H8I8J8K8L10A10B10C20A···20F
order122244444444444458···8888810101020···20
size11112244555510102020410···10202020204448···8

38 irreducible representations

dim11111111222244488
type++++++-++-+-
imageC1C2C2C2C2C2C4C4Q8C4○D4M4(2)C8○D4F5C2×F5C22.F5Q8.F5Q8×F5
kernelC20.6M4(2)C4×C5⋊C8C20⋊C8C10.C42Dic5⋊C8Q8×Dic5C4⋊Dic5Q8×C10C5⋊C8Dic5C20C10C2×Q8C2×C4C4C2C2
# reps11122162224413411

Matrix representation of C20.6M4(2) in GL8(𝔽41)

400000000
040000000
003200000
004090000
000000040
000010040
000001040
000000140
,
2216000000
1919000000
0032390000
00090000
00003982740
00002573638
0000345324
0000132233
,
4039000000
01000000
0032390000
00090000
000040000
000004000
000000400
000000040

G:=sub<GL(8,GF(41))| [40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,32,40,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,40,40,40,40],[22,19,0,0,0,0,0,0,16,19,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,39,9,0,0,0,0,0,0,0,0,39,25,34,1,0,0,0,0,8,7,5,32,0,0,0,0,27,36,3,2,0,0,0,0,40,38,24,33],[40,0,0,0,0,0,0,0,39,1,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,39,9,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40] >;

C20.6M4(2) in GAP, Magma, Sage, TeX

C_{20}._6M_4(2)
% in TeX

G:=Group("C20.6M4(2)");
// GroupNames label

G:=SmallGroup(320,1126);
// by ID

G=gap.SmallGroup(320,1126);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,120,758,219,100,136,6278,1595]);
// Polycyclic

G:=Group<a,b,c|a^20=b^8=1,c^2=a^10,b*a*b^-1=a^3,c*a*c^-1=a^11,c*b*c^-1=b^5>;
// generators/relations

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