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G = C20.48(C4⋊C4)  order 320 = 26·5

17th non-split extension by C20 of C4⋊C4 acting via C4⋊C4/C22=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C20.48(C4⋊C4), (C2×C20).19Q8, C54(C428C4), (C4×Dic5)⋊12C4, (C2×C20).139D4, (C2×C4).30Dic10, (C22×C4).39D10, C2.4(C4.Dic10), C4.17(C10.D4), C10.49(C4.4D4), C2.3(C20.17D4), C2.1(C20.23D4), C10.17(C42.C2), C22.28(C2×Dic10), C23.291(C22×D5), C10.54(C42⋊C2), C22.55(D42D5), (C22×C20).142C22, (C22×C10).341C23, C22.23(Q82D5), C10.10C42.17C2, (C22×Dic5).212C22, C10.60(C2×C4⋊C4), (C2×C4⋊C4).14D5, (C10×C4⋊C4).13C2, (C2×C4×Dic5).7C2, (C2×C4).153(C4×D5), (C2×C10).36(C2×Q8), C22.134(C2×C4×D5), (C2×C20).257(C2×C4), (C2×C10).446(C2×D4), (C2×C4⋊Dic5).35C2, C22.64(C2×C5⋊D4), C2.11(C4⋊C47D5), (C2×C4).128(C5⋊D4), C2.12(C2×C10.D4), (C2×C10).152(C4○D4), (C2×C10).218(C22×C4), (C2×Dic5).150(C2×C4), SmallGroup(320,604)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C20.48(C4⋊C4)
C1C5C10C2×C10C22×C10C22×Dic5C2×C4×Dic5 — C20.48(C4⋊C4)
C5C2×C10 — C20.48(C4⋊C4)
C1C23C2×C4⋊C4

Generators and relations for C20.48(C4⋊C4)
 G = < a,b,c | a20=b4=c4=1, bab-1=a9, cac-1=a11, cbc-1=a10b-1 >

Subgroups: 462 in 154 conjugacy classes, 79 normal (23 characteristic)
C1, C2 [×3], C2 [×4], C4 [×4], C4 [×8], C22 [×3], C22 [×4], C5, C2×C4 [×6], C2×C4 [×20], C23, C10 [×3], C10 [×4], C42 [×4], C4⋊C4 [×4], C22×C4, C22×C4 [×2], C22×C4 [×4], Dic5 [×6], C20 [×4], C20 [×2], C2×C10 [×3], C2×C10 [×4], C2.C42 [×4], C2×C42, C2×C4⋊C4, C2×C4⋊C4, C2×Dic5 [×4], C2×Dic5 [×10], C2×C20 [×6], C2×C20 [×6], C22×C10, C428C4, C4×Dic5 [×4], C4⋊Dic5 [×2], C5×C4⋊C4 [×2], C22×Dic5 [×4], C22×C20, C22×C20 [×2], C10.10C42 [×4], C2×C4×Dic5, C2×C4⋊Dic5, C10×C4⋊C4, C20.48(C4⋊C4)
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×2], Q8 [×2], C23, D5, C4⋊C4 [×4], C22×C4, C2×D4, C2×Q8, C4○D4 [×4], D10 [×3], C2×C4⋊C4, C42⋊C2 [×2], C4.4D4 [×2], C42.C2 [×2], Dic10 [×2], C4×D5 [×2], C5⋊D4 [×2], C22×D5, C428C4, C10.D4 [×4], C2×Dic10, C2×C4×D5, D42D5 [×2], Q82D5 [×2], C2×C5⋊D4, C4.Dic10 [×2], C4⋊C47D5 [×2], C2×C10.D4, C20.17D4, C20.23D4, C20.48(C4⋊C4)

Smallest permutation representation of C20.48(C4⋊C4)
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)
(1 209 41 32)(2 218 42 21)(3 207 43 30)(4 216 44 39)(5 205 45 28)(6 214 46 37)(7 203 47 26)(8 212 48 35)(9 201 49 24)(10 210 50 33)(11 219 51 22)(12 208 52 31)(13 217 53 40)(14 206 54 29)(15 215 55 38)(16 204 56 27)(17 213 57 36)(18 202 58 25)(19 211 59 34)(20 220 60 23)(61 255 168 145)(62 244 169 154)(63 253 170 143)(64 242 171 152)(65 251 172 141)(66 260 173 150)(67 249 174 159)(68 258 175 148)(69 247 176 157)(70 256 177 146)(71 245 178 155)(72 254 179 144)(73 243 180 153)(74 252 161 142)(75 241 162 151)(76 250 163 160)(77 259 164 149)(78 248 165 158)(79 257 166 147)(80 246 167 156)(81 115 301 298)(82 104 302 287)(83 113 303 296)(84 102 304 285)(85 111 305 294)(86 120 306 283)(87 109 307 292)(88 118 308 281)(89 107 309 290)(90 116 310 299)(91 105 311 288)(92 114 312 297)(93 103 313 286)(94 112 314 295)(95 101 315 284)(96 110 316 293)(97 119 317 282)(98 108 318 291)(99 117 319 300)(100 106 320 289)(121 221 193 269)(122 230 194 278)(123 239 195 267)(124 228 196 276)(125 237 197 265)(126 226 198 274)(127 235 199 263)(128 224 200 272)(129 233 181 261)(130 222 182 270)(131 231 183 279)(132 240 184 268)(133 229 185 277)(134 238 186 266)(135 227 187 275)(136 236 188 264)(137 225 189 273)(138 234 190 262)(139 223 191 271)(140 232 192 280)
(1 225 77 289)(2 236 78 300)(3 227 79 291)(4 238 80 282)(5 229 61 293)(6 240 62 284)(7 231 63 295)(8 222 64 286)(9 233 65 297)(10 224 66 288)(11 235 67 299)(12 226 68 290)(13 237 69 281)(14 228 70 292)(15 239 71 283)(16 230 72 294)(17 221 73 285)(18 232 74 296)(19 223 75 287)(20 234 76 298)(21 198 158 89)(22 189 159 100)(23 200 160 91)(24 191 141 82)(25 182 142 93)(26 193 143 84)(27 184 144 95)(28 195 145 86)(29 186 146 97)(30 197 147 88)(31 188 148 99)(32 199 149 90)(33 190 150 81)(34 181 151 92)(35 192 152 83)(36 183 153 94)(37 194 154 85)(38 185 155 96)(39 196 156 87)(40 187 157 98)(41 273 164 106)(42 264 165 117)(43 275 166 108)(44 266 167 119)(45 277 168 110)(46 268 169 101)(47 279 170 112)(48 270 171 103)(49 261 172 114)(50 272 173 105)(51 263 174 116)(52 274 175 107)(53 265 176 118)(54 276 177 109)(55 267 178 120)(56 278 179 111)(57 269 180 102)(58 280 161 113)(59 271 162 104)(60 262 163 115)(121 253 304 203)(122 244 305 214)(123 255 306 205)(124 246 307 216)(125 257 308 207)(126 248 309 218)(127 259 310 209)(128 250 311 220)(129 241 312 211)(130 252 313 202)(131 243 314 213)(132 254 315 204)(133 245 316 215)(134 256 317 206)(135 247 318 217)(136 258 319 208)(137 249 320 219)(138 260 301 210)(139 251 302 201)(140 242 303 212)

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

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

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

68 conjugacy classes

class 1 2A···2G4A4B4C4D4E4F4G4H4I···4P4Q4R4S4T5A5B10A···10N20A···20X
order12···2444444444···444445510···1020···20
size11···12222444410···1020202020222···24···4

68 irreducible representations

dim1111112222222244
type++++++-++--+
imageC1C2C2C2C2C4D4Q8D5C4○D4D10Dic10C4×D5C5⋊D4D42D5Q82D5
kernelC20.48(C4⋊C4)C10.10C42C2×C4×Dic5C2×C4⋊Dic5C10×C4⋊C4C4×Dic5C2×C20C2×C20C2×C4⋊C4C2×C10C22×C4C2×C4C2×C4C2×C4C22C22
# reps1411182228688844

Matrix representation of C20.48(C4⋊C4) in GL6(𝔽41)

34400000
100000
002900
0043900
000071
0000400
,
770000
40340000
009000
000900
00001828
00002523
,
3200000
0320000
0032900
000900
00003032
0000911

G:=sub<GL(6,GF(41))| [34,1,0,0,0,0,40,0,0,0,0,0,0,0,2,4,0,0,0,0,9,39,0,0,0,0,0,0,7,40,0,0,0,0,1,0],[7,40,0,0,0,0,7,34,0,0,0,0,0,0,9,0,0,0,0,0,0,9,0,0,0,0,0,0,18,25,0,0,0,0,28,23],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,9,9,0,0,0,0,0,0,30,9,0,0,0,0,32,11] >;

C20.48(C4⋊C4) in GAP, Magma, Sage, TeX

C_{20}._{48}(C_4\rtimes C_4)
% in TeX

G:=Group("C20.48(C4:C4)");
// GroupNames label

G:=SmallGroup(320,604);
// by ID

G=gap.SmallGroup(320,604);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,232,1094,387,58,12550]);
// Polycyclic

G:=Group<a,b,c|a^20=b^4=c^4=1,b*a*b^-1=a^9,c*a*c^-1=a^11,c*b*c^-1=a^10*b^-1>;
// generators/relations

׿
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