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G = C204(C4⋊C4)  order 320 = 26·5

1st semidirect product of C20 and C4⋊C4 acting via C4⋊C4/C22=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C204(C4⋊C4), C4⋊Dic519C4, C10.87(C4×D4), C2.3(C20⋊Q8), C10.29(C4×Q8), (C2×C20).17Q8, (C2×C20).136D4, C10.19(C4⋊Q8), C22.19(Q8×D5), C41(C10.D4), C2.3(C202D4), (C2×Dic5).21Q8, (C2×C4).28Dic10, C22.105(D4×D5), C10.88(C4⋊D4), C2.1(D103Q8), (C2×Dic5).152D4, (C22×C4).331D10, C10.69(C22⋊Q8), C2.3(C4.Dic10), C2.17(D208C4), C10.16(C42.C2), C22.26(C2×Dic10), C23.287(C22×D5), C2.10(Dic53Q8), C22.52(D42D5), (C22×C20).140C22, (C22×C10).337C23, C55(C23.65C23), C22.21(Q82D5), C10.10C42.15C2, (C22×Dic5).49C22, (C10×C4⋊C4).9C2, C10.58(C2×C4⋊C4), (C2×C4⋊C4).11D5, (C2×C4).77(C4×D5), (C2×C4×Dic5).3C2, (C2×C10).73(C2×Q8), C22.131(C2×C4×D5), (C2×C20).253(C2×C4), (C2×C10).327(C2×D4), (C2×C4⋊Dic5).32C2, C22.61(C2×C5⋊D4), (C2×C4).183(C5⋊D4), (C2×Dic5).30(C2×C4), C2.10(C2×C10.D4), (C2×C10).186(C4○D4), (C2×C10).214(C22×C4), (C2×C10.D4).13C2, SmallGroup(320,600)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C204(C4⋊C4)
C1C5C10C2×C10C22×C10C22×Dic5C2×C4×Dic5 — C204(C4⋊C4)
C5C2×C10 — C204(C4⋊C4)
C1C23C2×C4⋊C4

Generators and relations for C204(C4⋊C4)
 G = < a,b,c | a20=b4=c4=1, bab-1=a-1, cac-1=a11, cbc-1=b-1 >

Subgroups: 510 in 170 conjugacy classes, 83 normal (41 characteristic)
C1, C2 [×7], C4 [×4], C4 [×10], C22 [×7], C5, C2×C4 [×6], C2×C4 [×22], C23, C10 [×7], C42 [×2], C4⋊C4 [×10], C22×C4, C22×C4 [×2], C22×C4 [×4], Dic5 [×8], C20 [×4], C20 [×2], C2×C10 [×7], C2.C42 [×2], C2×C42, C2×C4⋊C4, C2×C4⋊C4 [×3], C2×Dic5 [×8], C2×Dic5 [×8], C2×C20 [×6], C2×C20 [×6], C22×C10, C23.65C23, C4×Dic5 [×2], C10.D4 [×4], C4⋊Dic5 [×4], C5×C4⋊C4 [×2], C22×Dic5 [×2], C22×Dic5 [×2], C22×C20, C22×C20 [×2], C10.10C42 [×2], C2×C4×Dic5, C2×C10.D4 [×2], C2×C4⋊Dic5, C10×C4⋊C4, C204(C4⋊C4)
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×4], Q8 [×4], C23, D5, C4⋊C4 [×4], C22×C4, C2×D4 [×2], C2×Q8 [×2], C4○D4 [×2], D10 [×3], C2×C4⋊C4, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C42.C2, C4⋊Q8, Dic10 [×2], C4×D5 [×2], C5⋊D4 [×2], C22×D5, C23.65C23, C10.D4 [×4], C2×Dic10, C2×C4×D5, D4×D5, D42D5, Q8×D5, Q82D5, C2×C5⋊D4, Dic53Q8, C20⋊Q8, C4.Dic10, D208C4, C2×C10.D4, C202D4, D103Q8, C204(C4⋊C4)

Smallest permutation representation of C204(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)
(1 156 180 219)(2 155 161 218)(3 154 162 217)(4 153 163 216)(5 152 164 215)(6 151 165 214)(7 150 166 213)(8 149 167 212)(9 148 168 211)(10 147 169 210)(11 146 170 209)(12 145 171 208)(13 144 172 207)(14 143 173 206)(15 142 174 205)(16 141 175 204)(17 160 176 203)(18 159 177 202)(19 158 178 201)(20 157 179 220)(21 195 226 94)(22 194 227 93)(23 193 228 92)(24 192 229 91)(25 191 230 90)(26 190 231 89)(27 189 232 88)(28 188 233 87)(29 187 234 86)(30 186 235 85)(31 185 236 84)(32 184 237 83)(33 183 238 82)(34 182 239 81)(35 181 240 100)(36 200 221 99)(37 199 222 98)(38 198 223 97)(39 197 224 96)(40 196 225 95)(41 123 289 113)(42 122 290 112)(43 121 291 111)(44 140 292 110)(45 139 293 109)(46 138 294 108)(47 137 295 107)(48 136 296 106)(49 135 297 105)(50 134 298 104)(51 133 299 103)(52 132 300 102)(53 131 281 101)(54 130 282 120)(55 129 283 119)(56 128 284 118)(57 127 285 117)(58 126 286 116)(59 125 287 115)(60 124 288 114)(61 249 275 318)(62 248 276 317)(63 247 277 316)(64 246 278 315)(65 245 279 314)(66 244 280 313)(67 243 261 312)(68 242 262 311)(69 241 263 310)(70 260 264 309)(71 259 265 308)(72 258 266 307)(73 257 267 306)(74 256 268 305)(75 255 269 304)(76 254 270 303)(77 253 271 302)(78 252 272 301)(79 251 273 320)(80 250 274 319)
(1 184 280 138)(2 195 261 129)(3 186 262 140)(4 197 263 131)(5 188 264 122)(6 199 265 133)(7 190 266 124)(8 181 267 135)(9 192 268 126)(10 183 269 137)(11 194 270 128)(12 185 271 139)(13 196 272 130)(14 187 273 121)(15 198 274 132)(16 189 275 123)(17 200 276 134)(18 191 277 125)(19 182 278 136)(20 193 279 127)(21 312 55 155)(22 303 56 146)(23 314 57 157)(24 305 58 148)(25 316 59 159)(26 307 60 150)(27 318 41 141)(28 309 42 152)(29 320 43 143)(30 311 44 154)(31 302 45 145)(32 313 46 156)(33 304 47 147)(34 315 48 158)(35 306 49 149)(36 317 50 160)(37 308 51 151)(38 319 52 142)(39 310 53 153)(40 301 54 144)(61 113 175 88)(62 104 176 99)(63 115 177 90)(64 106 178 81)(65 117 179 92)(66 108 180 83)(67 119 161 94)(68 110 162 85)(69 101 163 96)(70 112 164 87)(71 103 165 98)(72 114 166 89)(73 105 167 100)(74 116 168 91)(75 107 169 82)(76 118 170 93)(77 109 171 84)(78 120 172 95)(79 111 173 86)(80 102 174 97)(201 239 246 296)(202 230 247 287)(203 221 248 298)(204 232 249 289)(205 223 250 300)(206 234 251 291)(207 225 252 282)(208 236 253 293)(209 227 254 284)(210 238 255 295)(211 229 256 286)(212 240 257 297)(213 231 258 288)(214 222 259 299)(215 233 260 290)(216 224 241 281)(217 235 242 292)(218 226 243 283)(219 237 244 294)(220 228 245 285)

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

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

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

68 conjugacy classes

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

68 irreducible representations

dim111111122222222224444
type+++++++-+-++-+--+
imageC1C2C2C2C2C2C4D4Q8D4Q8D5C4○D4D10Dic10C4×D5C5⋊D4D4×D5D42D5Q8×D5Q82D5
kernelC204(C4⋊C4)C10.10C42C2×C4×Dic5C2×C10.D4C2×C4⋊Dic5C10×C4⋊C4C4⋊Dic5C2×Dic5C2×Dic5C2×C20C2×C20C2×C4⋊C4C2×C10C22×C4C2×C4C2×C4C2×C4C22C22C22C22
# reps121211822222468882222

Matrix representation of C204(C4⋊C4) in GL6(𝔽41)

3910000
3620000
0032000
000900
000061
000051
,
18110000
4230000
000900
0032000
0000019
0000280
,
910000
0320000
000100
0040000
000029
0000439

G:=sub<GL(6,GF(41))| [39,36,0,0,0,0,1,2,0,0,0,0,0,0,32,0,0,0,0,0,0,9,0,0,0,0,0,0,6,5,0,0,0,0,1,1],[18,4,0,0,0,0,11,23,0,0,0,0,0,0,0,32,0,0,0,0,9,0,0,0,0,0,0,0,0,28,0,0,0,0,19,0],[9,0,0,0,0,0,1,32,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,2,4,0,0,0,0,9,39] >;

C204(C4⋊C4) in GAP, Magma, Sage, TeX

C_{20}\rtimes_4(C_4\rtimes C_4)
% in TeX

G:=Group("C20:4(C4:C4)");
// GroupNames label

G:=SmallGroup(320,600);
// by ID

G=gap.SmallGroup(320,600);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,120,254,219,184,12550]);
// Polycyclic

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

׿
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