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G = C4⋊C4×C20order 320 = 26·5

Direct product of C20 and C4⋊C4

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

Aliases: C4⋊C4×C20, C427C20, C207C42, C4⋊(C4×C20), (C4×C20)⋊27C4, C2.2(D4×C20), C2.1(Q8×C20), (C2×C20).82Q8, C10.38(C4×Q8), (C2×C20).534D4, C10.134(C4×D4), (C2×C42).3C10, C22.8(Q8×C10), C10.52(C2×C42), C22.28(D4×C10), C23.51(C22×C10), C22.15(C22×C20), C10.71(C42⋊C2), C2.C42.12C10, (C22×C10).442C23, (C22×C20).489C22, C2.4(C2×C4×C20), (C2×C4×C20).5C2, C2.2(C10×C4⋊C4), C10.81(C2×C4⋊C4), (C10×C4⋊C4).50C2, (C2×C4⋊C4).21C10, (C2×C4).24(C5×Q8), (C2×C4).43(C2×C20), (C2×C4).144(C5×D4), (C2×C20).384(C2×C4), (C2×C10).595(C2×D4), C2.3(C5×C42⋊C2), (C2×C10).100(C2×Q8), C22.14(C5×C4○D4), (C22×C4).83(C2×C10), (C2×C10).204(C4○D4), (C2×C10).315(C22×C4), (C5×C2.C42).30C2, SmallGroup(320,879)

Series: Derived Chief Lower central Upper central

C1C2 — C4⋊C4×C20
C1C2C22C23C22×C10C22×C20C5×C2.C42 — C4⋊C4×C20
C1C2 — C4⋊C4×C20
C1C22×C20 — C4⋊C4×C20

Generators and relations for C4⋊C4×C20
 G = < a,b,c | a20=b4=c4=1, ab=ba, ac=ca, cbc-1=b-1 >

Subgroups: 242 in 194 conjugacy classes, 146 normal (26 characteristic)
C1, C2 [×3], C2 [×4], C4 [×8], C4 [×10], C22 [×3], C22 [×4], C5, C2×C4 [×22], C2×C4 [×10], C23, C10 [×3], C10 [×4], C42 [×4], C42 [×4], C4⋊C4 [×8], C22×C4 [×3], C22×C4 [×4], C20 [×8], C20 [×10], C2×C10 [×3], C2×C10 [×4], C2.C42 [×2], C2×C42, C2×C42 [×2], C2×C4⋊C4 [×2], C2×C20 [×22], C2×C20 [×10], C22×C10, C4×C4⋊C4, C4×C20 [×4], C4×C20 [×4], C5×C4⋊C4 [×8], C22×C20 [×3], C22×C20 [×4], C5×C2.C42 [×2], C2×C4×C20, C2×C4×C20 [×2], C10×C4⋊C4 [×2], C4⋊C4×C20
Quotients: C1, C2 [×7], C4 [×12], C22 [×7], C5, C2×C4 [×18], D4 [×2], Q8 [×2], C23, C10 [×7], C42 [×4], C4⋊C4 [×4], C22×C4 [×3], C2×D4, C2×Q8, C4○D4 [×2], C20 [×12], C2×C10 [×7], C2×C42, C2×C4⋊C4, C42⋊C2, C4×D4 [×2], C4×Q8 [×2], C2×C20 [×18], C5×D4 [×2], C5×Q8 [×2], C22×C10, C4×C4⋊C4, C4×C20 [×4], C5×C4⋊C4 [×4], C22×C20 [×3], D4×C10, Q8×C10, C5×C4○D4 [×2], C2×C4×C20, C10×C4⋊C4, C5×C42⋊C2, D4×C20 [×2], Q8×C20 [×2], C4⋊C4×C20

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

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

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

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

200 conjugacy classes

class 1 2A···2G4A···4H4I···4AF5A5B5C5D10A···10AB20A···20AF20AG···20DX
order12···24···44···4555510···1020···2020···20
size11···11···12···211111···11···12···2

200 irreducible representations

dim111111111111222222
type+++++-
imageC1C2C2C2C4C4C5C10C10C10C20C20D4Q8C4○D4C5×D4C5×Q8C5×C4○D4
kernelC4⋊C4×C20C5×C2.C42C2×C4×C20C10×C4⋊C4C4×C20C5×C4⋊C4C4×C4⋊C4C2.C42C2×C42C2×C4⋊C4C42C4⋊C4C2×C20C2×C20C2×C10C2×C4C2×C4C22
# reps12328164812832642248816

Matrix representation of C4⋊C4×C20 in GL4(𝔽41) generated by

32000
03200
00390
00039
,
40000
04000
00325
001638
,
32000
0100
0009
0090
G:=sub<GL(4,GF(41))| [32,0,0,0,0,32,0,0,0,0,39,0,0,0,0,39],[40,0,0,0,0,40,0,0,0,0,3,16,0,0,25,38],[32,0,0,0,0,1,0,0,0,0,0,9,0,0,9,0] >;

C4⋊C4×C20 in GAP, Magma, Sage, TeX

C_4\rtimes C_4\times C_{20}
% in TeX

G:=Group("C4:C4xC20");
// GroupNames label

G:=SmallGroup(320,879);
// by ID

G=gap.SmallGroup(320,879);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,560,589,1128,646]);
// Polycyclic

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

׿
×
𝔽