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, C5⋊4(C42⋊8C4), (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(D4⋊2D5), (C22×C20).142C22, (C22×C10).341C23, C22.23(Q8⋊2D5), 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⋊C4⋊7D5), (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
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, C2, C4, C4, C22, C22, C5, C2×C4, C2×C4, C23, C10, C10, C42, C4⋊C4, C22×C4, C22×C4, C22×C4, Dic5, C20, C20, C2×C10, C2×C10, C2.C42, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×C10, C42⋊8C4, C4×Dic5, C4⋊Dic5, C5×C4⋊C4, C22×Dic5, C22×C20, C22×C20, C10.10C42, C2×C4×Dic5, C2×C4⋊Dic5, C10×C4⋊C4, C20.48(C4⋊C4)
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, D10, C2×C4⋊C4, C42⋊C2, C4.4D4, C42.C2, Dic10, C4×D5, C5⋊D4, C22×D5, C42⋊8C4, C10.D4, C2×Dic10, C2×C4×D5, D4⋊2D5, Q8⋊2D5, C2×C5⋊D4, C4.Dic10, C4⋊C4⋊7D5, C2×C10.D4, C20.17D4, C20.23D4, 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)
(1 193 299 119)(2 182 300 108)(3 191 281 117)(4 200 282 106)(5 189 283 115)(6 198 284 104)(7 187 285 113)(8 196 286 102)(9 185 287 111)(10 194 288 120)(11 183 289 109)(12 192 290 118)(13 181 291 107)(14 190 292 116)(15 199 293 105)(16 188 294 114)(17 197 295 103)(18 186 296 112)(19 195 297 101)(20 184 298 110)(21 67 243 312)(22 76 244 301)(23 65 245 310)(24 74 246 319)(25 63 247 308)(26 72 248 317)(27 61 249 306)(28 70 250 315)(29 79 251 304)(30 68 252 313)(31 77 253 302)(32 66 254 311)(33 75 255 320)(34 64 256 309)(35 73 257 318)(36 62 258 307)(37 71 259 316)(38 80 260 305)(39 69 241 314)(40 78 242 303)(41 82 177 240)(42 91 178 229)(43 100 179 238)(44 89 180 227)(45 98 161 236)(46 87 162 225)(47 96 163 234)(48 85 164 223)(49 94 165 232)(50 83 166 221)(51 92 167 230)(52 81 168 239)(53 90 169 228)(54 99 170 237)(55 88 171 226)(56 97 172 235)(57 86 173 224)(58 95 174 233)(59 84 175 222)(60 93 176 231)(121 158 265 202)(122 147 266 211)(123 156 267 220)(124 145 268 209)(125 154 269 218)(126 143 270 207)(127 152 271 216)(128 141 272 205)(129 150 273 214)(130 159 274 203)(131 148 275 212)(132 157 276 201)(133 146 277 210)(134 155 278 219)(135 144 279 208)(136 153 280 217)(137 142 261 206)(138 151 262 215)(139 160 263 204)(140 149 264 213)
(1 28 239 146)(2 39 240 157)(3 30 221 148)(4 21 222 159)(5 32 223 150)(6 23 224 141)(7 34 225 152)(8 25 226 143)(9 36 227 154)(10 27 228 145)(11 38 229 156)(12 29 230 147)(13 40 231 158)(14 31 232 149)(15 22 233 160)(16 33 234 151)(17 24 235 142)(18 35 236 153)(19 26 237 144)(20 37 238 155)(41 122 182 304)(42 133 183 315)(43 124 184 306)(44 135 185 317)(45 126 186 308)(46 137 187 319)(47 128 188 310)(48 139 189 301)(49 130 190 312)(50 121 191 303)(51 132 192 314)(52 123 193 305)(53 134 194 316)(54 125 195 307)(55 136 196 318)(56 127 197 309)(57 138 198 320)(58 129 199 311)(59 140 200 302)(60 131 181 313)(61 179 268 110)(62 170 269 101)(63 161 270 112)(64 172 271 103)(65 163 272 114)(66 174 273 105)(67 165 274 116)(68 176 275 107)(69 167 276 118)(70 178 277 109)(71 169 278 120)(72 180 279 111)(73 171 280 102)(74 162 261 113)(75 173 262 104)(76 164 263 115)(77 175 264 106)(78 166 265 117)(79 177 266 108)(80 168 267 119)(81 210 299 250)(82 201 300 241)(83 212 281 252)(84 203 282 243)(85 214 283 254)(86 205 284 245)(87 216 285 256)(88 207 286 247)(89 218 287 258)(90 209 288 249)(91 220 289 260)(92 211 290 251)(93 202 291 242)(94 213 292 253)(95 204 293 244)(96 215 294 255)(97 206 295 246)(98 217 296 257)(99 208 297 248)(100 219 298 259)
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), (1,193,299,119)(2,182,300,108)(3,191,281,117)(4,200,282,106)(5,189,283,115)(6,198,284,104)(7,187,285,113)(8,196,286,102)(9,185,287,111)(10,194,288,120)(11,183,289,109)(12,192,290,118)(13,181,291,107)(14,190,292,116)(15,199,293,105)(16,188,294,114)(17,197,295,103)(18,186,296,112)(19,195,297,101)(20,184,298,110)(21,67,243,312)(22,76,244,301)(23,65,245,310)(24,74,246,319)(25,63,247,308)(26,72,248,317)(27,61,249,306)(28,70,250,315)(29,79,251,304)(30,68,252,313)(31,77,253,302)(32,66,254,311)(33,75,255,320)(34,64,256,309)(35,73,257,318)(36,62,258,307)(37,71,259,316)(38,80,260,305)(39,69,241,314)(40,78,242,303)(41,82,177,240)(42,91,178,229)(43,100,179,238)(44,89,180,227)(45,98,161,236)(46,87,162,225)(47,96,163,234)(48,85,164,223)(49,94,165,232)(50,83,166,221)(51,92,167,230)(52,81,168,239)(53,90,169,228)(54,99,170,237)(55,88,171,226)(56,97,172,235)(57,86,173,224)(58,95,174,233)(59,84,175,222)(60,93,176,231)(121,158,265,202)(122,147,266,211)(123,156,267,220)(124,145,268,209)(125,154,269,218)(126,143,270,207)(127,152,271,216)(128,141,272,205)(129,150,273,214)(130,159,274,203)(131,148,275,212)(132,157,276,201)(133,146,277,210)(134,155,278,219)(135,144,279,208)(136,153,280,217)(137,142,261,206)(138,151,262,215)(139,160,263,204)(140,149,264,213), (1,28,239,146)(2,39,240,157)(3,30,221,148)(4,21,222,159)(5,32,223,150)(6,23,224,141)(7,34,225,152)(8,25,226,143)(9,36,227,154)(10,27,228,145)(11,38,229,156)(12,29,230,147)(13,40,231,158)(14,31,232,149)(15,22,233,160)(16,33,234,151)(17,24,235,142)(18,35,236,153)(19,26,237,144)(20,37,238,155)(41,122,182,304)(42,133,183,315)(43,124,184,306)(44,135,185,317)(45,126,186,308)(46,137,187,319)(47,128,188,310)(48,139,189,301)(49,130,190,312)(50,121,191,303)(51,132,192,314)(52,123,193,305)(53,134,194,316)(54,125,195,307)(55,136,196,318)(56,127,197,309)(57,138,198,320)(58,129,199,311)(59,140,200,302)(60,131,181,313)(61,179,268,110)(62,170,269,101)(63,161,270,112)(64,172,271,103)(65,163,272,114)(66,174,273,105)(67,165,274,116)(68,176,275,107)(69,167,276,118)(70,178,277,109)(71,169,278,120)(72,180,279,111)(73,171,280,102)(74,162,261,113)(75,173,262,104)(76,164,263,115)(77,175,264,106)(78,166,265,117)(79,177,266,108)(80,168,267,119)(81,210,299,250)(82,201,300,241)(83,212,281,252)(84,203,282,243)(85,214,283,254)(86,205,284,245)(87,216,285,256)(88,207,286,247)(89,218,287,258)(90,209,288,249)(91,220,289,260)(92,211,290,251)(93,202,291,242)(94,213,292,253)(95,204,293,244)(96,215,294,255)(97,206,295,246)(98,217,296,257)(99,208,297,248)(100,219,298,259)>;
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), (1,193,299,119)(2,182,300,108)(3,191,281,117)(4,200,282,106)(5,189,283,115)(6,198,284,104)(7,187,285,113)(8,196,286,102)(9,185,287,111)(10,194,288,120)(11,183,289,109)(12,192,290,118)(13,181,291,107)(14,190,292,116)(15,199,293,105)(16,188,294,114)(17,197,295,103)(18,186,296,112)(19,195,297,101)(20,184,298,110)(21,67,243,312)(22,76,244,301)(23,65,245,310)(24,74,246,319)(25,63,247,308)(26,72,248,317)(27,61,249,306)(28,70,250,315)(29,79,251,304)(30,68,252,313)(31,77,253,302)(32,66,254,311)(33,75,255,320)(34,64,256,309)(35,73,257,318)(36,62,258,307)(37,71,259,316)(38,80,260,305)(39,69,241,314)(40,78,242,303)(41,82,177,240)(42,91,178,229)(43,100,179,238)(44,89,180,227)(45,98,161,236)(46,87,162,225)(47,96,163,234)(48,85,164,223)(49,94,165,232)(50,83,166,221)(51,92,167,230)(52,81,168,239)(53,90,169,228)(54,99,170,237)(55,88,171,226)(56,97,172,235)(57,86,173,224)(58,95,174,233)(59,84,175,222)(60,93,176,231)(121,158,265,202)(122,147,266,211)(123,156,267,220)(124,145,268,209)(125,154,269,218)(126,143,270,207)(127,152,271,216)(128,141,272,205)(129,150,273,214)(130,159,274,203)(131,148,275,212)(132,157,276,201)(133,146,277,210)(134,155,278,219)(135,144,279,208)(136,153,280,217)(137,142,261,206)(138,151,262,215)(139,160,263,204)(140,149,264,213), (1,28,239,146)(2,39,240,157)(3,30,221,148)(4,21,222,159)(5,32,223,150)(6,23,224,141)(7,34,225,152)(8,25,226,143)(9,36,227,154)(10,27,228,145)(11,38,229,156)(12,29,230,147)(13,40,231,158)(14,31,232,149)(15,22,233,160)(16,33,234,151)(17,24,235,142)(18,35,236,153)(19,26,237,144)(20,37,238,155)(41,122,182,304)(42,133,183,315)(43,124,184,306)(44,135,185,317)(45,126,186,308)(46,137,187,319)(47,128,188,310)(48,139,189,301)(49,130,190,312)(50,121,191,303)(51,132,192,314)(52,123,193,305)(53,134,194,316)(54,125,195,307)(55,136,196,318)(56,127,197,309)(57,138,198,320)(58,129,199,311)(59,140,200,302)(60,131,181,313)(61,179,268,110)(62,170,269,101)(63,161,270,112)(64,172,271,103)(65,163,272,114)(66,174,273,105)(67,165,274,116)(68,176,275,107)(69,167,276,118)(70,178,277,109)(71,169,278,120)(72,180,279,111)(73,171,280,102)(74,162,261,113)(75,173,262,104)(76,164,263,115)(77,175,264,106)(78,166,265,117)(79,177,266,108)(80,168,267,119)(81,210,299,250)(82,201,300,241)(83,212,281,252)(84,203,282,243)(85,214,283,254)(86,205,284,245)(87,216,285,256)(88,207,286,247)(89,218,287,258)(90,209,288,249)(91,220,289,260)(92,211,290,251)(93,202,291,242)(94,213,292,253)(95,204,293,244)(96,215,294,255)(97,206,295,246)(98,217,296,257)(99,208,297,248)(100,219,298,259) );
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)], [(1,193,299,119),(2,182,300,108),(3,191,281,117),(4,200,282,106),(5,189,283,115),(6,198,284,104),(7,187,285,113),(8,196,286,102),(9,185,287,111),(10,194,288,120),(11,183,289,109),(12,192,290,118),(13,181,291,107),(14,190,292,116),(15,199,293,105),(16,188,294,114),(17,197,295,103),(18,186,296,112),(19,195,297,101),(20,184,298,110),(21,67,243,312),(22,76,244,301),(23,65,245,310),(24,74,246,319),(25,63,247,308),(26,72,248,317),(27,61,249,306),(28,70,250,315),(29,79,251,304),(30,68,252,313),(31,77,253,302),(32,66,254,311),(33,75,255,320),(34,64,256,309),(35,73,257,318),(36,62,258,307),(37,71,259,316),(38,80,260,305),(39,69,241,314),(40,78,242,303),(41,82,177,240),(42,91,178,229),(43,100,179,238),(44,89,180,227),(45,98,161,236),(46,87,162,225),(47,96,163,234),(48,85,164,223),(49,94,165,232),(50,83,166,221),(51,92,167,230),(52,81,168,239),(53,90,169,228),(54,99,170,237),(55,88,171,226),(56,97,172,235),(57,86,173,224),(58,95,174,233),(59,84,175,222),(60,93,176,231),(121,158,265,202),(122,147,266,211),(123,156,267,220),(124,145,268,209),(125,154,269,218),(126,143,270,207),(127,152,271,216),(128,141,272,205),(129,150,273,214),(130,159,274,203),(131,148,275,212),(132,157,276,201),(133,146,277,210),(134,155,278,219),(135,144,279,208),(136,153,280,217),(137,142,261,206),(138,151,262,215),(139,160,263,204),(140,149,264,213)], [(1,28,239,146),(2,39,240,157),(3,30,221,148),(4,21,222,159),(5,32,223,150),(6,23,224,141),(7,34,225,152),(8,25,226,143),(9,36,227,154),(10,27,228,145),(11,38,229,156),(12,29,230,147),(13,40,231,158),(14,31,232,149),(15,22,233,160),(16,33,234,151),(17,24,235,142),(18,35,236,153),(19,26,237,144),(20,37,238,155),(41,122,182,304),(42,133,183,315),(43,124,184,306),(44,135,185,317),(45,126,186,308),(46,137,187,319),(47,128,188,310),(48,139,189,301),(49,130,190,312),(50,121,191,303),(51,132,192,314),(52,123,193,305),(53,134,194,316),(54,125,195,307),(55,136,196,318),(56,127,197,309),(57,138,198,320),(58,129,199,311),(59,140,200,302),(60,131,181,313),(61,179,268,110),(62,170,269,101),(63,161,270,112),(64,172,271,103),(65,163,272,114),(66,174,273,105),(67,165,274,116),(68,176,275,107),(69,167,276,118),(70,178,277,109),(71,169,278,120),(72,180,279,111),(73,171,280,102),(74,162,261,113),(75,173,262,104),(76,164,263,115),(77,175,264,106),(78,166,265,117),(79,177,266,108),(80,168,267,119),(81,210,299,250),(82,201,300,241),(83,212,281,252),(84,203,282,243),(85,214,283,254),(86,205,284,245),(87,216,285,256),(88,207,286,247),(89,218,287,258),(90,209,288,249),(91,220,289,260),(92,211,290,251),(93,202,291,242),(94,213,292,253),(95,204,293,244),(96,215,294,255),(97,206,295,246),(98,217,296,257),(99,208,297,248),(100,219,298,259)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 4S | 4T | 5A | 5B | 10A | ··· | 10N | 20A | ··· | 20X |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | - | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | Q8 | D5 | C4○D4 | D10 | Dic10 | C4×D5 | C5⋊D4 | D4⋊2D5 | Q8⋊2D5 |
| kernel | C20.48(C4⋊C4) | C10.10C42 | C2×C4×Dic5 | C2×C4⋊Dic5 | C10×C4⋊C4 | C4×Dic5 | C2×C20 | C2×C20 | C2×C4⋊C4 | C2×C10 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 2 | 2 | 2 | 8 | 6 | 8 | 8 | 8 | 4 | 4 |
Matrix representation of C20.48(C4⋊C4) ►in GL6(𝔽41)
| 34 | 40 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 9 | 0 | 0 |
| 0 | 0 | 4 | 39 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 1 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 7 | 7 | 0 | 0 | 0 | 0 |
| 40 | 34 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 28 |
| 0 | 0 | 0 | 0 | 25 | 23 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 9 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 32 |
| 0 | 0 | 0 | 0 | 9 | 11 |
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