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G = Q16×C20order 320 = 26·5

Direct product of C20 and Q16

direct product, metabelian, nilpotent (class 3), monomial, 2-elementary

Aliases: Q16×C20, (C4×C8).6C10, (C4×C40).24C2, C8.10(C2×C20), C2.14(D4×C20), (C4×Q8).2C10, Q8.1(C2×C20), C2.3(C10×Q16), C2.D8.9C10, C40.107(C2×C4), (C2×C20).362D4, C10.146(C4×D4), (Q8×C20).15C2, (C2×Q16).7C10, C10.50(C2×Q16), C4.11(C22×C20), C42.72(C2×C10), (C10×Q16).14C2, Q8⋊C4.8C10, C22.53(D4×C10), C20.258(C4○D4), C10.118(C4○D8), C20.215(C22×C4), (C2×C40).422C22, (C4×C20).357C22, (C2×C20).906C23, (Q8×C10).255C22, C2.5(C5×C4○D8), C4.3(C5×C4○D4), (C2×C4).52(C5×D4), C4⋊C4.47(C2×C10), (C2×C8).67(C2×C10), (C5×Q8).34(C2×C4), (C5×C2.D8).18C2, (C2×C10).629(C2×D4), (C2×Q8).40(C2×C10), (C5×C4⋊C4).368C22, (C2×C4).81(C22×C10), (C5×Q8⋊C4).17C2, SmallGroup(320,940)

Series: Derived Chief Lower central Upper central

C1C4 — Q16×C20
C1C2C22C2×C4C2×C20C5×C4⋊C4C5×Q8⋊C4 — Q16×C20
C1C2C4 — Q16×C20
C1C2×C20C4×C20 — Q16×C20

Generators and relations for Q16×C20
 G = < a,b,c | a20=b8=1, c2=b4, ab=ba, ac=ca, cbc-1=b-1 >

Subgroups: 154 in 110 conjugacy classes, 74 normal (34 characteristic)
C1, C2 [×3], C4 [×2], C4 [×2], C4 [×7], C22, C5, C8 [×2], C8, C2×C4 [×3], C2×C4 [×4], Q8 [×4], Q8 [×2], C10 [×3], C42, C42 [×2], C4⋊C4 [×2], C4⋊C4 [×2], C2×C8 [×2], Q16 [×4], C2×Q8 [×2], C20 [×2], C20 [×2], C20 [×7], C2×C10, C4×C8, Q8⋊C4 [×2], C2.D8, C4×Q8 [×2], C2×Q16, C40 [×2], C40, C2×C20 [×3], C2×C20 [×4], C5×Q8 [×4], C5×Q8 [×2], C4×Q16, C4×C20, C4×C20 [×2], C5×C4⋊C4 [×2], C5×C4⋊C4 [×2], C2×C40 [×2], C5×Q16 [×4], Q8×C10 [×2], C4×C40, C5×Q8⋊C4 [×2], C5×C2.D8, Q8×C20 [×2], C10×Q16, Q16×C20
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C5, C2×C4 [×6], D4 [×2], C23, C10 [×7], Q16 [×2], C22×C4, C2×D4, C4○D4, C20 [×4], C2×C10 [×7], C4×D4, C2×Q16, C4○D8, C2×C20 [×6], C5×D4 [×2], C22×C10, C4×Q16, C5×Q16 [×2], C22×C20, D4×C10, C5×C4○D4, D4×C20, C10×Q16, C5×C4○D8, Q16×C20

Smallest permutation representation of Q16×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)
(1 237 96 139 115 275 183 154)(2 238 97 140 116 276 184 155)(3 239 98 121 117 277 185 156)(4 240 99 122 118 278 186 157)(5 221 100 123 119 279 187 158)(6 222 81 124 120 280 188 159)(7 223 82 125 101 261 189 160)(8 224 83 126 102 262 190 141)(9 225 84 127 103 263 191 142)(10 226 85 128 104 264 192 143)(11 227 86 129 105 265 193 144)(12 228 87 130 106 266 194 145)(13 229 88 131 107 267 195 146)(14 230 89 132 108 268 196 147)(15 231 90 133 109 269 197 148)(16 232 91 134 110 270 198 149)(17 233 92 135 111 271 199 150)(18 234 93 136 112 272 200 151)(19 235 94 137 113 273 181 152)(20 236 95 138 114 274 182 153)(21 256 63 173 219 50 290 317)(22 257 64 174 220 51 291 318)(23 258 65 175 201 52 292 319)(24 259 66 176 202 53 293 320)(25 260 67 177 203 54 294 301)(26 241 68 178 204 55 295 302)(27 242 69 179 205 56 296 303)(28 243 70 180 206 57 297 304)(29 244 71 161 207 58 298 305)(30 245 72 162 208 59 299 306)(31 246 73 163 209 60 300 307)(32 247 74 164 210 41 281 308)(33 248 75 165 211 42 282 309)(34 249 76 166 212 43 283 310)(35 250 77 167 213 44 284 311)(36 251 78 168 214 45 285 312)(37 252 79 169 215 46 286 313)(38 253 80 170 216 47 287 314)(39 254 61 171 217 48 288 315)(40 255 62 172 218 49 289 316)
(1 251 115 45)(2 252 116 46)(3 253 117 47)(4 254 118 48)(5 255 119 49)(6 256 120 50)(7 257 101 51)(8 258 102 52)(9 259 103 53)(10 260 104 54)(11 241 105 55)(12 242 106 56)(13 243 107 57)(14 244 108 58)(15 245 109 59)(16 246 110 60)(17 247 111 41)(18 248 112 42)(19 249 113 43)(20 250 114 44)(21 280 219 222)(22 261 220 223)(23 262 201 224)(24 263 202 225)(25 264 203 226)(26 265 204 227)(27 266 205 228)(28 267 206 229)(29 268 207 230)(30 269 208 231)(31 270 209 232)(32 271 210 233)(33 272 211 234)(34 273 212 235)(35 274 213 236)(36 275 214 237)(37 276 215 238)(38 277 216 239)(39 278 217 240)(40 279 218 221)(61 122 288 157)(62 123 289 158)(63 124 290 159)(64 125 291 160)(65 126 292 141)(66 127 293 142)(67 128 294 143)(68 129 295 144)(69 130 296 145)(70 131 297 146)(71 132 298 147)(72 133 299 148)(73 134 300 149)(74 135 281 150)(75 136 282 151)(76 137 283 152)(77 138 284 153)(78 139 285 154)(79 140 286 155)(80 121 287 156)(81 317 188 173)(82 318 189 174)(83 319 190 175)(84 320 191 176)(85 301 192 177)(86 302 193 178)(87 303 194 179)(88 304 195 180)(89 305 196 161)(90 306 197 162)(91 307 198 163)(92 308 199 164)(93 309 200 165)(94 310 181 166)(95 311 182 167)(96 312 183 168)(97 313 184 169)(98 314 185 170)(99 315 186 171)(100 316 187 172)

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

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

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

140 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I···4P5A5B5C5D8A···8H10A···10L20A···20P20Q···20AF20AG···20BL40A···40AF
order1222444444444···455558···810···1020···2020···2020···2040···40
size1111111122224···411112···21···11···12···24···42···2

140 irreducible representations

dim1111111111111122222222
type+++++++-
imageC1C2C2C2C2C2C4C5C10C10C10C10C10C20D4Q16C4○D4C4○D8C5×D4C5×Q16C5×C4○D4C5×C4○D8
kernelQ16×C20C4×C40C5×Q8⋊C4C5×C2.D8Q8×C20C10×Q16C5×Q16C4×Q16C4×C8Q8⋊C4C2.D8C4×Q8C2×Q16Q16C2×C20C20C20C10C2×C4C4C4C2
# reps1121218448484322424816816

Matrix representation of Q16×C20 in GL3(𝔽41) generated by

3200
020
002
,
100
02912
02929
,
4000
0639
03935
G:=sub<GL(3,GF(41))| [32,0,0,0,2,0,0,0,2],[1,0,0,0,29,29,0,12,29],[40,0,0,0,6,39,0,39,35] >;

Q16×C20 in GAP, Magma, Sage, TeX

Q_{16}\times C_{20}
% in TeX

G:=Group("Q16xC20");
// GroupNames label

G:=SmallGroup(320,940);
// by ID

G=gap.SmallGroup(320,940);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,560,589,1128,1276,7004,3511,172]);
// Polycyclic

G:=Group<a,b,c|a^20=b^8=1,c^2=b^4,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

׿
×
𝔽