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
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, C4, C4, C4, C22, C5, C8, C8, C2×C4, C2×C4, Q8, Q8, C10, C42, C42, C4⋊C4, C4⋊C4, C2×C8, Q16, C2×Q8, C20, C20, C20, C2×C10, C4×C8, Q8⋊C4, C2.D8, C4×Q8, C2×Q16, C40, C40, C2×C20, C2×C20, C5×Q8, C5×Q8, C4×Q16, C4×C20, C4×C20, C5×C4⋊C4, C5×C4⋊C4, C2×C40, C5×Q16, Q8×C10, C4×C40, C5×Q8⋊C4, C5×C2.D8, Q8×C20, C10×Q16, Q16×C20
Quotients: C1, C2, C4, C22, C5, C2×C4, D4, C23, C10, Q16, C22×C4, C2×D4, C4○D4, C20, C2×C10, C4×D4, C2×Q16, C4○D8, C2×C20, C5×D4, C22×C10, C4×Q16, C5×Q16, C22×C20, D4×C10, C5×C4○D4, D4×C20, C10×Q16, C5×C4○D8, 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)
(1 261 284 254 25 309 90 124)(2 262 285 255 26 310 91 125)(3 263 286 256 27 311 92 126)(4 264 287 257 28 312 93 127)(5 265 288 258 29 313 94 128)(6 266 289 259 30 314 95 129)(7 267 290 260 31 315 96 130)(8 268 291 241 32 316 97 131)(9 269 292 242 33 317 98 132)(10 270 293 243 34 318 99 133)(11 271 294 244 35 319 100 134)(12 272 295 245 36 320 81 135)(13 273 296 246 37 301 82 136)(14 274 297 247 38 302 83 137)(15 275 298 248 39 303 84 138)(16 276 299 249 40 304 85 139)(17 277 300 250 21 305 86 140)(18 278 281 251 22 306 87 121)(19 279 282 252 23 307 88 122)(20 280 283 253 24 308 89 123)(41 66 174 152 184 227 119 217)(42 67 175 153 185 228 120 218)(43 68 176 154 186 229 101 219)(44 69 177 155 187 230 102 220)(45 70 178 156 188 231 103 201)(46 71 179 157 189 232 104 202)(47 72 180 158 190 233 105 203)(48 73 161 159 191 234 106 204)(49 74 162 160 192 235 107 205)(50 75 163 141 193 236 108 206)(51 76 164 142 194 237 109 207)(52 77 165 143 195 238 110 208)(53 78 166 144 196 239 111 209)(54 79 167 145 197 240 112 210)(55 80 168 146 198 221 113 211)(56 61 169 147 199 222 114 212)(57 62 170 148 200 223 115 213)(58 63 171 149 181 224 116 214)(59 64 172 150 182 225 117 215)(60 65 173 151 183 226 118 216)
(1 199 25 56)(2 200 26 57)(3 181 27 58)(4 182 28 59)(5 183 29 60)(6 184 30 41)(7 185 31 42)(8 186 32 43)(9 187 33 44)(10 188 34 45)(11 189 35 46)(12 190 36 47)(13 191 37 48)(14 192 38 49)(15 193 39 50)(16 194 40 51)(17 195 21 52)(18 196 22 53)(19 197 23 54)(20 198 24 55)(61 124 222 254)(62 125 223 255)(63 126 224 256)(64 127 225 257)(65 128 226 258)(66 129 227 259)(67 130 228 260)(68 131 229 241)(69 132 230 242)(70 133 231 243)(71 134 232 244)(72 135 233 245)(73 136 234 246)(74 137 235 247)(75 138 236 248)(76 139 237 249)(77 140 238 250)(78 121 239 251)(79 122 240 252)(80 123 221 253)(81 105 295 180)(82 106 296 161)(83 107 297 162)(84 108 298 163)(85 109 299 164)(86 110 300 165)(87 111 281 166)(88 112 282 167)(89 113 283 168)(90 114 284 169)(91 115 285 170)(92 116 286 171)(93 117 287 172)(94 118 288 173)(95 119 289 174)(96 120 290 175)(97 101 291 176)(98 102 292 177)(99 103 293 178)(100 104 294 179)(141 303 206 275)(142 304 207 276)(143 305 208 277)(144 306 209 278)(145 307 210 279)(146 308 211 280)(147 309 212 261)(148 310 213 262)(149 311 214 263)(150 312 215 264)(151 313 216 265)(152 314 217 266)(153 315 218 267)(154 316 219 268)(155 317 220 269)(156 318 201 270)(157 319 202 271)(158 320 203 272)(159 301 204 273)(160 302 205 274)
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), (1,261,284,254,25,309,90,124)(2,262,285,255,26,310,91,125)(3,263,286,256,27,311,92,126)(4,264,287,257,28,312,93,127)(5,265,288,258,29,313,94,128)(6,266,289,259,30,314,95,129)(7,267,290,260,31,315,96,130)(8,268,291,241,32,316,97,131)(9,269,292,242,33,317,98,132)(10,270,293,243,34,318,99,133)(11,271,294,244,35,319,100,134)(12,272,295,245,36,320,81,135)(13,273,296,246,37,301,82,136)(14,274,297,247,38,302,83,137)(15,275,298,248,39,303,84,138)(16,276,299,249,40,304,85,139)(17,277,300,250,21,305,86,140)(18,278,281,251,22,306,87,121)(19,279,282,252,23,307,88,122)(20,280,283,253,24,308,89,123)(41,66,174,152,184,227,119,217)(42,67,175,153,185,228,120,218)(43,68,176,154,186,229,101,219)(44,69,177,155,187,230,102,220)(45,70,178,156,188,231,103,201)(46,71,179,157,189,232,104,202)(47,72,180,158,190,233,105,203)(48,73,161,159,191,234,106,204)(49,74,162,160,192,235,107,205)(50,75,163,141,193,236,108,206)(51,76,164,142,194,237,109,207)(52,77,165,143,195,238,110,208)(53,78,166,144,196,239,111,209)(54,79,167,145,197,240,112,210)(55,80,168,146,198,221,113,211)(56,61,169,147,199,222,114,212)(57,62,170,148,200,223,115,213)(58,63,171,149,181,224,116,214)(59,64,172,150,182,225,117,215)(60,65,173,151,183,226,118,216), (1,199,25,56)(2,200,26,57)(3,181,27,58)(4,182,28,59)(5,183,29,60)(6,184,30,41)(7,185,31,42)(8,186,32,43)(9,187,33,44)(10,188,34,45)(11,189,35,46)(12,190,36,47)(13,191,37,48)(14,192,38,49)(15,193,39,50)(16,194,40,51)(17,195,21,52)(18,196,22,53)(19,197,23,54)(20,198,24,55)(61,124,222,254)(62,125,223,255)(63,126,224,256)(64,127,225,257)(65,128,226,258)(66,129,227,259)(67,130,228,260)(68,131,229,241)(69,132,230,242)(70,133,231,243)(71,134,232,244)(72,135,233,245)(73,136,234,246)(74,137,235,247)(75,138,236,248)(76,139,237,249)(77,140,238,250)(78,121,239,251)(79,122,240,252)(80,123,221,253)(81,105,295,180)(82,106,296,161)(83,107,297,162)(84,108,298,163)(85,109,299,164)(86,110,300,165)(87,111,281,166)(88,112,282,167)(89,113,283,168)(90,114,284,169)(91,115,285,170)(92,116,286,171)(93,117,287,172)(94,118,288,173)(95,119,289,174)(96,120,290,175)(97,101,291,176)(98,102,292,177)(99,103,293,178)(100,104,294,179)(141,303,206,275)(142,304,207,276)(143,305,208,277)(144,306,209,278)(145,307,210,279)(146,308,211,280)(147,309,212,261)(148,310,213,262)(149,311,214,263)(150,312,215,264)(151,313,216,265)(152,314,217,266)(153,315,218,267)(154,316,219,268)(155,317,220,269)(156,318,201,270)(157,319,202,271)(158,320,203,272)(159,301,204,273)(160,302,205,274)>;
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), (1,261,284,254,25,309,90,124)(2,262,285,255,26,310,91,125)(3,263,286,256,27,311,92,126)(4,264,287,257,28,312,93,127)(5,265,288,258,29,313,94,128)(6,266,289,259,30,314,95,129)(7,267,290,260,31,315,96,130)(8,268,291,241,32,316,97,131)(9,269,292,242,33,317,98,132)(10,270,293,243,34,318,99,133)(11,271,294,244,35,319,100,134)(12,272,295,245,36,320,81,135)(13,273,296,246,37,301,82,136)(14,274,297,247,38,302,83,137)(15,275,298,248,39,303,84,138)(16,276,299,249,40,304,85,139)(17,277,300,250,21,305,86,140)(18,278,281,251,22,306,87,121)(19,279,282,252,23,307,88,122)(20,280,283,253,24,308,89,123)(41,66,174,152,184,227,119,217)(42,67,175,153,185,228,120,218)(43,68,176,154,186,229,101,219)(44,69,177,155,187,230,102,220)(45,70,178,156,188,231,103,201)(46,71,179,157,189,232,104,202)(47,72,180,158,190,233,105,203)(48,73,161,159,191,234,106,204)(49,74,162,160,192,235,107,205)(50,75,163,141,193,236,108,206)(51,76,164,142,194,237,109,207)(52,77,165,143,195,238,110,208)(53,78,166,144,196,239,111,209)(54,79,167,145,197,240,112,210)(55,80,168,146,198,221,113,211)(56,61,169,147,199,222,114,212)(57,62,170,148,200,223,115,213)(58,63,171,149,181,224,116,214)(59,64,172,150,182,225,117,215)(60,65,173,151,183,226,118,216), (1,199,25,56)(2,200,26,57)(3,181,27,58)(4,182,28,59)(5,183,29,60)(6,184,30,41)(7,185,31,42)(8,186,32,43)(9,187,33,44)(10,188,34,45)(11,189,35,46)(12,190,36,47)(13,191,37,48)(14,192,38,49)(15,193,39,50)(16,194,40,51)(17,195,21,52)(18,196,22,53)(19,197,23,54)(20,198,24,55)(61,124,222,254)(62,125,223,255)(63,126,224,256)(64,127,225,257)(65,128,226,258)(66,129,227,259)(67,130,228,260)(68,131,229,241)(69,132,230,242)(70,133,231,243)(71,134,232,244)(72,135,233,245)(73,136,234,246)(74,137,235,247)(75,138,236,248)(76,139,237,249)(77,140,238,250)(78,121,239,251)(79,122,240,252)(80,123,221,253)(81,105,295,180)(82,106,296,161)(83,107,297,162)(84,108,298,163)(85,109,299,164)(86,110,300,165)(87,111,281,166)(88,112,282,167)(89,113,283,168)(90,114,284,169)(91,115,285,170)(92,116,286,171)(93,117,287,172)(94,118,288,173)(95,119,289,174)(96,120,290,175)(97,101,291,176)(98,102,292,177)(99,103,293,178)(100,104,294,179)(141,303,206,275)(142,304,207,276)(143,305,208,277)(144,306,209,278)(145,307,210,279)(146,308,211,280)(147,309,212,261)(148,310,213,262)(149,311,214,263)(150,312,215,264)(151,313,216,265)(152,314,217,266)(153,315,218,267)(154,316,219,268)(155,317,220,269)(156,318,201,270)(157,319,202,271)(158,320,203,272)(159,301,204,273)(160,302,205,274) );
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)], [(1,261,284,254,25,309,90,124),(2,262,285,255,26,310,91,125),(3,263,286,256,27,311,92,126),(4,264,287,257,28,312,93,127),(5,265,288,258,29,313,94,128),(6,266,289,259,30,314,95,129),(7,267,290,260,31,315,96,130),(8,268,291,241,32,316,97,131),(9,269,292,242,33,317,98,132),(10,270,293,243,34,318,99,133),(11,271,294,244,35,319,100,134),(12,272,295,245,36,320,81,135),(13,273,296,246,37,301,82,136),(14,274,297,247,38,302,83,137),(15,275,298,248,39,303,84,138),(16,276,299,249,40,304,85,139),(17,277,300,250,21,305,86,140),(18,278,281,251,22,306,87,121),(19,279,282,252,23,307,88,122),(20,280,283,253,24,308,89,123),(41,66,174,152,184,227,119,217),(42,67,175,153,185,228,120,218),(43,68,176,154,186,229,101,219),(44,69,177,155,187,230,102,220),(45,70,178,156,188,231,103,201),(46,71,179,157,189,232,104,202),(47,72,180,158,190,233,105,203),(48,73,161,159,191,234,106,204),(49,74,162,160,192,235,107,205),(50,75,163,141,193,236,108,206),(51,76,164,142,194,237,109,207),(52,77,165,143,195,238,110,208),(53,78,166,144,196,239,111,209),(54,79,167,145,197,240,112,210),(55,80,168,146,198,221,113,211),(56,61,169,147,199,222,114,212),(57,62,170,148,200,223,115,213),(58,63,171,149,181,224,116,214),(59,64,172,150,182,225,117,215),(60,65,173,151,183,226,118,216)], [(1,199,25,56),(2,200,26,57),(3,181,27,58),(4,182,28,59),(5,183,29,60),(6,184,30,41),(7,185,31,42),(8,186,32,43),(9,187,33,44),(10,188,34,45),(11,189,35,46),(12,190,36,47),(13,191,37,48),(14,192,38,49),(15,193,39,50),(16,194,40,51),(17,195,21,52),(18,196,22,53),(19,197,23,54),(20,198,24,55),(61,124,222,254),(62,125,223,255),(63,126,224,256),(64,127,225,257),(65,128,226,258),(66,129,227,259),(67,130,228,260),(68,131,229,241),(69,132,230,242),(70,133,231,243),(71,134,232,244),(72,135,233,245),(73,136,234,246),(74,137,235,247),(75,138,236,248),(76,139,237,249),(77,140,238,250),(78,121,239,251),(79,122,240,252),(80,123,221,253),(81,105,295,180),(82,106,296,161),(83,107,297,162),(84,108,298,163),(85,109,299,164),(86,110,300,165),(87,111,281,166),(88,112,282,167),(89,113,283,168),(90,114,284,169),(91,115,285,170),(92,116,286,171),(93,117,287,172),(94,118,288,173),(95,119,289,174),(96,120,290,175),(97,101,291,176),(98,102,292,177),(99,103,293,178),(100,104,294,179),(141,303,206,275),(142,304,207,276),(143,305,208,277),(144,306,209,278),(145,307,210,279),(146,308,211,280),(147,309,212,261),(148,310,213,262),(149,311,214,263),(150,312,215,264),(151,313,216,265),(152,314,217,266),(153,315,218,267),(154,316,219,268),(155,317,220,269),(156,318,201,270),(157,319,202,271),(158,320,203,272),(159,301,204,273),(160,302,205,274)]])
140 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 5A | 5B | 5C | 5D | 8A | ··· | 8H | 10A | ··· | 10L | 20A | ··· | 20P | 20Q | ··· | 20AF | 20AG | ··· | 20BL | 40A | ··· | 40AF |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 |
140 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | - | ||||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C5 | C10 | C10 | C10 | C10 | C10 | C20 | D4 | Q16 | C4○D4 | C4○D8 | C5×D4 | C5×Q16 | C5×C4○D4 | C5×C4○D8 |
| kernel | Q16×C20 | C4×C40 | C5×Q8⋊C4 | C5×C2.D8 | Q8×C20 | C10×Q16 | C5×Q16 | C4×Q16 | C4×C8 | Q8⋊C4 | C2.D8 | C4×Q8 | C2×Q16 | Q16 | C2×C20 | C20 | C20 | C10 | C2×C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 8 | 4 | 4 | 8 | 4 | 8 | 4 | 32 | 2 | 4 | 2 | 4 | 8 | 16 | 8 | 16 |
Matrix representation of Q16×C20 ►in GL3(𝔽41) generated by
| 32 | 0 | 0 |
| 0 | 2 | 0 |
| 0 | 0 | 2 |
| 1 | 0 | 0 |
| 0 | 29 | 12 |
| 0 | 29 | 29 |
| 40 | 0 | 0 |
| 0 | 6 | 39 |
| 0 | 39 | 35 |
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