metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C40⋊2Q8, C8⋊4Dic10, Dic5.6D8, Dic5.4Q16, C5⋊2C8⋊6Q8, C2.12(D5×D8), C5⋊2(C8⋊2Q8), C20⋊Q8.8C2, C4.26(Q8×D5), C4⋊C4.43D10, C10.27(C2×D8), C2.D8.4D5, C20.17(C2×Q8), C2.12(D5×Q16), (C2×C8).227D10, C2.11(C20⋊Q8), C10.16(C4⋊Q8), C10.21(C2×Q16), (C8×Dic5).2C2, C40⋊5C4.14C2, (C2×C40).79C22, C4.23(C2×Dic10), C10.D8.7C2, C22.223(D4×D5), (C2×C20).290C23, (C2×Dic5).145D4, C4⋊Dic5.116C22, (C4×Dic5).264C22, (C5×C2.D8).5C2, (C2×C10).295(C2×D4), (C5×C4⋊C4).83C22, (C2×C4).393(C22×D5), (C2×C5⋊2C8).239C22, SmallGroup(320,501)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C40⋊2Q8
G = < a,b,c | a40=b4=1, c2=b2, bab-1=a31, cac-1=a9, cbc-1=b-1 >
Subgroups: 382 in 98 conjugacy classes, 47 normal (27 characteristic)
C1, C2, C4, C4, C22, C5, C8, C8, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C2×Q8, Dic5, Dic5, C20, C20, C2×C10, C4×C8, C2.D8, C2.D8, C4⋊Q8, C5⋊2C8, C40, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C8⋊2Q8, C2×C5⋊2C8, C4×Dic5, C10.D4, C4⋊Dic5, C5×C4⋊C4, C2×C40, C2×Dic10, C10.D8, C8×Dic5, C40⋊5C4, C5×C2.D8, C20⋊Q8, C40⋊2Q8
Quotients: C1, C2, C22, D4, Q8, C23, D5, D8, Q16, C2×D4, C2×Q8, D10, C4⋊Q8, C2×D8, C2×Q16, Dic10, C22×D5, C8⋊2Q8, C2×Dic10, D4×D5, Q8×D5, C20⋊Q8, D5×D8, D5×Q16, C40⋊2Q8
►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)
(1 302 70 240)(2 293 71 231)(3 284 72 222)(4 315 73 213)(5 306 74 204)(6 297 75 235)(7 288 76 226)(8 319 77 217)(9 310 78 208)(10 301 79 239)(11 292 80 230)(12 283 41 221)(13 314 42 212)(14 305 43 203)(15 296 44 234)(16 287 45 225)(17 318 46 216)(18 309 47 207)(19 300 48 238)(20 291 49 229)(21 282 50 220)(22 313 51 211)(23 304 52 202)(24 295 53 233)(25 286 54 224)(26 317 55 215)(27 308 56 206)(28 299 57 237)(29 290 58 228)(30 281 59 219)(31 312 60 210)(32 303 61 201)(33 294 62 232)(34 285 63 223)(35 316 64 214)(36 307 65 205)(37 298 66 236)(38 289 67 227)(39 320 68 218)(40 311 69 209)(81 274 175 157)(82 265 176 148)(83 256 177 139)(84 247 178 130)(85 278 179 121)(86 269 180 152)(87 260 181 143)(88 251 182 134)(89 242 183 125)(90 273 184 156)(91 264 185 147)(92 255 186 138)(93 246 187 129)(94 277 188 160)(95 268 189 151)(96 259 190 142)(97 250 191 133)(98 241 192 124)(99 272 193 155)(100 263 194 146)(101 254 195 137)(102 245 196 128)(103 276 197 159)(104 267 198 150)(105 258 199 141)(106 249 200 132)(107 280 161 123)(108 271 162 154)(109 262 163 145)(110 253 164 136)(111 244 165 127)(112 275 166 158)(113 266 167 149)(114 257 168 140)(115 248 169 131)(116 279 170 122)(117 270 171 153)(118 261 172 144)(119 252 173 135)(120 243 174 126)
(1 101 70 195)(2 110 71 164)(3 119 72 173)(4 88 73 182)(5 97 74 191)(6 106 75 200)(7 115 76 169)(8 84 77 178)(9 93 78 187)(10 102 79 196)(11 111 80 165)(12 120 41 174)(13 89 42 183)(14 98 43 192)(15 107 44 161)(16 116 45 170)(17 85 46 179)(18 94 47 188)(19 103 48 197)(20 112 49 166)(21 81 50 175)(22 90 51 184)(23 99 52 193)(24 108 53 162)(25 117 54 171)(26 86 55 180)(27 95 56 189)(28 104 57 198)(29 113 58 167)(30 82 59 176)(31 91 60 185)(32 100 61 194)(33 109 62 163)(34 118 63 172)(35 87 64 181)(36 96 65 190)(37 105 66 199)(38 114 67 168)(39 83 68 177)(40 92 69 186)(121 216 278 318)(122 225 279 287)(123 234 280 296)(124 203 241 305)(125 212 242 314)(126 221 243 283)(127 230 244 292)(128 239 245 301)(129 208 246 310)(130 217 247 319)(131 226 248 288)(132 235 249 297)(133 204 250 306)(134 213 251 315)(135 222 252 284)(136 231 253 293)(137 240 254 302)(138 209 255 311)(139 218 256 320)(140 227 257 289)(141 236 258 298)(142 205 259 307)(143 214 260 316)(144 223 261 285)(145 232 262 294)(146 201 263 303)(147 210 264 312)(148 219 265 281)(149 228 266 290)(150 237 267 299)(151 206 268 308)(152 215 269 317)(153 224 270 286)(154 233 271 295)(155 202 272 304)(156 211 273 313)(157 220 274 282)(158 229 275 291)(159 238 276 300)(160 207 277 309)
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), (1,302,70,240)(2,293,71,231)(3,284,72,222)(4,315,73,213)(5,306,74,204)(6,297,75,235)(7,288,76,226)(8,319,77,217)(9,310,78,208)(10,301,79,239)(11,292,80,230)(12,283,41,221)(13,314,42,212)(14,305,43,203)(15,296,44,234)(16,287,45,225)(17,318,46,216)(18,309,47,207)(19,300,48,238)(20,291,49,229)(21,282,50,220)(22,313,51,211)(23,304,52,202)(24,295,53,233)(25,286,54,224)(26,317,55,215)(27,308,56,206)(28,299,57,237)(29,290,58,228)(30,281,59,219)(31,312,60,210)(32,303,61,201)(33,294,62,232)(34,285,63,223)(35,316,64,214)(36,307,65,205)(37,298,66,236)(38,289,67,227)(39,320,68,218)(40,311,69,209)(81,274,175,157)(82,265,176,148)(83,256,177,139)(84,247,178,130)(85,278,179,121)(86,269,180,152)(87,260,181,143)(88,251,182,134)(89,242,183,125)(90,273,184,156)(91,264,185,147)(92,255,186,138)(93,246,187,129)(94,277,188,160)(95,268,189,151)(96,259,190,142)(97,250,191,133)(98,241,192,124)(99,272,193,155)(100,263,194,146)(101,254,195,137)(102,245,196,128)(103,276,197,159)(104,267,198,150)(105,258,199,141)(106,249,200,132)(107,280,161,123)(108,271,162,154)(109,262,163,145)(110,253,164,136)(111,244,165,127)(112,275,166,158)(113,266,167,149)(114,257,168,140)(115,248,169,131)(116,279,170,122)(117,270,171,153)(118,261,172,144)(119,252,173,135)(120,243,174,126), (1,101,70,195)(2,110,71,164)(3,119,72,173)(4,88,73,182)(5,97,74,191)(6,106,75,200)(7,115,76,169)(8,84,77,178)(9,93,78,187)(10,102,79,196)(11,111,80,165)(12,120,41,174)(13,89,42,183)(14,98,43,192)(15,107,44,161)(16,116,45,170)(17,85,46,179)(18,94,47,188)(19,103,48,197)(20,112,49,166)(21,81,50,175)(22,90,51,184)(23,99,52,193)(24,108,53,162)(25,117,54,171)(26,86,55,180)(27,95,56,189)(28,104,57,198)(29,113,58,167)(30,82,59,176)(31,91,60,185)(32,100,61,194)(33,109,62,163)(34,118,63,172)(35,87,64,181)(36,96,65,190)(37,105,66,199)(38,114,67,168)(39,83,68,177)(40,92,69,186)(121,216,278,318)(122,225,279,287)(123,234,280,296)(124,203,241,305)(125,212,242,314)(126,221,243,283)(127,230,244,292)(128,239,245,301)(129,208,246,310)(130,217,247,319)(131,226,248,288)(132,235,249,297)(133,204,250,306)(134,213,251,315)(135,222,252,284)(136,231,253,293)(137,240,254,302)(138,209,255,311)(139,218,256,320)(140,227,257,289)(141,236,258,298)(142,205,259,307)(143,214,260,316)(144,223,261,285)(145,232,262,294)(146,201,263,303)(147,210,264,312)(148,219,265,281)(149,228,266,290)(150,237,267,299)(151,206,268,308)(152,215,269,317)(153,224,270,286)(154,233,271,295)(155,202,272,304)(156,211,273,313)(157,220,274,282)(158,229,275,291)(159,238,276,300)(160,207,277,309)>;
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), (1,302,70,240)(2,293,71,231)(3,284,72,222)(4,315,73,213)(5,306,74,204)(6,297,75,235)(7,288,76,226)(8,319,77,217)(9,310,78,208)(10,301,79,239)(11,292,80,230)(12,283,41,221)(13,314,42,212)(14,305,43,203)(15,296,44,234)(16,287,45,225)(17,318,46,216)(18,309,47,207)(19,300,48,238)(20,291,49,229)(21,282,50,220)(22,313,51,211)(23,304,52,202)(24,295,53,233)(25,286,54,224)(26,317,55,215)(27,308,56,206)(28,299,57,237)(29,290,58,228)(30,281,59,219)(31,312,60,210)(32,303,61,201)(33,294,62,232)(34,285,63,223)(35,316,64,214)(36,307,65,205)(37,298,66,236)(38,289,67,227)(39,320,68,218)(40,311,69,209)(81,274,175,157)(82,265,176,148)(83,256,177,139)(84,247,178,130)(85,278,179,121)(86,269,180,152)(87,260,181,143)(88,251,182,134)(89,242,183,125)(90,273,184,156)(91,264,185,147)(92,255,186,138)(93,246,187,129)(94,277,188,160)(95,268,189,151)(96,259,190,142)(97,250,191,133)(98,241,192,124)(99,272,193,155)(100,263,194,146)(101,254,195,137)(102,245,196,128)(103,276,197,159)(104,267,198,150)(105,258,199,141)(106,249,200,132)(107,280,161,123)(108,271,162,154)(109,262,163,145)(110,253,164,136)(111,244,165,127)(112,275,166,158)(113,266,167,149)(114,257,168,140)(115,248,169,131)(116,279,170,122)(117,270,171,153)(118,261,172,144)(119,252,173,135)(120,243,174,126), (1,101,70,195)(2,110,71,164)(3,119,72,173)(4,88,73,182)(5,97,74,191)(6,106,75,200)(7,115,76,169)(8,84,77,178)(9,93,78,187)(10,102,79,196)(11,111,80,165)(12,120,41,174)(13,89,42,183)(14,98,43,192)(15,107,44,161)(16,116,45,170)(17,85,46,179)(18,94,47,188)(19,103,48,197)(20,112,49,166)(21,81,50,175)(22,90,51,184)(23,99,52,193)(24,108,53,162)(25,117,54,171)(26,86,55,180)(27,95,56,189)(28,104,57,198)(29,113,58,167)(30,82,59,176)(31,91,60,185)(32,100,61,194)(33,109,62,163)(34,118,63,172)(35,87,64,181)(36,96,65,190)(37,105,66,199)(38,114,67,168)(39,83,68,177)(40,92,69,186)(121,216,278,318)(122,225,279,287)(123,234,280,296)(124,203,241,305)(125,212,242,314)(126,221,243,283)(127,230,244,292)(128,239,245,301)(129,208,246,310)(130,217,247,319)(131,226,248,288)(132,235,249,297)(133,204,250,306)(134,213,251,315)(135,222,252,284)(136,231,253,293)(137,240,254,302)(138,209,255,311)(139,218,256,320)(140,227,257,289)(141,236,258,298)(142,205,259,307)(143,214,260,316)(144,223,261,285)(145,232,262,294)(146,201,263,303)(147,210,264,312)(148,219,265,281)(149,228,266,290)(150,237,267,299)(151,206,268,308)(152,215,269,317)(153,224,270,286)(154,233,271,295)(155,202,272,304)(156,211,273,313)(157,220,274,282)(158,229,275,291)(159,238,276,300)(160,207,277,309) );
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)], [(1,302,70,240),(2,293,71,231),(3,284,72,222),(4,315,73,213),(5,306,74,204),(6,297,75,235),(7,288,76,226),(8,319,77,217),(9,310,78,208),(10,301,79,239),(11,292,80,230),(12,283,41,221),(13,314,42,212),(14,305,43,203),(15,296,44,234),(16,287,45,225),(17,318,46,216),(18,309,47,207),(19,300,48,238),(20,291,49,229),(21,282,50,220),(22,313,51,211),(23,304,52,202),(24,295,53,233),(25,286,54,224),(26,317,55,215),(27,308,56,206),(28,299,57,237),(29,290,58,228),(30,281,59,219),(31,312,60,210),(32,303,61,201),(33,294,62,232),(34,285,63,223),(35,316,64,214),(36,307,65,205),(37,298,66,236),(38,289,67,227),(39,320,68,218),(40,311,69,209),(81,274,175,157),(82,265,176,148),(83,256,177,139),(84,247,178,130),(85,278,179,121),(86,269,180,152),(87,260,181,143),(88,251,182,134),(89,242,183,125),(90,273,184,156),(91,264,185,147),(92,255,186,138),(93,246,187,129),(94,277,188,160),(95,268,189,151),(96,259,190,142),(97,250,191,133),(98,241,192,124),(99,272,193,155),(100,263,194,146),(101,254,195,137),(102,245,196,128),(103,276,197,159),(104,267,198,150),(105,258,199,141),(106,249,200,132),(107,280,161,123),(108,271,162,154),(109,262,163,145),(110,253,164,136),(111,244,165,127),(112,275,166,158),(113,266,167,149),(114,257,168,140),(115,248,169,131),(116,279,170,122),(117,270,171,153),(118,261,172,144),(119,252,173,135),(120,243,174,126)], [(1,101,70,195),(2,110,71,164),(3,119,72,173),(4,88,73,182),(5,97,74,191),(6,106,75,200),(7,115,76,169),(8,84,77,178),(9,93,78,187),(10,102,79,196),(11,111,80,165),(12,120,41,174),(13,89,42,183),(14,98,43,192),(15,107,44,161),(16,116,45,170),(17,85,46,179),(18,94,47,188),(19,103,48,197),(20,112,49,166),(21,81,50,175),(22,90,51,184),(23,99,52,193),(24,108,53,162),(25,117,54,171),(26,86,55,180),(27,95,56,189),(28,104,57,198),(29,113,58,167),(30,82,59,176),(31,91,60,185),(32,100,61,194),(33,109,62,163),(34,118,63,172),(35,87,64,181),(36,96,65,190),(37,105,66,199),(38,114,67,168),(39,83,68,177),(40,92,69,186),(121,216,278,318),(122,225,279,287),(123,234,280,296),(124,203,241,305),(125,212,242,314),(126,221,243,283),(127,230,244,292),(128,239,245,301),(129,208,246,310),(130,217,247,319),(131,226,248,288),(132,235,249,297),(133,204,250,306),(134,213,251,315),(135,222,252,284),(136,231,253,293),(137,240,254,302),(138,209,255,311),(139,218,256,320),(140,227,257,289),(141,236,258,298),(142,205,259,307),(143,214,260,316),(144,223,261,285),(145,232,262,294),(146,201,263,303),(147,210,264,312),(148,219,265,281),(149,228,266,290),(150,237,267,299),(151,206,268,308),(152,215,269,317),(153,224,270,286),(154,233,271,295),(155,202,272,304),(156,211,273,313),(157,220,274,282),(158,229,275,291),(159,238,276,300),(160,207,277,309)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 10A | ··· | 10F | 20A | 20B | 20C | 20D | 20E | ··· | 20L | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 8 | 10 | 10 | 10 | 10 | 40 | 40 | 2 | 2 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | - | + | + | + | - | + | + | - | - | + | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | Q8 | Q8 | D4 | D5 | D8 | Q16 | D10 | D10 | Dic10 | Q8×D5 | D4×D5 | D5×D8 | D5×Q16 |
| kernel | C40⋊2Q8 | C10.D8 | C8×Dic5 | C40⋊5C4 | C5×C2.D8 | C20⋊Q8 | C5⋊2C8 | C40 | C2×Dic5 | C2.D8 | Dic5 | Dic5 | C4⋊C4 | C2×C8 | C8 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 2 | 8 | 2 | 2 | 4 | 4 |
Matrix representation of C40⋊2Q8 ►in GL4(𝔽41) generated by
| 7 | 35 | 0 | 0 |
| 7 | 0 | 0 | 0 |
| 0 | 0 | 17 | 7 |
| 0 | 0 | 35 | 0 |
| 11 | 28 | 0 | 0 |
| 22 | 30 | 0 | 0 |
| 0 | 0 | 12 | 38 |
| 0 | 0 | 21 | 29 |
| 13 | 26 | 0 | 0 |
| 25 | 28 | 0 | 0 |
| 0 | 0 | 40 | 4 |
| 0 | 0 | 20 | 1 |
G:=sub<GL(4,GF(41))| [7,7,0,0,35,0,0,0,0,0,17,35,0,0,7,0],[11,22,0,0,28,30,0,0,0,0,12,21,0,0,38,29],[13,25,0,0,26,28,0,0,0,0,40,20,0,0,4,1] >;
C40⋊2Q8 in GAP, Magma, Sage, TeX
C_{40}\rtimes_2Q_8 % in TeX
G:=Group("C40:2Q8"); // GroupNames label
G:=SmallGroup(320,501);
// by ID
G=gap.SmallGroup(320,501);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,120,254,219,58,438,102,12550]);
// Polycyclic
G:=Group<a,b,c|a^40=b^4=1,c^2=b^2,b*a*b^-1=a^31,c*a*c^-1=a^9,c*b*c^-1=b^-1>;
// generators/relations