metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C40⋊11Q8, C8⋊9Dic10, C42.251D10, C20.37M4(2), C5⋊4(C8⋊4Q8), (C4×C8).16D5, (C4×C40).22C2, C10.15(C4×Q8), C20.80(C2×Q8), C20⋊3C8.4C2, C40⋊8C4.6C2, (C2×C8).280D10, C4.6(C8⋊D5), C4⋊Dic5.18C4, C2.8(C4×Dic10), C10.26(C8○D4), (C4×Dic10).2C2, C4.45(C2×Dic10), C20.8Q8.1C2, C4.123(C4○D20), C20.239(C4○D4), (C2×C40).339C22, (C2×C20).801C23, (C4×C20).322C22, (C2×Dic10).18C4, C10.D4.11C4, C10.35(C2×M4(2)), C2.6(D20.3C4), (C4×Dic5).198C22, C2.6(C2×C8⋊D5), C22.94(C2×C4×D5), (C2×C4).102(C4×D5), (C2×C20).392(C2×C4), (C2×Dic5).12(C2×C4), (C2×C4).743(C22×D5), (C2×C10).157(C22×C4), (C2×C5⋊2C8).190C22, SmallGroup(320,306)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C40⋊11Q8
G = < a,b,c | a40=b4=1, c2=b2, ab=ba, cac-1=a29, cbc-1=b-1 >
Subgroups: 254 in 94 conjugacy classes, 55 normal (33 characteristic)
C1, C2, C4, C4, C4, C22, C5, C8, C8, C2×C4, C2×C4, Q8, C10, C42, C42, C4⋊C4, C2×C8, C2×C8, C2×Q8, Dic5, C20, C20, C20, C2×C10, C4×C8, C8⋊C4, C4⋊C8, C4×Q8, C5⋊2C8, C40, C40, Dic10, C2×Dic5, C2×C20, C8⋊4Q8, C2×C5⋊2C8, C4×Dic5, C10.D4, C4⋊Dic5, C4×C20, C2×C40, C2×Dic10, C20⋊3C8, C20.8Q8, C40⋊8C4, C4×C40, C4×Dic10, C40⋊11Q8
Quotients: C1, C2, C4, C22, C2×C4, Q8, C23, D5, M4(2), C22×C4, C2×Q8, C4○D4, D10, C4×Q8, C2×M4(2), C8○D4, Dic10, C4×D5, C22×D5, C8⋊4Q8, C8⋊D5, C2×Dic10, C2×C4×D5, C4○D20, C4×Dic10, C2×C8⋊D5, D20.3C4, C40⋊11Q8
►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)
(1 269 94 217)(2 270 95 218)(3 271 96 219)(4 272 97 220)(5 273 98 221)(6 274 99 222)(7 275 100 223)(8 276 101 224)(9 277 102 225)(10 278 103 226)(11 279 104 227)(12 280 105 228)(13 241 106 229)(14 242 107 230)(15 243 108 231)(16 244 109 232)(17 245 110 233)(18 246 111 234)(19 247 112 235)(20 248 113 236)(21 249 114 237)(22 250 115 238)(23 251 116 239)(24 252 117 240)(25 253 118 201)(26 254 119 202)(27 255 120 203)(28 256 81 204)(29 257 82 205)(30 258 83 206)(31 259 84 207)(32 260 85 208)(33 261 86 209)(34 262 87 210)(35 263 88 211)(36 264 89 212)(37 265 90 213)(38 266 91 214)(39 267 92 215)(40 268 93 216)(41 200 287 153)(42 161 288 154)(43 162 289 155)(44 163 290 156)(45 164 291 157)(46 165 292 158)(47 166 293 159)(48 167 294 160)(49 168 295 121)(50 169 296 122)(51 170 297 123)(52 171 298 124)(53 172 299 125)(54 173 300 126)(55 174 301 127)(56 175 302 128)(57 176 303 129)(58 177 304 130)(59 178 305 131)(60 179 306 132)(61 180 307 133)(62 181 308 134)(63 182 309 135)(64 183 310 136)(65 184 311 137)(66 185 312 138)(67 186 313 139)(68 187 314 140)(69 188 315 141)(70 189 316 142)(71 190 317 143)(72 191 318 144)(73 192 319 145)(74 193 320 146)(75 194 281 147)(76 195 282 148)(77 196 283 149)(78 197 284 150)(79 198 285 151)(80 199 286 152)
(1 59 94 305)(2 48 95 294)(3 77 96 283)(4 66 97 312)(5 55 98 301)(6 44 99 290)(7 73 100 319)(8 62 101 308)(9 51 102 297)(10 80 103 286)(11 69 104 315)(12 58 105 304)(13 47 106 293)(14 76 107 282)(15 65 108 311)(16 54 109 300)(17 43 110 289)(18 72 111 318)(19 61 112 307)(20 50 113 296)(21 79 114 285)(22 68 115 314)(23 57 116 303)(24 46 117 292)(25 75 118 281)(26 64 119 310)(27 53 120 299)(28 42 81 288)(29 71 82 317)(30 60 83 306)(31 49 84 295)(32 78 85 284)(33 67 86 313)(34 56 87 302)(35 45 88 291)(36 74 89 320)(37 63 90 309)(38 52 91 298)(39 41 92 287)(40 70 93 316)(121 207 168 259)(122 236 169 248)(123 225 170 277)(124 214 171 266)(125 203 172 255)(126 232 173 244)(127 221 174 273)(128 210 175 262)(129 239 176 251)(130 228 177 280)(131 217 178 269)(132 206 179 258)(133 235 180 247)(134 224 181 276)(135 213 182 265)(136 202 183 254)(137 231 184 243)(138 220 185 272)(139 209 186 261)(140 238 187 250)(141 227 188 279)(142 216 189 268)(143 205 190 257)(144 234 191 246)(145 223 192 275)(146 212 193 264)(147 201 194 253)(148 230 195 242)(149 219 196 271)(150 208 197 260)(151 237 198 249)(152 226 199 278)(153 215 200 267)(154 204 161 256)(155 233 162 245)(156 222 163 274)(157 211 164 263)(158 240 165 252)(159 229 166 241)(160 218 167 270)
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), (1,269,94,217)(2,270,95,218)(3,271,96,219)(4,272,97,220)(5,273,98,221)(6,274,99,222)(7,275,100,223)(8,276,101,224)(9,277,102,225)(10,278,103,226)(11,279,104,227)(12,280,105,228)(13,241,106,229)(14,242,107,230)(15,243,108,231)(16,244,109,232)(17,245,110,233)(18,246,111,234)(19,247,112,235)(20,248,113,236)(21,249,114,237)(22,250,115,238)(23,251,116,239)(24,252,117,240)(25,253,118,201)(26,254,119,202)(27,255,120,203)(28,256,81,204)(29,257,82,205)(30,258,83,206)(31,259,84,207)(32,260,85,208)(33,261,86,209)(34,262,87,210)(35,263,88,211)(36,264,89,212)(37,265,90,213)(38,266,91,214)(39,267,92,215)(40,268,93,216)(41,200,287,153)(42,161,288,154)(43,162,289,155)(44,163,290,156)(45,164,291,157)(46,165,292,158)(47,166,293,159)(48,167,294,160)(49,168,295,121)(50,169,296,122)(51,170,297,123)(52,171,298,124)(53,172,299,125)(54,173,300,126)(55,174,301,127)(56,175,302,128)(57,176,303,129)(58,177,304,130)(59,178,305,131)(60,179,306,132)(61,180,307,133)(62,181,308,134)(63,182,309,135)(64,183,310,136)(65,184,311,137)(66,185,312,138)(67,186,313,139)(68,187,314,140)(69,188,315,141)(70,189,316,142)(71,190,317,143)(72,191,318,144)(73,192,319,145)(74,193,320,146)(75,194,281,147)(76,195,282,148)(77,196,283,149)(78,197,284,150)(79,198,285,151)(80,199,286,152), (1,59,94,305)(2,48,95,294)(3,77,96,283)(4,66,97,312)(5,55,98,301)(6,44,99,290)(7,73,100,319)(8,62,101,308)(9,51,102,297)(10,80,103,286)(11,69,104,315)(12,58,105,304)(13,47,106,293)(14,76,107,282)(15,65,108,311)(16,54,109,300)(17,43,110,289)(18,72,111,318)(19,61,112,307)(20,50,113,296)(21,79,114,285)(22,68,115,314)(23,57,116,303)(24,46,117,292)(25,75,118,281)(26,64,119,310)(27,53,120,299)(28,42,81,288)(29,71,82,317)(30,60,83,306)(31,49,84,295)(32,78,85,284)(33,67,86,313)(34,56,87,302)(35,45,88,291)(36,74,89,320)(37,63,90,309)(38,52,91,298)(39,41,92,287)(40,70,93,316)(121,207,168,259)(122,236,169,248)(123,225,170,277)(124,214,171,266)(125,203,172,255)(126,232,173,244)(127,221,174,273)(128,210,175,262)(129,239,176,251)(130,228,177,280)(131,217,178,269)(132,206,179,258)(133,235,180,247)(134,224,181,276)(135,213,182,265)(136,202,183,254)(137,231,184,243)(138,220,185,272)(139,209,186,261)(140,238,187,250)(141,227,188,279)(142,216,189,268)(143,205,190,257)(144,234,191,246)(145,223,192,275)(146,212,193,264)(147,201,194,253)(148,230,195,242)(149,219,196,271)(150,208,197,260)(151,237,198,249)(152,226,199,278)(153,215,200,267)(154,204,161,256)(155,233,162,245)(156,222,163,274)(157,211,164,263)(158,240,165,252)(159,229,166,241)(160,218,167,270)>;
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), (1,269,94,217)(2,270,95,218)(3,271,96,219)(4,272,97,220)(5,273,98,221)(6,274,99,222)(7,275,100,223)(8,276,101,224)(9,277,102,225)(10,278,103,226)(11,279,104,227)(12,280,105,228)(13,241,106,229)(14,242,107,230)(15,243,108,231)(16,244,109,232)(17,245,110,233)(18,246,111,234)(19,247,112,235)(20,248,113,236)(21,249,114,237)(22,250,115,238)(23,251,116,239)(24,252,117,240)(25,253,118,201)(26,254,119,202)(27,255,120,203)(28,256,81,204)(29,257,82,205)(30,258,83,206)(31,259,84,207)(32,260,85,208)(33,261,86,209)(34,262,87,210)(35,263,88,211)(36,264,89,212)(37,265,90,213)(38,266,91,214)(39,267,92,215)(40,268,93,216)(41,200,287,153)(42,161,288,154)(43,162,289,155)(44,163,290,156)(45,164,291,157)(46,165,292,158)(47,166,293,159)(48,167,294,160)(49,168,295,121)(50,169,296,122)(51,170,297,123)(52,171,298,124)(53,172,299,125)(54,173,300,126)(55,174,301,127)(56,175,302,128)(57,176,303,129)(58,177,304,130)(59,178,305,131)(60,179,306,132)(61,180,307,133)(62,181,308,134)(63,182,309,135)(64,183,310,136)(65,184,311,137)(66,185,312,138)(67,186,313,139)(68,187,314,140)(69,188,315,141)(70,189,316,142)(71,190,317,143)(72,191,318,144)(73,192,319,145)(74,193,320,146)(75,194,281,147)(76,195,282,148)(77,196,283,149)(78,197,284,150)(79,198,285,151)(80,199,286,152), (1,59,94,305)(2,48,95,294)(3,77,96,283)(4,66,97,312)(5,55,98,301)(6,44,99,290)(7,73,100,319)(8,62,101,308)(9,51,102,297)(10,80,103,286)(11,69,104,315)(12,58,105,304)(13,47,106,293)(14,76,107,282)(15,65,108,311)(16,54,109,300)(17,43,110,289)(18,72,111,318)(19,61,112,307)(20,50,113,296)(21,79,114,285)(22,68,115,314)(23,57,116,303)(24,46,117,292)(25,75,118,281)(26,64,119,310)(27,53,120,299)(28,42,81,288)(29,71,82,317)(30,60,83,306)(31,49,84,295)(32,78,85,284)(33,67,86,313)(34,56,87,302)(35,45,88,291)(36,74,89,320)(37,63,90,309)(38,52,91,298)(39,41,92,287)(40,70,93,316)(121,207,168,259)(122,236,169,248)(123,225,170,277)(124,214,171,266)(125,203,172,255)(126,232,173,244)(127,221,174,273)(128,210,175,262)(129,239,176,251)(130,228,177,280)(131,217,178,269)(132,206,179,258)(133,235,180,247)(134,224,181,276)(135,213,182,265)(136,202,183,254)(137,231,184,243)(138,220,185,272)(139,209,186,261)(140,238,187,250)(141,227,188,279)(142,216,189,268)(143,205,190,257)(144,234,191,246)(145,223,192,275)(146,212,193,264)(147,201,194,253)(148,230,195,242)(149,219,196,271)(150,208,197,260)(151,237,198,249)(152,226,199,278)(153,215,200,267)(154,204,161,256)(155,233,162,245)(156,222,163,274)(157,211,164,263)(158,240,165,252)(159,229,166,241)(160,218,167,270) );
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)], [(1,269,94,217),(2,270,95,218),(3,271,96,219),(4,272,97,220),(5,273,98,221),(6,274,99,222),(7,275,100,223),(8,276,101,224),(9,277,102,225),(10,278,103,226),(11,279,104,227),(12,280,105,228),(13,241,106,229),(14,242,107,230),(15,243,108,231),(16,244,109,232),(17,245,110,233),(18,246,111,234),(19,247,112,235),(20,248,113,236),(21,249,114,237),(22,250,115,238),(23,251,116,239),(24,252,117,240),(25,253,118,201),(26,254,119,202),(27,255,120,203),(28,256,81,204),(29,257,82,205),(30,258,83,206),(31,259,84,207),(32,260,85,208),(33,261,86,209),(34,262,87,210),(35,263,88,211),(36,264,89,212),(37,265,90,213),(38,266,91,214),(39,267,92,215),(40,268,93,216),(41,200,287,153),(42,161,288,154),(43,162,289,155),(44,163,290,156),(45,164,291,157),(46,165,292,158),(47,166,293,159),(48,167,294,160),(49,168,295,121),(50,169,296,122),(51,170,297,123),(52,171,298,124),(53,172,299,125),(54,173,300,126),(55,174,301,127),(56,175,302,128),(57,176,303,129),(58,177,304,130),(59,178,305,131),(60,179,306,132),(61,180,307,133),(62,181,308,134),(63,182,309,135),(64,183,310,136),(65,184,311,137),(66,185,312,138),(67,186,313,139),(68,187,314,140),(69,188,315,141),(70,189,316,142),(71,190,317,143),(72,191,318,144),(73,192,319,145),(74,193,320,146),(75,194,281,147),(76,195,282,148),(77,196,283,149),(78,197,284,150),(79,198,285,151),(80,199,286,152)], [(1,59,94,305),(2,48,95,294),(3,77,96,283),(4,66,97,312),(5,55,98,301),(6,44,99,290),(7,73,100,319),(8,62,101,308),(9,51,102,297),(10,80,103,286),(11,69,104,315),(12,58,105,304),(13,47,106,293),(14,76,107,282),(15,65,108,311),(16,54,109,300),(17,43,110,289),(18,72,111,318),(19,61,112,307),(20,50,113,296),(21,79,114,285),(22,68,115,314),(23,57,116,303),(24,46,117,292),(25,75,118,281),(26,64,119,310),(27,53,120,299),(28,42,81,288),(29,71,82,317),(30,60,83,306),(31,49,84,295),(32,78,85,284),(33,67,86,313),(34,56,87,302),(35,45,88,291),(36,74,89,320),(37,63,90,309),(38,52,91,298),(39,41,92,287),(40,70,93,316),(121,207,168,259),(122,236,169,248),(123,225,170,277),(124,214,171,266),(125,203,172,255),(126,232,173,244),(127,221,174,273),(128,210,175,262),(129,239,176,251),(130,228,177,280),(131,217,178,269),(132,206,179,258),(133,235,180,247),(134,224,181,276),(135,213,182,265),(136,202,183,254),(137,231,184,243),(138,220,185,272),(139,209,186,261),(140,238,187,250),(141,227,188,279),(142,216,189,268),(143,205,190,257),(144,234,191,246),(145,223,192,275),(146,212,193,264),(147,201,194,253),(148,230,195,242),(149,219,196,271),(150,208,197,260),(151,237,198,249),(152,226,199,278),(153,215,200,267),(154,204,161,256),(155,233,162,245),(156,222,163,274),(157,211,164,263),(158,240,165,252),(159,229,166,241),(160,218,167,270)]])
92 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 10A | ··· | 10F | 20A | ··· | 20X | 40A | ··· | 40AF |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | + | + | - | ||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | Q8 | D5 | M4(2) | C4○D4 | D10 | D10 | C8○D4 | Dic10 | C4×D5 | C8⋊D5 | C4○D20 | D20.3C4 |
| kernel | C40⋊11Q8 | C20⋊3C8 | C20.8Q8 | C40⋊8C4 | C4×C40 | C4×Dic10 | C10.D4 | C4⋊Dic5 | C2×Dic10 | C40 | C4×C8 | C20 | C20 | C42 | C2×C8 | C10 | C8 | C2×C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 4 | 2 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 4 | 8 | 8 | 16 | 8 | 16 |
Matrix representation of C40⋊11Q8 ►in GL4(𝔽41) generated by
| 35 | 6 | 0 | 0 |
| 35 | 40 | 0 | 0 |
| 0 | 0 | 6 | 7 |
| 0 | 0 | 34 | 7 |
| 2 | 28 | 0 | 0 |
| 13 | 39 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 14 | 4 | 0 | 0 |
| 2 | 27 | 0 | 0 |
| 0 | 0 | 5 | 8 |
| 0 | 0 | 38 | 36 |
G:=sub<GL(4,GF(41))| [35,35,0,0,6,40,0,0,0,0,6,34,0,0,7,7],[2,13,0,0,28,39,0,0,0,0,1,0,0,0,0,1],[14,2,0,0,4,27,0,0,0,0,5,38,0,0,8,36] >;
C40⋊11Q8 in GAP, Magma, Sage, TeX
C_{40}\rtimes_{11}Q_8 % in TeX
G:=Group("C40:11Q8"); // GroupNames label
G:=SmallGroup(320,306);
// by ID
G=gap.SmallGroup(320,306);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,253,120,758,58,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^40=b^4=1,c^2=b^2,a*b=b*a,c*a*c^-1=a^29,c*b*c^-1=b^-1>;
// generators/relations