metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C40⋊5Q8, C8⋊5Dic10, Dic5.10SD16, C5⋊2C8⋊5Q8, C5⋊2(C8⋊3Q8), C20⋊Q8.6C2, C4.20(Q8×D5), C4⋊C4.32D10, C4.Q8.5D5, C2.8(C20⋊Q8), C20.10(C2×Q8), (C2×C8).256D10, C10.13(C4⋊Q8), (C8×Dic5).6C2, C40⋊6C4.13C2, C2.21(D5×SD16), C4.20(C2×Dic10), C10.36(C2×SD16), C22.210(D4×D5), C20.Q8.5C2, (C2×C40).157C22, (C2×C20).271C23, (C2×Dic5).141D4, C4⋊Dic5.103C22, (C4×Dic5).260C22, (C5×C4.Q8).4C2, (C2×C10).276(C2×D4), (C5×C4⋊C4).64C22, (C2×C4).374(C22×D5), (C2×C5⋊2C8).232C22, SmallGroup(320,482)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C40⋊5Q8
G = < a,b,c | a40=b4=1, c2=b2, bab-1=a11, cac-1=a9, cbc-1=b-1 >
Subgroups: 382 in 98 conjugacy classes, 47 normal (21 characteristic)
C1, C2, C2, C4, C4, C22, C5, C8, C8, C2×C4, C2×C4, Q8, C10, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C2×Q8, Dic5, Dic5, C20, C20, C2×C10, C4×C8, C4.Q8, C4.Q8, C4⋊Q8, C5⋊2C8, C40, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C8⋊3Q8, C2×C5⋊2C8, C4×Dic5, C10.D4, C4⋊Dic5, C5×C4⋊C4, C2×C40, C2×Dic10, C20.Q8, C8×Dic5, C40⋊6C4, C5×C4.Q8, C20⋊Q8, C40⋊5Q8
Quotients: C1, C2, C22, D4, Q8, C23, D5, SD16, C2×D4, C2×Q8, D10, C4⋊Q8, C2×SD16, Dic10, C22×D5, C8⋊3Q8, C2×Dic10, D4×D5, Q8×D5, C20⋊Q8, D5×SD16, C40⋊5Q8
►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)
(1 114 191 260)(2 85 192 271)(3 96 193 242)(4 107 194 253)(5 118 195 264)(6 89 196 275)(7 100 197 246)(8 111 198 257)(9 82 199 268)(10 93 200 279)(11 104 161 250)(12 115 162 261)(13 86 163 272)(14 97 164 243)(15 108 165 254)(16 119 166 265)(17 90 167 276)(18 101 168 247)(19 112 169 258)(20 83 170 269)(21 94 171 280)(22 105 172 251)(23 116 173 262)(24 87 174 273)(25 98 175 244)(26 109 176 255)(27 120 177 266)(28 91 178 277)(29 102 179 248)(30 113 180 259)(31 84 181 270)(32 95 182 241)(33 106 183 252)(34 117 184 263)(35 88 185 274)(36 99 186 245)(37 110 187 256)(38 81 188 267)(39 92 189 278)(40 103 190 249)(41 125 207 307)(42 136 208 318)(43 147 209 289)(44 158 210 300)(45 129 211 311)(46 140 212 282)(47 151 213 293)(48 122 214 304)(49 133 215 315)(50 144 216 286)(51 155 217 297)(52 126 218 308)(53 137 219 319)(54 148 220 290)(55 159 221 301)(56 130 222 312)(57 141 223 283)(58 152 224 294)(59 123 225 305)(60 134 226 316)(61 145 227 287)(62 156 228 298)(63 127 229 309)(64 138 230 320)(65 149 231 291)(66 160 232 302)(67 131 233 313)(68 142 234 284)(69 153 235 295)(70 124 236 306)(71 135 237 317)(72 146 238 288)(73 157 239 299)(74 128 240 310)(75 139 201 281)(76 150 202 292)(77 121 203 303)(78 132 204 314)(79 143 205 285)(80 154 206 296)
(1 287 191 145)(2 296 192 154)(3 305 193 123)(4 314 194 132)(5 283 195 141)(6 292 196 150)(7 301 197 159)(8 310 198 128)(9 319 199 137)(10 288 200 146)(11 297 161 155)(12 306 162 124)(13 315 163 133)(14 284 164 142)(15 293 165 151)(16 302 166 160)(17 311 167 129)(18 320 168 138)(19 289 169 147)(20 298 170 156)(21 307 171 125)(22 316 172 134)(23 285 173 143)(24 294 174 152)(25 303 175 121)(26 312 176 130)(27 281 177 139)(28 290 178 148)(29 299 179 157)(30 308 180 126)(31 317 181 135)(32 286 182 144)(33 295 183 153)(34 304 184 122)(35 313 185 131)(36 282 186 140)(37 291 187 149)(38 300 188 158)(39 309 189 127)(40 318 190 136)(41 94 207 280)(42 103 208 249)(43 112 209 258)(44 81 210 267)(45 90 211 276)(46 99 212 245)(47 108 213 254)(48 117 214 263)(49 86 215 272)(50 95 216 241)(51 104 217 250)(52 113 218 259)(53 82 219 268)(54 91 220 277)(55 100 221 246)(56 109 222 255)(57 118 223 264)(58 87 224 273)(59 96 225 242)(60 105 226 251)(61 114 227 260)(62 83 228 269)(63 92 229 278)(64 101 230 247)(65 110 231 256)(66 119 232 265)(67 88 233 274)(68 97 234 243)(69 106 235 252)(70 115 236 261)(71 84 237 270)(72 93 238 279)(73 102 239 248)(74 111 240 257)(75 120 201 266)(76 89 202 275)(77 98 203 244)(78 107 204 253)(79 116 205 262)(80 85 206 271)
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), (1,114,191,260)(2,85,192,271)(3,96,193,242)(4,107,194,253)(5,118,195,264)(6,89,196,275)(7,100,197,246)(8,111,198,257)(9,82,199,268)(10,93,200,279)(11,104,161,250)(12,115,162,261)(13,86,163,272)(14,97,164,243)(15,108,165,254)(16,119,166,265)(17,90,167,276)(18,101,168,247)(19,112,169,258)(20,83,170,269)(21,94,171,280)(22,105,172,251)(23,116,173,262)(24,87,174,273)(25,98,175,244)(26,109,176,255)(27,120,177,266)(28,91,178,277)(29,102,179,248)(30,113,180,259)(31,84,181,270)(32,95,182,241)(33,106,183,252)(34,117,184,263)(35,88,185,274)(36,99,186,245)(37,110,187,256)(38,81,188,267)(39,92,189,278)(40,103,190,249)(41,125,207,307)(42,136,208,318)(43,147,209,289)(44,158,210,300)(45,129,211,311)(46,140,212,282)(47,151,213,293)(48,122,214,304)(49,133,215,315)(50,144,216,286)(51,155,217,297)(52,126,218,308)(53,137,219,319)(54,148,220,290)(55,159,221,301)(56,130,222,312)(57,141,223,283)(58,152,224,294)(59,123,225,305)(60,134,226,316)(61,145,227,287)(62,156,228,298)(63,127,229,309)(64,138,230,320)(65,149,231,291)(66,160,232,302)(67,131,233,313)(68,142,234,284)(69,153,235,295)(70,124,236,306)(71,135,237,317)(72,146,238,288)(73,157,239,299)(74,128,240,310)(75,139,201,281)(76,150,202,292)(77,121,203,303)(78,132,204,314)(79,143,205,285)(80,154,206,296), (1,287,191,145)(2,296,192,154)(3,305,193,123)(4,314,194,132)(5,283,195,141)(6,292,196,150)(7,301,197,159)(8,310,198,128)(9,319,199,137)(10,288,200,146)(11,297,161,155)(12,306,162,124)(13,315,163,133)(14,284,164,142)(15,293,165,151)(16,302,166,160)(17,311,167,129)(18,320,168,138)(19,289,169,147)(20,298,170,156)(21,307,171,125)(22,316,172,134)(23,285,173,143)(24,294,174,152)(25,303,175,121)(26,312,176,130)(27,281,177,139)(28,290,178,148)(29,299,179,157)(30,308,180,126)(31,317,181,135)(32,286,182,144)(33,295,183,153)(34,304,184,122)(35,313,185,131)(36,282,186,140)(37,291,187,149)(38,300,188,158)(39,309,189,127)(40,318,190,136)(41,94,207,280)(42,103,208,249)(43,112,209,258)(44,81,210,267)(45,90,211,276)(46,99,212,245)(47,108,213,254)(48,117,214,263)(49,86,215,272)(50,95,216,241)(51,104,217,250)(52,113,218,259)(53,82,219,268)(54,91,220,277)(55,100,221,246)(56,109,222,255)(57,118,223,264)(58,87,224,273)(59,96,225,242)(60,105,226,251)(61,114,227,260)(62,83,228,269)(63,92,229,278)(64,101,230,247)(65,110,231,256)(66,119,232,265)(67,88,233,274)(68,97,234,243)(69,106,235,252)(70,115,236,261)(71,84,237,270)(72,93,238,279)(73,102,239,248)(74,111,240,257)(75,120,201,266)(76,89,202,275)(77,98,203,244)(78,107,204,253)(79,116,205,262)(80,85,206,271)>;
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), (1,114,191,260)(2,85,192,271)(3,96,193,242)(4,107,194,253)(5,118,195,264)(6,89,196,275)(7,100,197,246)(8,111,198,257)(9,82,199,268)(10,93,200,279)(11,104,161,250)(12,115,162,261)(13,86,163,272)(14,97,164,243)(15,108,165,254)(16,119,166,265)(17,90,167,276)(18,101,168,247)(19,112,169,258)(20,83,170,269)(21,94,171,280)(22,105,172,251)(23,116,173,262)(24,87,174,273)(25,98,175,244)(26,109,176,255)(27,120,177,266)(28,91,178,277)(29,102,179,248)(30,113,180,259)(31,84,181,270)(32,95,182,241)(33,106,183,252)(34,117,184,263)(35,88,185,274)(36,99,186,245)(37,110,187,256)(38,81,188,267)(39,92,189,278)(40,103,190,249)(41,125,207,307)(42,136,208,318)(43,147,209,289)(44,158,210,300)(45,129,211,311)(46,140,212,282)(47,151,213,293)(48,122,214,304)(49,133,215,315)(50,144,216,286)(51,155,217,297)(52,126,218,308)(53,137,219,319)(54,148,220,290)(55,159,221,301)(56,130,222,312)(57,141,223,283)(58,152,224,294)(59,123,225,305)(60,134,226,316)(61,145,227,287)(62,156,228,298)(63,127,229,309)(64,138,230,320)(65,149,231,291)(66,160,232,302)(67,131,233,313)(68,142,234,284)(69,153,235,295)(70,124,236,306)(71,135,237,317)(72,146,238,288)(73,157,239,299)(74,128,240,310)(75,139,201,281)(76,150,202,292)(77,121,203,303)(78,132,204,314)(79,143,205,285)(80,154,206,296), (1,287,191,145)(2,296,192,154)(3,305,193,123)(4,314,194,132)(5,283,195,141)(6,292,196,150)(7,301,197,159)(8,310,198,128)(9,319,199,137)(10,288,200,146)(11,297,161,155)(12,306,162,124)(13,315,163,133)(14,284,164,142)(15,293,165,151)(16,302,166,160)(17,311,167,129)(18,320,168,138)(19,289,169,147)(20,298,170,156)(21,307,171,125)(22,316,172,134)(23,285,173,143)(24,294,174,152)(25,303,175,121)(26,312,176,130)(27,281,177,139)(28,290,178,148)(29,299,179,157)(30,308,180,126)(31,317,181,135)(32,286,182,144)(33,295,183,153)(34,304,184,122)(35,313,185,131)(36,282,186,140)(37,291,187,149)(38,300,188,158)(39,309,189,127)(40,318,190,136)(41,94,207,280)(42,103,208,249)(43,112,209,258)(44,81,210,267)(45,90,211,276)(46,99,212,245)(47,108,213,254)(48,117,214,263)(49,86,215,272)(50,95,216,241)(51,104,217,250)(52,113,218,259)(53,82,219,268)(54,91,220,277)(55,100,221,246)(56,109,222,255)(57,118,223,264)(58,87,224,273)(59,96,225,242)(60,105,226,251)(61,114,227,260)(62,83,228,269)(63,92,229,278)(64,101,230,247)(65,110,231,256)(66,119,232,265)(67,88,233,274)(68,97,234,243)(69,106,235,252)(70,115,236,261)(71,84,237,270)(72,93,238,279)(73,102,239,248)(74,111,240,257)(75,120,201,266)(76,89,202,275)(77,98,203,244)(78,107,204,253)(79,116,205,262)(80,85,206,271) );
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)], [(1,114,191,260),(2,85,192,271),(3,96,193,242),(4,107,194,253),(5,118,195,264),(6,89,196,275),(7,100,197,246),(8,111,198,257),(9,82,199,268),(10,93,200,279),(11,104,161,250),(12,115,162,261),(13,86,163,272),(14,97,164,243),(15,108,165,254),(16,119,166,265),(17,90,167,276),(18,101,168,247),(19,112,169,258),(20,83,170,269),(21,94,171,280),(22,105,172,251),(23,116,173,262),(24,87,174,273),(25,98,175,244),(26,109,176,255),(27,120,177,266),(28,91,178,277),(29,102,179,248),(30,113,180,259),(31,84,181,270),(32,95,182,241),(33,106,183,252),(34,117,184,263),(35,88,185,274),(36,99,186,245),(37,110,187,256),(38,81,188,267),(39,92,189,278),(40,103,190,249),(41,125,207,307),(42,136,208,318),(43,147,209,289),(44,158,210,300),(45,129,211,311),(46,140,212,282),(47,151,213,293),(48,122,214,304),(49,133,215,315),(50,144,216,286),(51,155,217,297),(52,126,218,308),(53,137,219,319),(54,148,220,290),(55,159,221,301),(56,130,222,312),(57,141,223,283),(58,152,224,294),(59,123,225,305),(60,134,226,316),(61,145,227,287),(62,156,228,298),(63,127,229,309),(64,138,230,320),(65,149,231,291),(66,160,232,302),(67,131,233,313),(68,142,234,284),(69,153,235,295),(70,124,236,306),(71,135,237,317),(72,146,238,288),(73,157,239,299),(74,128,240,310),(75,139,201,281),(76,150,202,292),(77,121,203,303),(78,132,204,314),(79,143,205,285),(80,154,206,296)], [(1,287,191,145),(2,296,192,154),(3,305,193,123),(4,314,194,132),(5,283,195,141),(6,292,196,150),(7,301,197,159),(8,310,198,128),(9,319,199,137),(10,288,200,146),(11,297,161,155),(12,306,162,124),(13,315,163,133),(14,284,164,142),(15,293,165,151),(16,302,166,160),(17,311,167,129),(18,320,168,138),(19,289,169,147),(20,298,170,156),(21,307,171,125),(22,316,172,134),(23,285,173,143),(24,294,174,152),(25,303,175,121),(26,312,176,130),(27,281,177,139),(28,290,178,148),(29,299,179,157),(30,308,180,126),(31,317,181,135),(32,286,182,144),(33,295,183,153),(34,304,184,122),(35,313,185,131),(36,282,186,140),(37,291,187,149),(38,300,188,158),(39,309,189,127),(40,318,190,136),(41,94,207,280),(42,103,208,249),(43,112,209,258),(44,81,210,267),(45,90,211,276),(46,99,212,245),(47,108,213,254),(48,117,214,263),(49,86,215,272),(50,95,216,241),(51,104,217,250),(52,113,218,259),(53,82,219,268),(54,91,220,277),(55,100,221,246),(56,109,222,255),(57,118,223,264),(58,87,224,273),(59,96,225,242),(60,105,226,251),(61,114,227,260),(62,83,228,269),(63,92,229,278),(64,101,230,247),(65,110,231,256),(66,119,232,265),(67,88,233,274),(68,97,234,243),(69,106,235,252),(70,115,236,261),(71,84,237,270),(72,93,238,279),(73,102,239,248),(74,111,240,257),(75,120,201,266),(76,89,202,275),(77,98,203,244),(78,107,204,253),(79,116,205,262),(80,85,206,271)]])
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 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | - | + | + | + | + | - | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | Q8 | Q8 | D4 | D5 | SD16 | D10 | D10 | Dic10 | Q8×D5 | D4×D5 | D5×SD16 |
| kernel | C40⋊5Q8 | C20.Q8 | C8×Dic5 | C40⋊6C4 | C5×C4.Q8 | C20⋊Q8 | C5⋊2C8 | C40 | C2×Dic5 | C4.Q8 | Dic5 | C4⋊C4 | C2×C8 | C8 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 8 | 4 | 2 | 8 | 2 | 2 | 8 |
Matrix representation of C40⋊5Q8 ►in GL4(𝔽41) generated by
| 26 | 15 | 0 | 0 |
| 26 | 26 | 0 | 0 |
| 0 | 0 | 0 | 34 |
| 0 | 0 | 6 | 6 |
| 21 | 3 | 0 | 0 |
| 3 | 20 | 0 | 0 |
| 0 | 0 | 2 | 32 |
| 0 | 0 | 37 | 39 |
| 0 | 40 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 20 | 3 |
| 0 | 0 | 3 | 21 |
G:=sub<GL(4,GF(41))| [26,26,0,0,15,26,0,0,0,0,0,6,0,0,34,6],[21,3,0,0,3,20,0,0,0,0,2,37,0,0,32,39],[0,1,0,0,40,0,0,0,0,0,20,3,0,0,3,21] >;
C40⋊5Q8 in GAP, Magma, Sage, TeX
C_{40}\rtimes_5Q_8 % in TeX
G:=Group("C40:5Q8"); // GroupNames label
G:=SmallGroup(320,482);
// by ID
G=gap.SmallGroup(320,482);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,120,254,555,58,438,102,12550]);
// Polycyclic
G:=Group<a,b,c|a^40=b^4=1,c^2=b^2,b*a*b^-1=a^11,c*a*c^-1=a^9,c*b*c^-1=b^-1>;
// generators/relations