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G = C20.6M4(2)  order 320 = 26·5

6th non-split extension by C20 of M4(2) acting via M4(2)/C2=C2×C4

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C20.6M4(2), C5⋊C8⋊3Q8, C2.8(Q8×F5), C5⋊3(C8⋊4Q8), (C2×Q8).6F5, C10.8(C4×Q8), C4⋊Dic5.8C4, (Q8×C10).7C4, C20⋊C8.6C2, C2.9(Q8.F5), C10.24(C8○D4), (Q8×Dic5).16C2, Dic5.32(C2×Q8), C4.3(C22.F5), Dic5⋊C8.3C2, C10.32(C2×M4(2)), Dic5.71(C4○D4), C22.98(C22×F5), C10.C42.2C2, (C4×Dic5).197C22, (C2×Dic5).358C23, (C4×C5⋊C8).5C2, (C2×C4).42(C2×F5), (C2×C20).27(C2×C4), (C2×C5⋊C8).42C22, C2.11(C2×C22.F5), (C2×C10).87(C22×C4), (C2×Dic5).77(C2×C4), SmallGroup(320,1126)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C10 — C20.6M4(2)
Chief series
C1 — C5 — C10 — Dic5 — C2×Dic5 — C2×C5⋊C8 — C4×C5⋊C8 — C20.6M4(2)
Lower central
C5 — C2×C10 — C20.6M4(2)
Upper central
C1 — C22 — C2×Q8

Generators and relations for C20.6M4(2)
 G = < a,b,c | a20=b8=1, c2=a10, bab-1=a3, cac-1=a11, cbc-1=b5 >

Subgroups: 266 in 94 conjugacy classes, 48 normal (26 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C2×C8, C2×Q8, Dic5, Dic5, C20, C20, C2×C10, C4×C8, C8⋊C4, C4⋊C8, C4×Q8, C5⋊C8, C5⋊C8, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×Q8, C8⋊4Q8, C4×Dic5, C4×Dic5, C4⋊Dic5, C4⋊Dic5, C2×C5⋊C8, C2×C5⋊C8, Q8×C10, C4×C5⋊C8, C20⋊C8, C10.C42, Dic5⋊C8, Q8×Dic5, C20.6M4(2)
Quotients: C1, C2, C4, C22, C2×C4, Q8, C23, M4(2), C22×C4, C2×Q8, C4○D4, F5, C4×Q8, C2×M4(2), C8○D4, C2×F5, C8⋊4Q8, C22.F5, C22×F5, Q8.F5, Q8×F5, C2×C22.F5, C20.6M4(2)

Smallest permutation representation of C20.6M4(2)
►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 67 111 196 155 233 307 255)(2 74 120 199 156 240 316 258)(3 61 109 182 157 227 305 241)(4 68 118 185 158 234 314 244)(5 75 107 188 159 221 303 247)(6 62 116 191 160 228 312 250)(7 69 105 194 141 235 301 253)(8 76 114 197 142 222 310 256)(9 63 103 200 143 229 319 259)(10 70 112 183 144 236 308 242)(11 77 101 186 145 223 317 245)(12 64 110 189 146 230 306 248)(13 71 119 192 147 237 315 251)(14 78 108 195 148 224 304 254)(15 65 117 198 149 231 313 257)(16 72 106 181 150 238 302 260)(17 79 115 184 151 225 311 243)(18 66 104 187 152 232 320 246)(19 73 113 190 153 239 309 249)(20 80 102 193 154 226 318 252)(21 220 287 172 82 280 43 132)(22 207 296 175 83 267 52 135)(23 214 285 178 84 274 41 138)(24 201 294 161 85 261 50 121)(25 208 283 164 86 268 59 124)(26 215 292 167 87 275 48 127)(27 202 281 170 88 262 57 130)(28 209 290 173 89 269 46 133)(29 216 299 176 90 276 55 136)(30 203 288 179 91 263 44 139)(31 210 297 162 92 270 53 122)(32 217 286 165 93 277 42 125)(33 204 295 168 94 264 51 128)(34 211 284 171 95 271 60 131)(35 218 293 174 96 278 49 134)(36 205 282 177 97 265 58 137)(37 212 291 180 98 272 47 140)(38 219 300 163 99 279 56 123)(39 206 289 166 100 266 45 126)(40 213 298 169 81 273 54 129)

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

38 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J4K4L 5 8A···8H8I8J8K8L10A10B10C20A···20F
order122244444444444458···8888810101020···20
size11112244555510102020410···10202020204448···8

38 irreducible representations

dim11111111222244488
type++++++-++-+-
imageC1C2C2C2C2C2C4C4Q8C4○D4M4(2)C8○D4F5C2×F5C22.F5Q8.F5Q8×F5
kernelC20.6M4(2)C4×C5⋊C8C20⋊C8C10.C42Dic5⋊C8Q8×Dic5C4⋊Dic5Q8×C10C5⋊C8Dic5C20C10C2×Q8C2×C4C4C2C2
# reps11122162224413411

Matrix representation of C20.6M4(2) ►in GL8(𝔽41)

400000000
040000000
003200000
004090000
000000040
000010040
000001040
000000140
,
2216000000
1919000000
0032390000
00090000
00003982740
00002573638
0000345324
0000132233
,
4039000000
01000000
0032390000
00090000
000040000
000004000
000000400
000000040

G:=sub<GL(8,GF(41))| [40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,32,40,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,40,40,40,40],[22,19,0,0,0,0,0,0,16,19,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,39,9,0,0,0,0,0,0,0,0,39,25,34,1,0,0,0,0,8,7,5,32,0,0,0,0,27,36,3,2,0,0,0,0,40,38,24,33],[40,0,0,0,0,0,0,0,39,1,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,39,9,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40] >;
 

C20.6M4(2) in GAP, Magma, Sage, TeX 

C_{20}._6M_4(2)
 
% in TeX
 
G:=Group("C20.6M4(2)");
 
// GroupNames label
 
G:=SmallGroup(320,1126);
 
// by ID
 
G=gap.SmallGroup(320,1126);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,120,758,219,100,136,6278,1595]);
 
// Polycyclic
 
G:=Group<a,b,c|a^20=b^8=1,c^2=a^10,b*a*b^-1=a^3,c*a*c^-1=a^11,c*b*c^-1=b^5>;
 
// generators/relations
 

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