metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic5⋊3C16, C10.3M5(2), C20.32M4(2), C5⋊2(C4⋊C16), (C2×C8).8F5, (C2×C40).5C4, C10.7(C4⋊C8), C10.5(C2×C16), C5⋊2C8.38D4, C4.26(C4⋊F5), C20.26(C4⋊C4), C5⋊2C8.12Q8, C2.5(D5⋊C16), (C2×Dic5).11C8, (C8×Dic5).13C2, (C4×Dic5).42C4, C2.3(C8.F5), C22.10(D5⋊C8), C4.10(C22.F5), C2.1(Dic5⋊C8), (C2×C5⋊C16).4C2, (C2×C10).6(C2×C8), (C2×C4).156(C2×F5), (C2×C20).162(C2×C4), (C2×C5⋊2C8).346C22, SmallGroup(320,226)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.M5(2)
G = < a,b,c | a10=b16=1, c2=a5, bab-1=a7, cac-1=a-1, cbc-1=a5b9 >
Smallest permutation representation of C10.M5(2)
►Regular action on 320 points
Generators in S320
(1 282 289 138 181 248 305 62 66 30)(2 63 182 283 67 249 290 31 306 139)(3 32 68 64 307 250 183 140 291 284)(4 141 308 17 292 251 69 285 184 49)(5 286 293 142 185 252 309 50 70 18)(6 51 186 287 71 253 294 19 310 143)(7 20 72 52 311 254 187 144 295 288)(8 129 312 21 296 255 73 273 188 53)(9 274 297 130 189 256 313 54 74 22)(10 55 190 275 75 241 298 23 314 131)(11 24 76 56 315 242 191 132 299 276)(12 133 316 25 300 243 77 277 192 57)(13 278 301 134 177 244 317 58 78 26)(14 59 178 279 79 245 302 27 318 135)(15 28 80 60 319 246 179 136 303 280)(16 137 320 29 304 247 65 281 180 61)(33 233 259 211 82 156 202 164 120 98)(34 165 83 234 121 157 260 99 203 212)(35 100 122 166 204 158 84 213 261 235)(36 214 205 101 262 159 123 236 85 167)(37 237 263 215 86 160 206 168 124 102)(38 169 87 238 125 145 264 103 207 216)(39 104 126 170 208 146 88 217 265 239)(40 218 193 105 266 147 127 240 89 171)(41 225 267 219 90 148 194 172 128 106)(42 173 91 226 113 149 268 107 195 220)(43 108 114 174 196 150 92 221 269 227)(44 222 197 109 270 151 115 228 93 175)(45 229 271 223 94 152 198 176 116 110)(46 161 95 230 117 153 272 111 199 224)(47 112 118 162 200 154 96 209 257 231)(48 210 201 97 258 155 119 232 81 163)
(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)
(1 149 248 42)(2 35 249 158)(3 151 250 44)(4 37 251 160)(5 153 252 46)(6 39 253 146)(7 155 254 48)(8 41 255 148)(9 157 256 34)(10 43 241 150)(11 159 242 36)(12 45 243 152)(13 145 244 38)(14 47 245 154)(15 147 246 40)(16 33 247 156)(17 168 184 263)(18 272 185 161)(19 170 186 265)(20 258 187 163)(21 172 188 267)(22 260 189 165)(23 174 190 269)(24 262 191 167)(25 176 192 271)(26 264 177 169)(27 162 178 257)(28 266 179 171)(29 164 180 259)(30 268 181 173)(31 166 182 261)(32 270 183 175)(49 237 292 206)(50 199 293 230)(51 239 294 208)(52 201 295 232)(53 225 296 194)(54 203 297 234)(55 227 298 196)(56 205 299 236)(57 229 300 198)(58 207 301 238)(59 231 302 200)(60 193 303 240)(61 233 304 202)(62 195 289 226)(63 235 290 204)(64 197 291 228)(65 82 137 98)(66 107 138 91)(67 84 139 100)(68 109 140 93)(69 86 141 102)(70 111 142 95)(71 88 143 104)(72 97 144 81)(73 90 129 106)(74 99 130 83)(75 92 131 108)(76 101 132 85)(77 94 133 110)(78 103 134 87)(79 96 135 112)(80 105 136 89)(113 305 220 282)(114 275 221 314)(115 307 222 284)(116 277 223 316)(117 309 224 286)(118 279 209 318)(119 311 210 288)(120 281 211 320)(121 313 212 274)(122 283 213 306)(123 315 214 276)(124 285 215 308)(125 317 216 278)(126 287 217 310)(127 319 218 280)(128 273 219 312)
G:=sub<Sym(320)| (1,282,289,138,181,248,305,62,66,30)(2,63,182,283,67,249,290,31,306,139)(3,32,68,64,307,250,183,140,291,284)(4,141,308,17,292,251,69,285,184,49)(5,286,293,142,185,252,309,50,70,18)(6,51,186,287,71,253,294,19,310,143)(7,20,72,52,311,254,187,144,295,288)(8,129,312,21,296,255,73,273,188,53)(9,274,297,130,189,256,313,54,74,22)(10,55,190,275,75,241,298,23,314,131)(11,24,76,56,315,242,191,132,299,276)(12,133,316,25,300,243,77,277,192,57)(13,278,301,134,177,244,317,58,78,26)(14,59,178,279,79,245,302,27,318,135)(15,28,80,60,319,246,179,136,303,280)(16,137,320,29,304,247,65,281,180,61)(33,233,259,211,82,156,202,164,120,98)(34,165,83,234,121,157,260,99,203,212)(35,100,122,166,204,158,84,213,261,235)(36,214,205,101,262,159,123,236,85,167)(37,237,263,215,86,160,206,168,124,102)(38,169,87,238,125,145,264,103,207,216)(39,104,126,170,208,146,88,217,265,239)(40,218,193,105,266,147,127,240,89,171)(41,225,267,219,90,148,194,172,128,106)(42,173,91,226,113,149,268,107,195,220)(43,108,114,174,196,150,92,221,269,227)(44,222,197,109,270,151,115,228,93,175)(45,229,271,223,94,152,198,176,116,110)(46,161,95,230,117,153,272,111,199,224)(47,112,118,162,200,154,96,209,257,231)(48,210,201,97,258,155,119,232,81,163), (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), (1,149,248,42)(2,35,249,158)(3,151,250,44)(4,37,251,160)(5,153,252,46)(6,39,253,146)(7,155,254,48)(8,41,255,148)(9,157,256,34)(10,43,241,150)(11,159,242,36)(12,45,243,152)(13,145,244,38)(14,47,245,154)(15,147,246,40)(16,33,247,156)(17,168,184,263)(18,272,185,161)(19,170,186,265)(20,258,187,163)(21,172,188,267)(22,260,189,165)(23,174,190,269)(24,262,191,167)(25,176,192,271)(26,264,177,169)(27,162,178,257)(28,266,179,171)(29,164,180,259)(30,268,181,173)(31,166,182,261)(32,270,183,175)(49,237,292,206)(50,199,293,230)(51,239,294,208)(52,201,295,232)(53,225,296,194)(54,203,297,234)(55,227,298,196)(56,205,299,236)(57,229,300,198)(58,207,301,238)(59,231,302,200)(60,193,303,240)(61,233,304,202)(62,195,289,226)(63,235,290,204)(64,197,291,228)(65,82,137,98)(66,107,138,91)(67,84,139,100)(68,109,140,93)(69,86,141,102)(70,111,142,95)(71,88,143,104)(72,97,144,81)(73,90,129,106)(74,99,130,83)(75,92,131,108)(76,101,132,85)(77,94,133,110)(78,103,134,87)(79,96,135,112)(80,105,136,89)(113,305,220,282)(114,275,221,314)(115,307,222,284)(116,277,223,316)(117,309,224,286)(118,279,209,318)(119,311,210,288)(120,281,211,320)(121,313,212,274)(122,283,213,306)(123,315,214,276)(124,285,215,308)(125,317,216,278)(126,287,217,310)(127,319,218,280)(128,273,219,312)>;
G:=Group( (1,282,289,138,181,248,305,62,66,30)(2,63,182,283,67,249,290,31,306,139)(3,32,68,64,307,250,183,140,291,284)(4,141,308,17,292,251,69,285,184,49)(5,286,293,142,185,252,309,50,70,18)(6,51,186,287,71,253,294,19,310,143)(7,20,72,52,311,254,187,144,295,288)(8,129,312,21,296,255,73,273,188,53)(9,274,297,130,189,256,313,54,74,22)(10,55,190,275,75,241,298,23,314,131)(11,24,76,56,315,242,191,132,299,276)(12,133,316,25,300,243,77,277,192,57)(13,278,301,134,177,244,317,58,78,26)(14,59,178,279,79,245,302,27,318,135)(15,28,80,60,319,246,179,136,303,280)(16,137,320,29,304,247,65,281,180,61)(33,233,259,211,82,156,202,164,120,98)(34,165,83,234,121,157,260,99,203,212)(35,100,122,166,204,158,84,213,261,235)(36,214,205,101,262,159,123,236,85,167)(37,237,263,215,86,160,206,168,124,102)(38,169,87,238,125,145,264,103,207,216)(39,104,126,170,208,146,88,217,265,239)(40,218,193,105,266,147,127,240,89,171)(41,225,267,219,90,148,194,172,128,106)(42,173,91,226,113,149,268,107,195,220)(43,108,114,174,196,150,92,221,269,227)(44,222,197,109,270,151,115,228,93,175)(45,229,271,223,94,152,198,176,116,110)(46,161,95,230,117,153,272,111,199,224)(47,112,118,162,200,154,96,209,257,231)(48,210,201,97,258,155,119,232,81,163), (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), (1,149,248,42)(2,35,249,158)(3,151,250,44)(4,37,251,160)(5,153,252,46)(6,39,253,146)(7,155,254,48)(8,41,255,148)(9,157,256,34)(10,43,241,150)(11,159,242,36)(12,45,243,152)(13,145,244,38)(14,47,245,154)(15,147,246,40)(16,33,247,156)(17,168,184,263)(18,272,185,161)(19,170,186,265)(20,258,187,163)(21,172,188,267)(22,260,189,165)(23,174,190,269)(24,262,191,167)(25,176,192,271)(26,264,177,169)(27,162,178,257)(28,266,179,171)(29,164,180,259)(30,268,181,173)(31,166,182,261)(32,270,183,175)(49,237,292,206)(50,199,293,230)(51,239,294,208)(52,201,295,232)(53,225,296,194)(54,203,297,234)(55,227,298,196)(56,205,299,236)(57,229,300,198)(58,207,301,238)(59,231,302,200)(60,193,303,240)(61,233,304,202)(62,195,289,226)(63,235,290,204)(64,197,291,228)(65,82,137,98)(66,107,138,91)(67,84,139,100)(68,109,140,93)(69,86,141,102)(70,111,142,95)(71,88,143,104)(72,97,144,81)(73,90,129,106)(74,99,130,83)(75,92,131,108)(76,101,132,85)(77,94,133,110)(78,103,134,87)(79,96,135,112)(80,105,136,89)(113,305,220,282)(114,275,221,314)(115,307,222,284)(116,277,223,316)(117,309,224,286)(118,279,209,318)(119,311,210,288)(120,281,211,320)(121,313,212,274)(122,283,213,306)(123,315,214,276)(124,285,215,308)(125,317,216,278)(126,287,217,310)(127,319,218,280)(128,273,219,312) );
G=PermutationGroup([[(1,282,289,138,181,248,305,62,66,30),(2,63,182,283,67,249,290,31,306,139),(3,32,68,64,307,250,183,140,291,284),(4,141,308,17,292,251,69,285,184,49),(5,286,293,142,185,252,309,50,70,18),(6,51,186,287,71,253,294,19,310,143),(7,20,72,52,311,254,187,144,295,288),(8,129,312,21,296,255,73,273,188,53),(9,274,297,130,189,256,313,54,74,22),(10,55,190,275,75,241,298,23,314,131),(11,24,76,56,315,242,191,132,299,276),(12,133,316,25,300,243,77,277,192,57),(13,278,301,134,177,244,317,58,78,26),(14,59,178,279,79,245,302,27,318,135),(15,28,80,60,319,246,179,136,303,280),(16,137,320,29,304,247,65,281,180,61),(33,233,259,211,82,156,202,164,120,98),(34,165,83,234,121,157,260,99,203,212),(35,100,122,166,204,158,84,213,261,235),(36,214,205,101,262,159,123,236,85,167),(37,237,263,215,86,160,206,168,124,102),(38,169,87,238,125,145,264,103,207,216),(39,104,126,170,208,146,88,217,265,239),(40,218,193,105,266,147,127,240,89,171),(41,225,267,219,90,148,194,172,128,106),(42,173,91,226,113,149,268,107,195,220),(43,108,114,174,196,150,92,221,269,227),(44,222,197,109,270,151,115,228,93,175),(45,229,271,223,94,152,198,176,116,110),(46,161,95,230,117,153,272,111,199,224),(47,112,118,162,200,154,96,209,257,231),(48,210,201,97,258,155,119,232,81,163)], [(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)], [(1,149,248,42),(2,35,249,158),(3,151,250,44),(4,37,251,160),(5,153,252,46),(6,39,253,146),(7,155,254,48),(8,41,255,148),(9,157,256,34),(10,43,241,150),(11,159,242,36),(12,45,243,152),(13,145,244,38),(14,47,245,154),(15,147,246,40),(16,33,247,156),(17,168,184,263),(18,272,185,161),(19,170,186,265),(20,258,187,163),(21,172,188,267),(22,260,189,165),(23,174,190,269),(24,262,191,167),(25,176,192,271),(26,264,177,169),(27,162,178,257),(28,266,179,171),(29,164,180,259),(30,268,181,173),(31,166,182,261),(32,270,183,175),(49,237,292,206),(50,199,293,230),(51,239,294,208),(52,201,295,232),(53,225,296,194),(54,203,297,234),(55,227,298,196),(56,205,299,236),(57,229,300,198),(58,207,301,238),(59,231,302,200),(60,193,303,240),(61,233,304,202),(62,195,289,226),(63,235,290,204),(64,197,291,228),(65,82,137,98),(66,107,138,91),(67,84,139,100),(68,109,140,93),(69,86,141,102),(70,111,142,95),(71,88,143,104),(72,97,144,81),(73,90,129,106),(74,99,130,83),(75,92,131,108),(76,101,132,85),(77,94,133,110),(78,103,134,87),(79,96,135,112),(80,105,136,89),(113,305,220,282),(114,275,221,314),(115,307,222,284),(116,277,223,316),(117,309,224,286),(118,279,209,318),(119,311,210,288),(120,281,211,320),(121,313,212,274),(122,283,213,306),(123,315,214,276),(124,285,215,308),(125,317,216,278),(126,287,217,310),(127,319,218,280),(128,273,219,312)]])
56 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5 | 8A | 8B | 8C | 8D | 8E | ··· | 8L | 10A | 10B | 10C | 16A | ··· | 16P | 20A | 20B | 20C | 20D | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 8 | 8 | 8 | 8 | 8 | ··· | 8 | 10 | 10 | 10 | 16 | ··· | 16 | 20 | 20 | 20 | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 10 | 10 | 10 | 10 | 4 | 2 | 2 | 2 | 2 | 5 | ··· | 5 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
56 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | + | - | ||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | C16 | D4 | Q8 | M4(2) | M5(2) | F5 | C2×F5 | C4⋊F5 | C22.F5 | D5⋊C8 | D5⋊C16 | C8.F5 |
| kernel | C10.M5(2) | C8×Dic5 | C2×C5⋊C16 | C4×Dic5 | C2×C40 | C2×Dic5 | Dic5 | C5⋊2C8 | C5⋊2C8 | C20 | C10 | C2×C8 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 2 | 2 | 2 | 8 | 16 | 1 | 1 | 2 | 4 | 1 | 1 | 2 | 2 | 2 | 4 | 4 |
Matrix representation of C10.M5(2) ►in GL6(𝔽241)
| 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 238 | 223 | 0 | 0 | 0 | 0 |
| 188 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 212 | 56 | 221 | 127 |
| 0 | 0 | 147 | 20 | 232 | 76 |
| 0 | 0 | 85 | 9 | 156 | 29 |
| 0 | 0 | 114 | 85 | 170 | 94 |
| 234 | 231 | 0 | 0 | 0 | 0 |
| 5 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 231 | 89 | 89 | 196 |
| 0 | 0 | 99 | 99 | 206 | 10 |
| 0 | 0 | 0 | 107 | 152 | 142 |
| 0 | 0 | 107 | 152 | 142 | 0 |
G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,0,1,240,0,0,0,0,1,0,240,0,0,0,1,0,0,0,0,240,1,0,0],[238,188,0,0,0,0,223,3,0,0,0,0,0,0,212,147,85,114,0,0,56,20,9,85,0,0,221,232,156,170,0,0,127,76,29,94],[234,5,0,0,0,0,231,7,0,0,0,0,0,0,231,99,0,107,0,0,89,99,107,152,0,0,89,206,152,142,0,0,196,10,142,0] >;
C10.M5(2) in GAP, Magma, Sage, TeX
C_{10}.M_5(2) % in TeX
G:=Group("C10.M5(2)"); // GroupNames label
G:=SmallGroup(320,226);
// by ID
G=gap.SmallGroup(320,226);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,176,100,102,6278,3156]);
// Polycyclic
G:=Group<a,b,c|a^10=b^16=1,c^2=a^5,b*a*b^-1=a^7,c*a*c^-1=a^-1,c*b*c^-1=a^5*b^9>;
// generators/relations
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