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G = C2×C9⋊Q16order 288 = 25·32

Direct product of C2 and C9⋊Q16

Series: Derived Chief Lower central Upper central

 Derived series C1 — C36 — C2×C9⋊Q16
 Chief series C1 — C3 — C9 — C18 — C36 — Dic18 — C2×Dic18 — C2×C9⋊Q16
 Lower central C9 — C18 — C36 — C2×C9⋊Q16
 Upper central C1 — C22 — C2×C4 — C2×Q8

Generators and relations for C2×C9⋊Q16
G = < a,b,c,d | a2=b9=c8=1, d2=c4, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd-1=c-1 >

Subgroups: 304 in 90 conjugacy classes, 44 normal (24 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C8, C2×C4, C2×C4, Q8, Q8, C9, Dic3, C12, C12, C2×C6, C2×C8, Q16, C2×Q8, C2×Q8, C18, C18, C3⋊C8, Dic6, C2×Dic3, C2×C12, C2×C12, C3×Q8, C3×Q8, C2×Q16, Dic9, C36, C36, C2×C18, C2×C3⋊C8, C3⋊Q16, C2×Dic6, C6×Q8, C9⋊C8, Dic18, Dic18, C2×Dic9, C2×C36, C2×C36, Q8×C9, Q8×C9, C2×C3⋊Q16, C2×C9⋊C8, C9⋊Q16, C2×Dic18, Q8×C18, C2×C9⋊Q16
Quotients: C1, C2, C22, S3, D4, C23, D6, Q16, C2×D4, D9, C3⋊D4, C22×S3, C2×Q16, D18, C3⋊Q16, C2×C3⋊D4, C9⋊D4, C22×D9, C2×C3⋊Q16, C9⋊Q16, C2×C9⋊D4, C2×C9⋊Q16

Smallest permutation representation of C2×C9⋊Q16
Regular action on 288 points
Generators in S288
(1 76)(2 77)(3 78)(4 79)(5 80)(6 81)(7 73)(8 74)(9 75)(10 82)(11 83)(12 84)(13 85)(14 86)(15 87)(16 88)(17 89)(18 90)(19 91)(20 92)(21 93)(22 94)(23 95)(24 96)(25 97)(26 98)(27 99)(28 100)(29 101)(30 102)(31 103)(32 104)(33 105)(34 106)(35 107)(36 108)(37 109)(38 110)(39 111)(40 112)(41 113)(42 114)(43 115)(44 116)(45 117)(46 118)(47 119)(48 120)(49 121)(50 122)(51 123)(52 124)(53 125)(54 126)(55 127)(56 128)(57 129)(58 130)(59 131)(60 132)(61 133)(62 134)(63 135)(64 136)(65 137)(66 138)(67 139)(68 140)(69 141)(70 142)(71 143)(72 144)(145 217)(146 218)(147 219)(148 220)(149 221)(150 222)(151 223)(152 224)(153 225)(154 226)(155 227)(156 228)(157 229)(158 230)(159 231)(160 232)(161 233)(162 234)(163 235)(164 236)(165 237)(166 238)(167 239)(168 240)(169 241)(170 242)(171 243)(172 244)(173 245)(174 246)(175 247)(176 248)(177 249)(178 250)(179 251)(180 252)(181 253)(182 254)(183 255)(184 256)(185 257)(186 258)(187 259)(188 260)(189 261)(190 262)(191 263)(192 264)(193 265)(194 266)(195 267)(196 268)(197 269)(198 270)(199 271)(200 272)(201 273)(202 274)(203 275)(204 276)(205 277)(206 278)(207 279)(208 280)(209 281)(210 282)(211 283)(212 284)(213 285)(214 286)(215 287)(216 288)
(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)
(1 203 22 194 13 212 31 185)(2 202 23 193 14 211 32 184)(3 201 24 192 15 210 33 183)(4 200 25 191 16 209 34 182)(5 199 26 190 17 208 35 181)(6 207 27 198 18 216 36 189)(7 206 19 197 10 215 28 188)(8 205 20 196 11 214 29 187)(9 204 21 195 12 213 30 186)(37 170 64 152 46 179 55 161)(38 169 65 151 47 178 56 160)(39 168 66 150 48 177 57 159)(40 167 67 149 49 176 58 158)(41 166 68 148 50 175 59 157)(42 165 69 147 51 174 60 156)(43 164 70 146 52 173 61 155)(44 163 71 145 53 172 62 154)(45 171 72 153 54 180 63 162)(73 278 91 269 82 287 100 260)(74 277 92 268 83 286 101 259)(75 276 93 267 84 285 102 258)(76 275 94 266 85 284 103 257)(77 274 95 265 86 283 104 256)(78 273 96 264 87 282 105 255)(79 272 97 263 88 281 106 254)(80 271 98 262 89 280 107 253)(81 279 99 270 90 288 108 261)(109 242 136 224 118 251 127 233)(110 241 137 223 119 250 128 232)(111 240 138 222 120 249 129 231)(112 239 139 221 121 248 130 230)(113 238 140 220 122 247 131 229)(114 237 141 219 123 246 132 228)(115 236 142 218 124 245 133 227)(116 235 143 217 125 244 134 226)(117 243 144 225 126 252 135 234)
(1 121 13 112)(2 122 14 113)(3 123 15 114)(4 124 16 115)(5 125 17 116)(6 126 18 117)(7 118 10 109)(8 119 11 110)(9 120 12 111)(19 136 28 127)(20 137 29 128)(21 138 30 129)(22 139 31 130)(23 140 32 131)(24 141 33 132)(25 142 34 133)(26 143 35 134)(27 144 36 135)(37 73 46 82)(38 74 47 83)(39 75 48 84)(40 76 49 85)(41 77 50 86)(42 78 51 87)(43 79 52 88)(44 80 53 89)(45 81 54 90)(55 91 64 100)(56 92 65 101)(57 93 66 102)(58 94 67 103)(59 95 68 104)(60 96 69 105)(61 97 70 106)(62 98 71 107)(63 99 72 108)(145 280 154 271)(146 281 155 272)(147 282 156 273)(148 283 157 274)(149 284 158 275)(150 285 159 276)(151 286 160 277)(152 287 161 278)(153 288 162 279)(163 253 172 262)(164 254 173 263)(165 255 174 264)(166 256 175 265)(167 257 176 266)(168 258 177 267)(169 259 178 268)(170 260 179 269)(171 261 180 270)(181 244 190 235)(182 245 191 236)(183 246 192 237)(184 247 193 238)(185 248 194 239)(186 249 195 240)(187 250 196 241)(188 251 197 242)(189 252 198 243)(199 217 208 226)(200 218 209 227)(201 219 210 228)(202 220 211 229)(203 221 212 230)(204 222 213 231)(205 223 214 232)(206 224 215 233)(207 225 216 234)

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

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

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

54 conjugacy classes

 class 1 2A 2B 2C 3 4A 4B 4C 4D 4E 4F 6A 6B 6C 8A 8B 8C 8D 9A 9B 9C 12A ··· 12F 18A ··· 18I 36A ··· 36R order 1 2 2 2 3 4 4 4 4 4 4 6 6 6 8 8 8 8 9 9 9 12 ··· 12 18 ··· 18 36 ··· 36 size 1 1 1 1 2 2 2 4 4 36 36 2 2 2 18 18 18 18 2 2 2 4 ··· 4 2 ··· 2 4 ··· 4

54 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 type + + + + + + + + + + - + + + - - image C1 C2 C2 C2 C2 S3 D4 D4 D6 D6 Q16 D9 C3⋊D4 C3⋊D4 D18 D18 C9⋊D4 C9⋊D4 C3⋊Q16 C9⋊Q16 kernel C2×C9⋊Q16 C2×C9⋊C8 C9⋊Q16 C2×Dic18 Q8×C18 C6×Q8 C36 C2×C18 C2×C12 C3×Q8 C18 C2×Q8 C12 C2×C6 C2×C4 Q8 C4 C22 C6 C2 # reps 1 1 4 1 1 1 1 1 1 2 4 3 2 2 3 6 6 6 2 6

Matrix representation of C2×C9⋊Q16 in GL6(𝔽73)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 72 0 0 0 0 0 0 72 0 0 0 0 0 0 72 0 0 0 0 0 0 72
,
 70 28 0 0 0 0 45 42 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 36 11 0 0 0 0 48 37 0 0 0 0 0 0 40 64 0 0 0 0 40 33 0 0 0 0 0 0 0 25 0 0 0 0 35 32
,
 43 13 0 0 0 0 60 30 0 0 0 0 0 0 72 2 0 0 0 0 0 1 0 0 0 0 0 0 2 63 0 0 0 0 37 71

G:=sub<GL(6,GF(73))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72],[70,45,0,0,0,0,28,42,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[36,48,0,0,0,0,11,37,0,0,0,0,0,0,40,40,0,0,0,0,64,33,0,0,0,0,0,0,0,35,0,0,0,0,25,32],[43,60,0,0,0,0,13,30,0,0,0,0,0,0,72,0,0,0,0,0,2,1,0,0,0,0,0,0,2,37,0,0,0,0,63,71] >;

C2×C9⋊Q16 in GAP, Magma, Sage, TeX

C_2\times C_9\rtimes Q_{16}
% in TeX

G:=Group("C2xC9:Q16");
// GroupNames label

G:=SmallGroup(288,151);
// by ID

G=gap.SmallGroup(288,151);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,112,254,100,675,185,80,6725,292,9414]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^9=c^8=1,d^2=c^4,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽