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## G = C8×C3⋊Dic3order 288 = 25·32

### Direct product of C8 and C3⋊Dic3

Series: Derived Chief Lower central Upper central

 Derived series C1 — C32 — C8×C3⋊Dic3
 Chief series C1 — C3 — C32 — C3×C6 — C62 — C6×C12 — C4×C3⋊Dic3 — C8×C3⋊Dic3
 Lower central C32 — C8×C3⋊Dic3
 Upper central C1 — C2×C8

Generators and relations for C8×C3⋊Dic3
G = < a,b,c,d | a8=b3=c6=1, d2=c3, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c-1 >

Subgroups: 308 in 132 conjugacy classes, 77 normal (17 characteristic)
C1, C2, C2 [×2], C3 [×4], C4 [×2], C4 [×4], C22, C6 [×12], C8 [×2], C8 [×2], C2×C4, C2×C4 [×2], C32, Dic3 [×16], C12 [×8], C2×C6 [×4], C42, C2×C8, C2×C8, C3×C6, C3×C6 [×2], C3⋊C8 [×8], C24 [×8], C2×Dic3 [×8], C2×C12 [×4], C4×C8, C3⋊Dic3 [×4], C3×C12 [×2], C62, C2×C3⋊C8 [×4], C4×Dic3 [×4], C2×C24 [×4], C324C8 [×2], C3×C24 [×2], C2×C3⋊Dic3 [×2], C6×C12, C8×Dic3 [×4], C2×C324C8, C4×C3⋊Dic3, C6×C24, C8×C3⋊Dic3
Quotients: C1, C2 [×3], C4 [×6], C22, S3 [×4], C8 [×4], C2×C4 [×3], Dic3 [×8], D6 [×4], C42, C2×C8 [×2], C3⋊S3, C4×S3 [×8], C2×Dic3 [×4], C4×C8, C3⋊Dic3 [×2], C2×C3⋊S3, S3×C8 [×8], C4×Dic3 [×4], C4×C3⋊S3 [×2], C2×C3⋊Dic3, C8×Dic3 [×4], C8×C3⋊S3 [×2], C4×C3⋊Dic3, C8×C3⋊Dic3

Smallest permutation representation of C8×C3⋊Dic3
Regular action on 288 points
Generators in S288
(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)
(1 236 197)(2 237 198)(3 238 199)(4 239 200)(5 240 193)(6 233 194)(7 234 195)(8 235 196)(9 29 115)(10 30 116)(11 31 117)(12 32 118)(13 25 119)(14 26 120)(15 27 113)(16 28 114)(17 111 260)(18 112 261)(19 105 262)(20 106 263)(21 107 264)(22 108 257)(23 109 258)(24 110 259)(33 137 98)(34 138 99)(35 139 100)(36 140 101)(37 141 102)(38 142 103)(39 143 104)(40 144 97)(41 215 225)(42 216 226)(43 209 227)(44 210 228)(45 211 229)(46 212 230)(47 213 231)(48 214 232)(49 83 69)(50 84 70)(51 85 71)(52 86 72)(53 87 65)(54 88 66)(55 81 67)(56 82 68)(57 204 79)(58 205 80)(59 206 73)(60 207 74)(61 208 75)(62 201 76)(63 202 77)(64 203 78)(89 190 222)(90 191 223)(91 192 224)(92 185 217)(93 186 218)(94 187 219)(95 188 220)(96 189 221)(121 160 256)(122 153 249)(123 154 250)(124 155 251)(125 156 252)(126 157 253)(127 158 254)(128 159 255)(129 151 242)(130 152 243)(131 145 244)(132 146 245)(133 147 246)(134 148 247)(135 149 248)(136 150 241)(161 274 176)(162 275 169)(163 276 170)(164 277 171)(165 278 172)(166 279 173)(167 280 174)(168 273 175)(177 272 281)(178 265 282)(179 266 283)(180 267 284)(181 268 285)(182 269 286)(183 270 287)(184 271 288)
(1 141 204 66 45 95)(2 142 205 67 46 96)(3 143 206 68 47 89)(4 144 207 69 48 90)(5 137 208 70 41 91)(6 138 201 71 42 92)(7 139 202 72 43 93)(8 140 203 65 44 94)(9 106 129 169 249 270)(10 107 130 170 250 271)(11 108 131 171 251 272)(12 109 132 172 252 265)(13 110 133 173 253 266)(14 111 134 174 254 267)(15 112 135 175 255 268)(16 105 136 176 256 269)(17 247 280 158 180 120)(18 248 273 159 181 113)(19 241 274 160 182 114)(20 242 275 153 183 115)(21 243 276 154 184 116)(22 244 277 155 177 117)(23 245 278 156 178 118)(24 246 279 157 179 119)(25 259 147 166 126 283)(26 260 148 167 127 284)(27 261 149 168 128 285)(28 262 150 161 121 286)(29 263 151 162 122 287)(30 264 152 163 123 288)(31 257 145 164 124 281)(32 258 146 165 125 282)(33 61 84 225 224 193)(34 62 85 226 217 194)(35 63 86 227 218 195)(36 64 87 228 219 196)(37 57 88 229 220 197)(38 58 81 230 221 198)(39 59 82 231 222 199)(40 60 83 232 223 200)(49 214 191 239 97 74)(50 215 192 240 98 75)(51 216 185 233 99 76)(52 209 186 234 100 77)(53 210 187 235 101 78)(54 211 188 236 102 79)(55 212 189 237 103 80)(56 213 190 238 104 73)
(1 164 66 31)(2 165 67 32)(3 166 68 25)(4 167 69 26)(5 168 70 27)(6 161 71 28)(7 162 72 29)(8 163 65 30)(9 234 169 52)(10 235 170 53)(11 236 171 54)(12 237 172 55)(13 238 173 56)(14 239 174 49)(15 240 175 50)(16 233 176 51)(17 223 158 60)(18 224 159 61)(19 217 160 62)(20 218 153 63)(21 219 154 64)(22 220 155 57)(23 221 156 58)(24 222 157 59)(33 248 225 181)(34 241 226 182)(35 242 227 183)(36 243 228 184)(37 244 229 177)(38 245 230 178)(39 246 231 179)(40 247 232 180)(41 285 137 149)(42 286 138 150)(43 287 139 151)(44 288 140 152)(45 281 141 145)(46 282 142 146)(47 283 143 147)(48 284 144 148)(73 110 190 253)(74 111 191 254)(75 112 192 255)(76 105 185 256)(77 106 186 249)(78 107 187 250)(79 108 188 251)(80 109 189 252)(81 118 198 278)(82 119 199 279)(83 120 200 280)(84 113 193 273)(85 114 194 274)(86 115 195 275)(87 116 196 276)(88 117 197 277)(89 126 206 259)(90 127 207 260)(91 128 208 261)(92 121 201 262)(93 122 202 263)(94 123 203 264)(95 124 204 257)(96 125 205 258)(97 134 214 267)(98 135 215 268)(99 136 216 269)(100 129 209 270)(101 130 210 271)(102 131 211 272)(103 132 212 265)(104 133 213 266)

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

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

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

96 conjugacy classes

 class 1 2A 2B 2C 3A 3B 3C 3D 4A 4B 4C 4D 4E ··· 4L 6A ··· 6L 8A ··· 8H 8I ··· 8P 12A ··· 12P 24A ··· 24AF order 1 2 2 2 3 3 3 3 4 4 4 4 4 ··· 4 6 ··· 6 8 ··· 8 8 ··· 8 12 ··· 12 24 ··· 24 size 1 1 1 1 2 2 2 2 1 1 1 1 9 ··· 9 2 ··· 2 1 ··· 1 9 ··· 9 2 ··· 2 2 ··· 2

96 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 type + + + + + - + image C1 C2 C2 C2 C4 C4 C4 C8 S3 Dic3 D6 C4×S3 C4×S3 S3×C8 kernel C8×C3⋊Dic3 C2×C32⋊4C8 C4×C3⋊Dic3 C6×C24 C32⋊4C8 C3×C24 C2×C3⋊Dic3 C3⋊Dic3 C2×C24 C24 C2×C12 C12 C2×C6 C6 # reps 1 1 1 1 4 4 4 16 4 8 4 8 8 32

Matrix representation of C8×C3⋊Dic3 in GL4(𝔽73) generated by

 72 0 0 0 0 72 0 0 0 0 22 0 0 0 0 22
,
 1 0 0 0 0 1 0 0 0 0 72 1 0 0 72 0
,
 0 72 0 0 1 1 0 0 0 0 72 0 0 0 0 72
,
 30 60 0 0 30 43 0 0 0 0 13 30 0 0 43 60
G:=sub<GL(4,GF(73))| [72,0,0,0,0,72,0,0,0,0,22,0,0,0,0,22],[1,0,0,0,0,1,0,0,0,0,72,72,0,0,1,0],[0,1,0,0,72,1,0,0,0,0,72,0,0,0,0,72],[30,30,0,0,60,43,0,0,0,0,13,43,0,0,30,60] >;

C8×C3⋊Dic3 in GAP, Magma, Sage, TeX

C_8\times C_3\rtimes {\rm Dic}_3
% in TeX

G:=Group("C8xC3:Dic3");
// GroupNames label

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

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

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,28,64,80,2693,9414]);
// Polycyclic

G:=Group<a,b,c,d|a^8=b^3=c^6=1,d^2=c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽