direct product, metabelian, supersoluble, monomial, A-group
Aliases: C8×C33⋊C2, C24⋊4(C3⋊S3), (C3×C24)⋊15S3, C33⋊18(C2×C8), C32⋊13(S3×C8), (C32×C24)⋊10C2, C33⋊7C8⋊13C2, (C3×C12).227D6, C33⋊5C4.6C4, (C32×C12).95C22, C3⋊2(C8×C3⋊S3), C6.12(C4×C3⋊S3), C12.74(C2×C3⋊S3), (C3×C6).80(C4×S3), C2.1(C4×C33⋊C2), (C32×C6).59(C2×C4), (C4×C33⋊C2).6C2, (C2×C33⋊C2).6C4, C4.12(C2×C33⋊C2), SmallGroup(432,496)
Series: Derived ►Chief ►Lower central ►Upper central
| C33 — C8×C33⋊C2 |
Generators and relations for C8×C33⋊C2
G = < a,b,c,d,e | a8=b3=c3=d3=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, ebe=b-1, cd=dc, ece=c-1, ede=d-1 >
Subgroups: 1400 in 308 conjugacy classes, 119 normal (13 characteristic)
C1, C2, C2, C3, C4, C4, C22, S3, C6, C8, C8, C2×C4, C32, Dic3, C12, D6, C2×C8, C3⋊S3, C3×C6, C3⋊C8, C24, C4×S3, C33, C3⋊Dic3, C3×C12, C2×C3⋊S3, S3×C8, C33⋊C2, C32×C6, C32⋊4C8, C3×C24, C4×C3⋊S3, C33⋊5C4, C32×C12, C2×C33⋊C2, C8×C3⋊S3, C33⋊7C8, C32×C24, C4×C33⋊C2, C8×C33⋊C2
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, D6, C2×C8, C3⋊S3, C4×S3, C2×C3⋊S3, S3×C8, C33⋊C2, C4×C3⋊S3, C2×C33⋊C2, C8×C3⋊S3, C4×C33⋊C2, C8×C33⋊C2
►On 216 points
Generators in S216
(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)
(1 54 148)(2 55 149)(3 56 150)(4 49 151)(5 50 152)(6 51 145)(7 52 146)(8 53 147)(9 159 85)(10 160 86)(11 153 87)(12 154 88)(13 155 81)(14 156 82)(15 157 83)(16 158 84)(17 105 123)(18 106 124)(19 107 125)(20 108 126)(21 109 127)(22 110 128)(23 111 121)(24 112 122)(25 36 184)(26 37 177)(27 38 178)(28 39 179)(29 40 180)(30 33 181)(31 34 182)(32 35 183)(41 136 66)(42 129 67)(43 130 68)(44 131 69)(45 132 70)(46 133 71)(47 134 72)(48 135 65)(57 91 202)(58 92 203)(59 93 204)(60 94 205)(61 95 206)(62 96 207)(63 89 208)(64 90 201)(73 168 176)(74 161 169)(75 162 170)(76 163 171)(77 164 172)(78 165 173)(79 166 174)(80 167 175)(97 189 113)(98 190 114)(99 191 115)(100 192 116)(101 185 117)(102 186 118)(103 187 119)(104 188 120)(137 196 211)(138 197 212)(139 198 213)(140 199 214)(141 200 215)(142 193 216)(143 194 209)(144 195 210)
(1 198 182)(2 199 183)(3 200 184)(4 193 177)(5 194 178)(6 195 179)(7 196 180)(8 197 181)(9 64 65)(10 57 66)(11 58 67)(12 59 68)(13 60 69)(14 61 70)(15 62 71)(16 63 72)(17 118 76)(18 119 77)(19 120 78)(20 113 79)(21 114 80)(22 115 73)(23 116 74)(24 117 75)(25 56 215)(26 49 216)(27 50 209)(28 51 210)(29 52 211)(30 53 212)(31 54 213)(32 55 214)(33 147 138)(34 148 139)(35 149 140)(36 150 141)(37 151 142)(38 152 143)(39 145 144)(40 146 137)(41 160 91)(42 153 92)(43 154 93)(44 155 94)(45 156 95)(46 157 96)(47 158 89)(48 159 90)(81 205 131)(82 206 132)(83 207 133)(84 208 134)(85 201 135)(86 202 136)(87 203 129)(88 204 130)(97 166 108)(98 167 109)(99 168 110)(100 161 111)(101 162 112)(102 163 105)(103 164 106)(104 165 107)(121 192 169)(122 185 170)(123 186 171)(124 187 172)(125 188 173)(126 189 174)(127 190 175)(128 191 176)
(1 108 13)(2 109 14)(3 110 15)(4 111 16)(5 112 9)(6 105 10)(7 106 11)(8 107 12)(17 86 145)(18 87 146)(19 88 147)(20 81 148)(21 82 149)(22 83 150)(23 84 151)(24 85 152)(25 176 46)(26 169 47)(27 170 48)(28 171 41)(29 172 42)(30 173 43)(31 174 44)(32 175 45)(33 78 130)(34 79 131)(35 80 132)(36 73 133)(37 74 134)(38 75 135)(39 76 136)(40 77 129)(49 121 158)(50 122 159)(51 123 160)(52 124 153)(53 125 154)(54 126 155)(55 127 156)(56 128 157)(57 195 102)(58 196 103)(59 197 104)(60 198 97)(61 199 98)(62 200 99)(63 193 100)(64 194 101)(65 178 162)(66 179 163)(67 180 164)(68 181 165)(69 182 166)(70 183 167)(71 184 168)(72 177 161)(89 216 192)(90 209 185)(91 210 186)(92 211 187)(93 212 188)(94 213 189)(95 214 190)(96 215 191)(113 205 139)(114 206 140)(115 207 141)(116 208 142)(117 201 143)(118 202 144)(119 203 137)(120 204 138)
(1 5)(2 6)(3 7)(4 8)(9 108)(10 109)(11 110)(12 111)(13 112)(14 105)(15 106)(16 107)(17 156)(18 157)(19 158)(20 159)(21 160)(22 153)(23 154)(24 155)(25 137)(26 138)(27 139)(28 140)(29 141)(30 142)(31 143)(32 144)(33 216)(34 209)(35 210)(36 211)(37 212)(38 213)(39 214)(40 215)(41 114)(42 115)(43 116)(44 117)(45 118)(46 119)(47 120)(48 113)(49 147)(50 148)(51 149)(52 150)(53 151)(54 152)(55 145)(56 146)(57 167)(58 168)(59 161)(60 162)(61 163)(62 164)(63 165)(64 166)(65 97)(66 98)(67 99)(68 100)(69 101)(70 102)(71 103)(72 104)(73 92)(74 93)(75 94)(76 95)(77 96)(78 89)(79 90)(80 91)(81 122)(82 123)(83 124)(84 125)(85 126)(86 127)(87 128)(88 121)(129 191)(130 192)(131 185)(132 186)(133 187)(134 188)(135 189)(136 190)(169 204)(170 205)(171 206)(172 207)(173 208)(174 201)(175 202)(176 203)(177 197)(178 198)(179 199)(180 200)(181 193)(182 194)(183 195)(184 196)
G:=sub<Sym(216)| (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), (1,54,148)(2,55,149)(3,56,150)(4,49,151)(5,50,152)(6,51,145)(7,52,146)(8,53,147)(9,159,85)(10,160,86)(11,153,87)(12,154,88)(13,155,81)(14,156,82)(15,157,83)(16,158,84)(17,105,123)(18,106,124)(19,107,125)(20,108,126)(21,109,127)(22,110,128)(23,111,121)(24,112,122)(25,36,184)(26,37,177)(27,38,178)(28,39,179)(29,40,180)(30,33,181)(31,34,182)(32,35,183)(41,136,66)(42,129,67)(43,130,68)(44,131,69)(45,132,70)(46,133,71)(47,134,72)(48,135,65)(57,91,202)(58,92,203)(59,93,204)(60,94,205)(61,95,206)(62,96,207)(63,89,208)(64,90,201)(73,168,176)(74,161,169)(75,162,170)(76,163,171)(77,164,172)(78,165,173)(79,166,174)(80,167,175)(97,189,113)(98,190,114)(99,191,115)(100,192,116)(101,185,117)(102,186,118)(103,187,119)(104,188,120)(137,196,211)(138,197,212)(139,198,213)(140,199,214)(141,200,215)(142,193,216)(143,194,209)(144,195,210), (1,198,182)(2,199,183)(3,200,184)(4,193,177)(5,194,178)(6,195,179)(7,196,180)(8,197,181)(9,64,65)(10,57,66)(11,58,67)(12,59,68)(13,60,69)(14,61,70)(15,62,71)(16,63,72)(17,118,76)(18,119,77)(19,120,78)(20,113,79)(21,114,80)(22,115,73)(23,116,74)(24,117,75)(25,56,215)(26,49,216)(27,50,209)(28,51,210)(29,52,211)(30,53,212)(31,54,213)(32,55,214)(33,147,138)(34,148,139)(35,149,140)(36,150,141)(37,151,142)(38,152,143)(39,145,144)(40,146,137)(41,160,91)(42,153,92)(43,154,93)(44,155,94)(45,156,95)(46,157,96)(47,158,89)(48,159,90)(81,205,131)(82,206,132)(83,207,133)(84,208,134)(85,201,135)(86,202,136)(87,203,129)(88,204,130)(97,166,108)(98,167,109)(99,168,110)(100,161,111)(101,162,112)(102,163,105)(103,164,106)(104,165,107)(121,192,169)(122,185,170)(123,186,171)(124,187,172)(125,188,173)(126,189,174)(127,190,175)(128,191,176), (1,108,13)(2,109,14)(3,110,15)(4,111,16)(5,112,9)(6,105,10)(7,106,11)(8,107,12)(17,86,145)(18,87,146)(19,88,147)(20,81,148)(21,82,149)(22,83,150)(23,84,151)(24,85,152)(25,176,46)(26,169,47)(27,170,48)(28,171,41)(29,172,42)(30,173,43)(31,174,44)(32,175,45)(33,78,130)(34,79,131)(35,80,132)(36,73,133)(37,74,134)(38,75,135)(39,76,136)(40,77,129)(49,121,158)(50,122,159)(51,123,160)(52,124,153)(53,125,154)(54,126,155)(55,127,156)(56,128,157)(57,195,102)(58,196,103)(59,197,104)(60,198,97)(61,199,98)(62,200,99)(63,193,100)(64,194,101)(65,178,162)(66,179,163)(67,180,164)(68,181,165)(69,182,166)(70,183,167)(71,184,168)(72,177,161)(89,216,192)(90,209,185)(91,210,186)(92,211,187)(93,212,188)(94,213,189)(95,214,190)(96,215,191)(113,205,139)(114,206,140)(115,207,141)(116,208,142)(117,201,143)(118,202,144)(119,203,137)(120,204,138), (1,5)(2,6)(3,7)(4,8)(9,108)(10,109)(11,110)(12,111)(13,112)(14,105)(15,106)(16,107)(17,156)(18,157)(19,158)(20,159)(21,160)(22,153)(23,154)(24,155)(25,137)(26,138)(27,139)(28,140)(29,141)(30,142)(31,143)(32,144)(33,216)(34,209)(35,210)(36,211)(37,212)(38,213)(39,214)(40,215)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,113)(49,147)(50,148)(51,149)(52,150)(53,151)(54,152)(55,145)(56,146)(57,167)(58,168)(59,161)(60,162)(61,163)(62,164)(63,165)(64,166)(65,97)(66,98)(67,99)(68,100)(69,101)(70,102)(71,103)(72,104)(73,92)(74,93)(75,94)(76,95)(77,96)(78,89)(79,90)(80,91)(81,122)(82,123)(83,124)(84,125)(85,126)(86,127)(87,128)(88,121)(129,191)(130,192)(131,185)(132,186)(133,187)(134,188)(135,189)(136,190)(169,204)(170,205)(171,206)(172,207)(173,208)(174,201)(175,202)(176,203)(177,197)(178,198)(179,199)(180,200)(181,193)(182,194)(183,195)(184,196)>;
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), (1,54,148)(2,55,149)(3,56,150)(4,49,151)(5,50,152)(6,51,145)(7,52,146)(8,53,147)(9,159,85)(10,160,86)(11,153,87)(12,154,88)(13,155,81)(14,156,82)(15,157,83)(16,158,84)(17,105,123)(18,106,124)(19,107,125)(20,108,126)(21,109,127)(22,110,128)(23,111,121)(24,112,122)(25,36,184)(26,37,177)(27,38,178)(28,39,179)(29,40,180)(30,33,181)(31,34,182)(32,35,183)(41,136,66)(42,129,67)(43,130,68)(44,131,69)(45,132,70)(46,133,71)(47,134,72)(48,135,65)(57,91,202)(58,92,203)(59,93,204)(60,94,205)(61,95,206)(62,96,207)(63,89,208)(64,90,201)(73,168,176)(74,161,169)(75,162,170)(76,163,171)(77,164,172)(78,165,173)(79,166,174)(80,167,175)(97,189,113)(98,190,114)(99,191,115)(100,192,116)(101,185,117)(102,186,118)(103,187,119)(104,188,120)(137,196,211)(138,197,212)(139,198,213)(140,199,214)(141,200,215)(142,193,216)(143,194,209)(144,195,210), (1,198,182)(2,199,183)(3,200,184)(4,193,177)(5,194,178)(6,195,179)(7,196,180)(8,197,181)(9,64,65)(10,57,66)(11,58,67)(12,59,68)(13,60,69)(14,61,70)(15,62,71)(16,63,72)(17,118,76)(18,119,77)(19,120,78)(20,113,79)(21,114,80)(22,115,73)(23,116,74)(24,117,75)(25,56,215)(26,49,216)(27,50,209)(28,51,210)(29,52,211)(30,53,212)(31,54,213)(32,55,214)(33,147,138)(34,148,139)(35,149,140)(36,150,141)(37,151,142)(38,152,143)(39,145,144)(40,146,137)(41,160,91)(42,153,92)(43,154,93)(44,155,94)(45,156,95)(46,157,96)(47,158,89)(48,159,90)(81,205,131)(82,206,132)(83,207,133)(84,208,134)(85,201,135)(86,202,136)(87,203,129)(88,204,130)(97,166,108)(98,167,109)(99,168,110)(100,161,111)(101,162,112)(102,163,105)(103,164,106)(104,165,107)(121,192,169)(122,185,170)(123,186,171)(124,187,172)(125,188,173)(126,189,174)(127,190,175)(128,191,176), (1,108,13)(2,109,14)(3,110,15)(4,111,16)(5,112,9)(6,105,10)(7,106,11)(8,107,12)(17,86,145)(18,87,146)(19,88,147)(20,81,148)(21,82,149)(22,83,150)(23,84,151)(24,85,152)(25,176,46)(26,169,47)(27,170,48)(28,171,41)(29,172,42)(30,173,43)(31,174,44)(32,175,45)(33,78,130)(34,79,131)(35,80,132)(36,73,133)(37,74,134)(38,75,135)(39,76,136)(40,77,129)(49,121,158)(50,122,159)(51,123,160)(52,124,153)(53,125,154)(54,126,155)(55,127,156)(56,128,157)(57,195,102)(58,196,103)(59,197,104)(60,198,97)(61,199,98)(62,200,99)(63,193,100)(64,194,101)(65,178,162)(66,179,163)(67,180,164)(68,181,165)(69,182,166)(70,183,167)(71,184,168)(72,177,161)(89,216,192)(90,209,185)(91,210,186)(92,211,187)(93,212,188)(94,213,189)(95,214,190)(96,215,191)(113,205,139)(114,206,140)(115,207,141)(116,208,142)(117,201,143)(118,202,144)(119,203,137)(120,204,138), (1,5)(2,6)(3,7)(4,8)(9,108)(10,109)(11,110)(12,111)(13,112)(14,105)(15,106)(16,107)(17,156)(18,157)(19,158)(20,159)(21,160)(22,153)(23,154)(24,155)(25,137)(26,138)(27,139)(28,140)(29,141)(30,142)(31,143)(32,144)(33,216)(34,209)(35,210)(36,211)(37,212)(38,213)(39,214)(40,215)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,113)(49,147)(50,148)(51,149)(52,150)(53,151)(54,152)(55,145)(56,146)(57,167)(58,168)(59,161)(60,162)(61,163)(62,164)(63,165)(64,166)(65,97)(66,98)(67,99)(68,100)(69,101)(70,102)(71,103)(72,104)(73,92)(74,93)(75,94)(76,95)(77,96)(78,89)(79,90)(80,91)(81,122)(82,123)(83,124)(84,125)(85,126)(86,127)(87,128)(88,121)(129,191)(130,192)(131,185)(132,186)(133,187)(134,188)(135,189)(136,190)(169,204)(170,205)(171,206)(172,207)(173,208)(174,201)(175,202)(176,203)(177,197)(178,198)(179,199)(180,200)(181,193)(182,194)(183,195)(184,196) );
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)], [(1,54,148),(2,55,149),(3,56,150),(4,49,151),(5,50,152),(6,51,145),(7,52,146),(8,53,147),(9,159,85),(10,160,86),(11,153,87),(12,154,88),(13,155,81),(14,156,82),(15,157,83),(16,158,84),(17,105,123),(18,106,124),(19,107,125),(20,108,126),(21,109,127),(22,110,128),(23,111,121),(24,112,122),(25,36,184),(26,37,177),(27,38,178),(28,39,179),(29,40,180),(30,33,181),(31,34,182),(32,35,183),(41,136,66),(42,129,67),(43,130,68),(44,131,69),(45,132,70),(46,133,71),(47,134,72),(48,135,65),(57,91,202),(58,92,203),(59,93,204),(60,94,205),(61,95,206),(62,96,207),(63,89,208),(64,90,201),(73,168,176),(74,161,169),(75,162,170),(76,163,171),(77,164,172),(78,165,173),(79,166,174),(80,167,175),(97,189,113),(98,190,114),(99,191,115),(100,192,116),(101,185,117),(102,186,118),(103,187,119),(104,188,120),(137,196,211),(138,197,212),(139,198,213),(140,199,214),(141,200,215),(142,193,216),(143,194,209),(144,195,210)], [(1,198,182),(2,199,183),(3,200,184),(4,193,177),(5,194,178),(6,195,179),(7,196,180),(8,197,181),(9,64,65),(10,57,66),(11,58,67),(12,59,68),(13,60,69),(14,61,70),(15,62,71),(16,63,72),(17,118,76),(18,119,77),(19,120,78),(20,113,79),(21,114,80),(22,115,73),(23,116,74),(24,117,75),(25,56,215),(26,49,216),(27,50,209),(28,51,210),(29,52,211),(30,53,212),(31,54,213),(32,55,214),(33,147,138),(34,148,139),(35,149,140),(36,150,141),(37,151,142),(38,152,143),(39,145,144),(40,146,137),(41,160,91),(42,153,92),(43,154,93),(44,155,94),(45,156,95),(46,157,96),(47,158,89),(48,159,90),(81,205,131),(82,206,132),(83,207,133),(84,208,134),(85,201,135),(86,202,136),(87,203,129),(88,204,130),(97,166,108),(98,167,109),(99,168,110),(100,161,111),(101,162,112),(102,163,105),(103,164,106),(104,165,107),(121,192,169),(122,185,170),(123,186,171),(124,187,172),(125,188,173),(126,189,174),(127,190,175),(128,191,176)], [(1,108,13),(2,109,14),(3,110,15),(4,111,16),(5,112,9),(6,105,10),(7,106,11),(8,107,12),(17,86,145),(18,87,146),(19,88,147),(20,81,148),(21,82,149),(22,83,150),(23,84,151),(24,85,152),(25,176,46),(26,169,47),(27,170,48),(28,171,41),(29,172,42),(30,173,43),(31,174,44),(32,175,45),(33,78,130),(34,79,131),(35,80,132),(36,73,133),(37,74,134),(38,75,135),(39,76,136),(40,77,129),(49,121,158),(50,122,159),(51,123,160),(52,124,153),(53,125,154),(54,126,155),(55,127,156),(56,128,157),(57,195,102),(58,196,103),(59,197,104),(60,198,97),(61,199,98),(62,200,99),(63,193,100),(64,194,101),(65,178,162),(66,179,163),(67,180,164),(68,181,165),(69,182,166),(70,183,167),(71,184,168),(72,177,161),(89,216,192),(90,209,185),(91,210,186),(92,211,187),(93,212,188),(94,213,189),(95,214,190),(96,215,191),(113,205,139),(114,206,140),(115,207,141),(116,208,142),(117,201,143),(118,202,144),(119,203,137),(120,204,138)], [(1,5),(2,6),(3,7),(4,8),(9,108),(10,109),(11,110),(12,111),(13,112),(14,105),(15,106),(16,107),(17,156),(18,157),(19,158),(20,159),(21,160),(22,153),(23,154),(24,155),(25,137),(26,138),(27,139),(28,140),(29,141),(30,142),(31,143),(32,144),(33,216),(34,209),(35,210),(36,211),(37,212),(38,213),(39,214),(40,215),(41,114),(42,115),(43,116),(44,117),(45,118),(46,119),(47,120),(48,113),(49,147),(50,148),(51,149),(52,150),(53,151),(54,152),(55,145),(56,146),(57,167),(58,168),(59,161),(60,162),(61,163),(62,164),(63,165),(64,166),(65,97),(66,98),(67,99),(68,100),(69,101),(70,102),(71,103),(72,104),(73,92),(74,93),(75,94),(76,95),(77,96),(78,89),(79,90),(80,91),(81,122),(82,123),(83,124),(84,125),(85,126),(86,127),(87,128),(88,121),(129,191),(130,192),(131,185),(132,186),(133,187),(134,188),(135,189),(136,190),(169,204),(170,205),(171,206),(172,207),(173,208),(174,201),(175,202),(176,203),(177,197),(178,198),(179,199),(180,200),(181,193),(182,194),(183,195),(184,196)]])
120 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | ··· | 3M | 4A | 4B | 4C | 4D | 6A | ··· | 6M | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 12A | ··· | 12Z | 24A | ··· | 24AZ |
| order | 1 | 2 | 2 | 2 | 3 | ··· | 3 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 12 | ··· | 12 | 24 | ··· | 24 |
| size | 1 | 1 | 27 | 27 | 2 | ··· | 2 | 1 | 1 | 27 | 27 | 2 | ··· | 2 | 1 | 1 | 1 | 1 | 27 | 27 | 27 | 27 | 2 | ··· | 2 | 2 | ··· | 2 |
120 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C8 | S3 | D6 | C4×S3 | S3×C8 |
| kernel | C8×C33⋊C2 | C33⋊7C8 | C32×C24 | C4×C33⋊C2 | C33⋊5C4 | C2×C33⋊C2 | C33⋊C2 | C3×C24 | C3×C12 | C3×C6 | C32 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 13 | 13 | 26 | 52 |
Matrix representation of C8×C33⋊C2 ►in GL6(𝔽73)
| 51 | 0 | 0 | 0 | 0 | 0 |
| 0 | 51 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 0 |
| 0 | 0 | 0 | 0 | 0 | 22 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 1 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 72 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 3 |
| 0 | 0 | 0 | 0 | 72 | 71 |
| 72 | 1 | 0 | 0 | 0 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 72 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 3 |
| 0 | 0 | 0 | 0 | 72 | 71 |
| 72 | 1 | 0 | 0 | 0 | 0 |
| 72 | 0 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 72 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 72 | 72 |
G:=sub<GL(6,GF(73))| [51,0,0,0,0,0,0,51,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,22,0,0,0,0,0,0,22],[0,1,0,0,0,0,72,72,0,0,0,0,0,0,72,1,0,0,0,0,72,0,0,0,0,0,0,0,1,72,0,0,0,0,3,71],[72,72,0,0,0,0,1,0,0,0,0,0,0,0,0,72,0,0,0,0,1,72,0,0,0,0,0,0,1,72,0,0,0,0,3,71],[72,72,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,72,0,0,0,0,0,0,1,72,0,0,0,0,0,72,0,0,0,0,0,0,1,72,0,0,0,0,0,72] >;
C8×C33⋊C2 in GAP, Magma, Sage, TeX
C_8\times C_3^3\rtimes C_2
% in TeX
G:=Group("C8xC3^3:C2"); // GroupNames label
G:=SmallGroup(432,496);
// by ID
G=gap.SmallGroup(432,496);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,36,58,1124,4037,14118]);
// Polycyclic
G:=Group<a,b,c,d,e|a^8=b^3=c^3=d^3=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,e*b*e=b^-1,c*d=d*c,e*c*e=c^-1,e*d*e=d^-1>;
// generators/relations