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G = SD16×C33  order 432 = 24·33

Direct product of C33 and SD16

direct product, metabelian, nilpotent (class 3), monomial

Aliases: SD16×C33, C12.34C62, C24⋊6(C3×C6), (C3×C24)⋊18C6, C8⋊2(C32×C6), D4.(C32×C6), C4.2(C3×C62), Q8⋊2(C32×C6), C2.4(D4×C33), (C32×C24)⋊14C2, (Q8×C33)⋊10C2, (Q8×C32)⋊18C6, (D4×C33).4C2, C6.27(D4×C32), (C32×C6).88D4, (D4×C32).15C6, (C32×C12).103C22, (C3×Q8)⋊6(C3×C6), (C3×D4).8(C3×C6), (C3×C6).83(C3×D4), (C3×C12).108(C2×C6), SmallGroup(432,518)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C4 — SD16×C33
Chief series
C1 — C2 — C4 — C12 — C3×C12 — C32×C12 — Q8×C33 — SD16×C33
Lower central
C1 — C2 — C4 — SD16×C33
Upper central
C1 — C32×C6 — C32×C12 — SD16×C33

Generators and relations for SD16×C33
 G = < a,b,c,d,e | a3=b3=c3=d8=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede=d3 >

Subgroups: 420 in 280 conjugacy classes, 196 normal (14 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C8, D4, Q8, C32, C12, C12, C2×C6, SD16, C3×C6, C3×C6, C24, C3×D4, C3×Q8, C33, C3×C12, C3×C12, C62, C3×SD16, C32×C6, C32×C6, C3×C24, D4×C32, Q8×C32, C32×C12, C32×C12, C3×C62, C32×SD16, C32×C24, D4×C33, Q8×C33, SD16×C33
Quotients: C1, C2, C3, C22, C6, D4, C32, C2×C6, SD16, C3×C6, C3×D4, C33, C62, C3×SD16, C32×C6, D4×C32, C3×C62, C32×SD16, D4×C33, SD16×C33

Smallest permutation representation of SD16×C33
►On 216 points
Generators in S216
(1 106 38)(2 107 39)(3 108 40)(4 109 33)(5 110 34)(6 111 35)(7 112 36)(8 105 37)(9 214 190)(10 215 191)(11 216 192)(12 209 185)(13 210 186)(14 211 187)(15 212 188)(16 213 189)(17 97 89)(18 98 90)(19 99 91)(20 100 92)(21 101 93)(22 102 94)(23 103 95)(24 104 96)(25 123 155)(26 124 156)(27 125 157)(28 126 158)(29 127 159)(30 128 160)(31 121 153)(32 122 154)(41 113 150)(42 114 151)(43 115 152)(44 116 145)(45 117 146)(46 118 147)(47 119 148)(48 120 149)(49 179 171)(50 180 172)(51 181 173)(52 182 174)(53 183 175)(54 184 176)(55 177 169)(56 178 170)(57 81 166)(58 82 167)(59 83 168)(60 84 161)(61 85 162)(62 86 163)(63 87 164)(64 88 165)(65 198 137)(66 199 138)(67 200 139)(68 193 140)(69 194 141)(70 195 142)(71 196 143)(72 197 144)(73 206 134)(74 207 135)(75 208 136)(76 201 129)(77 202 130)(78 203 131)(79 204 132)(80 205 133)

(1 171 22)(2 172 23)(3 173 24)(4 174 17)(5 175 18)(6 176 19)(7 169 20)(8 170 21)(9 126 65)(10 127 66)(11 128 67)(12 121 68)(13 122 69)(14 123 70)(15 124 71)(16 125 72)(25 142 187)(26 143 188)(27 144 189)(28 137 190)(29 138 191)(30 139 192)(31 140 185)(32 141 186)(33 182 89)(34 183 90)(35 184 91)(36 177 92)(37 178 93)(38 179 94)(39 180 95)(40 181 96)(41 81 134)(42 82 135)(43 83 136)(44 84 129)(45 85 130)(46 86 131)(47 87 132)(48 88 133)(49 102 106)(50 103 107)(51 104 108)(52 97 109)(53 98 110)(54 99 111)(55 100 112)(56 101 105)(57 206 150)(58 207 151)(59 208 152)(60 201 145)(61 202 146)(62 203 147)(63 204 148)(64 205 149)(73 113 166)(74 114 167)(75 115 168)(76 116 161)(77 117 162)(78 118 163)(79 119 164)(80 120 165)(153 193 209)(154 194 210)(155 195 211)(156 196 212)(157 197 213)(158 198 214)(159 199 215)(160 200 216)

(1 163 14)(2 164 15)(3 165 16)(4 166 9)(5 167 10)(6 168 11)(7 161 12)(8 162 13)(17 113 65)(18 114 66)(19 115 67)(20 116 68)(21 117 69)(22 118 70)(23 119 71)(24 120 72)(25 179 131)(26 180 132)(27 181 133)(28 182 134)(29 183 135)(30 184 136)(31 177 129)(32 178 130)(33 81 190)(34 82 191)(35 83 192)(36 84 185)(37 85 186)(38 86 187)(39 87 188)(40 88 189)(41 137 89)(42 138 90)(43 139 91)(44 140 92)(45 141 93)(46 142 94)(47 143 95)(48 144 96)(49 203 155)(50 204 156)(51 205 157)(52 206 158)(53 207 159)(54 208 160)(55 201 153)(56 202 154)(57 214 109)(58 215 110)(59 216 111)(60 209 112)(61 210 105)(62 211 106)(63 212 107)(64 213 108)(73 126 174)(74 127 175)(75 128 176)(76 121 169)(77 122 170)(78 123 171)(79 124 172)(80 125 173)(97 150 198)(98 151 199)(99 152 200)(100 145 193)(101 146 194)(102 147 195)(103 148 196)(104 149 197)

(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)

(2 4)(3 7)(6 8)(9 15)(11 13)(12 16)(17 23)(19 21)(20 24)(26 28)(27 31)(30 32)(33 39)(35 37)(36 40)(41 47)(43 45)(44 48)(50 52)(51 55)(54 56)(57 63)(59 61)(60 64)(65 71)(67 69)(68 72)(73 79)(75 77)(76 80)(81 87)(83 85)(84 88)(89 95)(91 93)(92 96)(97 103)(99 101)(100 104)(105 111)(107 109)(108 112)(113 119)(115 117)(116 120)(121 125)(122 128)(124 126)(129 133)(130 136)(132 134)(137 143)(139 141)(140 144)(145 149)(146 152)(148 150)(153 157)(154 160)(156 158)(161 165)(162 168)(164 166)(169 173)(170 176)(172 174)(177 181)(178 184)(180 182)(185 189)(186 192)(188 190)(193 197)(194 200)(196 198)(201 205)(202 208)(204 206)(209 213)(210 216)(212 214)
 
G:=sub<Sym(216)| (1,106,38)(2,107,39)(3,108,40)(4,109,33)(5,110,34)(6,111,35)(7,112,36)(8,105,37)(9,214,190)(10,215,191)(11,216,192)(12,209,185)(13,210,186)(14,211,187)(15,212,188)(16,213,189)(17,97,89)(18,98,90)(19,99,91)(20,100,92)(21,101,93)(22,102,94)(23,103,95)(24,104,96)(25,123,155)(26,124,156)(27,125,157)(28,126,158)(29,127,159)(30,128,160)(31,121,153)(32,122,154)(41,113,150)(42,114,151)(43,115,152)(44,116,145)(45,117,146)(46,118,147)(47,119,148)(48,120,149)(49,179,171)(50,180,172)(51,181,173)(52,182,174)(53,183,175)(54,184,176)(55,177,169)(56,178,170)(57,81,166)(58,82,167)(59,83,168)(60,84,161)(61,85,162)(62,86,163)(63,87,164)(64,88,165)(65,198,137)(66,199,138)(67,200,139)(68,193,140)(69,194,141)(70,195,142)(71,196,143)(72,197,144)(73,206,134)(74,207,135)(75,208,136)(76,201,129)(77,202,130)(78,203,131)(79,204,132)(80,205,133), (1,171,22)(2,172,23)(3,173,24)(4,174,17)(5,175,18)(6,176,19)(7,169,20)(8,170,21)(9,126,65)(10,127,66)(11,128,67)(12,121,68)(13,122,69)(14,123,70)(15,124,71)(16,125,72)(25,142,187)(26,143,188)(27,144,189)(28,137,190)(29,138,191)(30,139,192)(31,140,185)(32,141,186)(33,182,89)(34,183,90)(35,184,91)(36,177,92)(37,178,93)(38,179,94)(39,180,95)(40,181,96)(41,81,134)(42,82,135)(43,83,136)(44,84,129)(45,85,130)(46,86,131)(47,87,132)(48,88,133)(49,102,106)(50,103,107)(51,104,108)(52,97,109)(53,98,110)(54,99,111)(55,100,112)(56,101,105)(57,206,150)(58,207,151)(59,208,152)(60,201,145)(61,202,146)(62,203,147)(63,204,148)(64,205,149)(73,113,166)(74,114,167)(75,115,168)(76,116,161)(77,117,162)(78,118,163)(79,119,164)(80,120,165)(153,193,209)(154,194,210)(155,195,211)(156,196,212)(157,197,213)(158,198,214)(159,199,215)(160,200,216), (1,163,14)(2,164,15)(3,165,16)(4,166,9)(5,167,10)(6,168,11)(7,161,12)(8,162,13)(17,113,65)(18,114,66)(19,115,67)(20,116,68)(21,117,69)(22,118,70)(23,119,71)(24,120,72)(25,179,131)(26,180,132)(27,181,133)(28,182,134)(29,183,135)(30,184,136)(31,177,129)(32,178,130)(33,81,190)(34,82,191)(35,83,192)(36,84,185)(37,85,186)(38,86,187)(39,87,188)(40,88,189)(41,137,89)(42,138,90)(43,139,91)(44,140,92)(45,141,93)(46,142,94)(47,143,95)(48,144,96)(49,203,155)(50,204,156)(51,205,157)(52,206,158)(53,207,159)(54,208,160)(55,201,153)(56,202,154)(57,214,109)(58,215,110)(59,216,111)(60,209,112)(61,210,105)(62,211,106)(63,212,107)(64,213,108)(73,126,174)(74,127,175)(75,128,176)(76,121,169)(77,122,170)(78,123,171)(79,124,172)(80,125,173)(97,150,198)(98,151,199)(99,152,200)(100,145,193)(101,146,194)(102,147,195)(103,148,196)(104,149,197), (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), (2,4)(3,7)(6,8)(9,15)(11,13)(12,16)(17,23)(19,21)(20,24)(26,28)(27,31)(30,32)(33,39)(35,37)(36,40)(41,47)(43,45)(44,48)(50,52)(51,55)(54,56)(57,63)(59,61)(60,64)(65,71)(67,69)(68,72)(73,79)(75,77)(76,80)(81,87)(83,85)(84,88)(89,95)(91,93)(92,96)(97,103)(99,101)(100,104)(105,111)(107,109)(108,112)(113,119)(115,117)(116,120)(121,125)(122,128)(124,126)(129,133)(130,136)(132,134)(137,143)(139,141)(140,144)(145,149)(146,152)(148,150)(153,157)(154,160)(156,158)(161,165)(162,168)(164,166)(169,173)(170,176)(172,174)(177,181)(178,184)(180,182)(185,189)(186,192)(188,190)(193,197)(194,200)(196,198)(201,205)(202,208)(204,206)(209,213)(210,216)(212,214)>;
 
G:=Group( (1,106,38)(2,107,39)(3,108,40)(4,109,33)(5,110,34)(6,111,35)(7,112,36)(8,105,37)(9,214,190)(10,215,191)(11,216,192)(12,209,185)(13,210,186)(14,211,187)(15,212,188)(16,213,189)(17,97,89)(18,98,90)(19,99,91)(20,100,92)(21,101,93)(22,102,94)(23,103,95)(24,104,96)(25,123,155)(26,124,156)(27,125,157)(28,126,158)(29,127,159)(30,128,160)(31,121,153)(32,122,154)(41,113,150)(42,114,151)(43,115,152)(44,116,145)(45,117,146)(46,118,147)(47,119,148)(48,120,149)(49,179,171)(50,180,172)(51,181,173)(52,182,174)(53,183,175)(54,184,176)(55,177,169)(56,178,170)(57,81,166)(58,82,167)(59,83,168)(60,84,161)(61,85,162)(62,86,163)(63,87,164)(64,88,165)(65,198,137)(66,199,138)(67,200,139)(68,193,140)(69,194,141)(70,195,142)(71,196,143)(72,197,144)(73,206,134)(74,207,135)(75,208,136)(76,201,129)(77,202,130)(78,203,131)(79,204,132)(80,205,133), (1,171,22)(2,172,23)(3,173,24)(4,174,17)(5,175,18)(6,176,19)(7,169,20)(8,170,21)(9,126,65)(10,127,66)(11,128,67)(12,121,68)(13,122,69)(14,123,70)(15,124,71)(16,125,72)(25,142,187)(26,143,188)(27,144,189)(28,137,190)(29,138,191)(30,139,192)(31,140,185)(32,141,186)(33,182,89)(34,183,90)(35,184,91)(36,177,92)(37,178,93)(38,179,94)(39,180,95)(40,181,96)(41,81,134)(42,82,135)(43,83,136)(44,84,129)(45,85,130)(46,86,131)(47,87,132)(48,88,133)(49,102,106)(50,103,107)(51,104,108)(52,97,109)(53,98,110)(54,99,111)(55,100,112)(56,101,105)(57,206,150)(58,207,151)(59,208,152)(60,201,145)(61,202,146)(62,203,147)(63,204,148)(64,205,149)(73,113,166)(74,114,167)(75,115,168)(76,116,161)(77,117,162)(78,118,163)(79,119,164)(80,120,165)(153,193,209)(154,194,210)(155,195,211)(156,196,212)(157,197,213)(158,198,214)(159,199,215)(160,200,216), (1,163,14)(2,164,15)(3,165,16)(4,166,9)(5,167,10)(6,168,11)(7,161,12)(8,162,13)(17,113,65)(18,114,66)(19,115,67)(20,116,68)(21,117,69)(22,118,70)(23,119,71)(24,120,72)(25,179,131)(26,180,132)(27,181,133)(28,182,134)(29,183,135)(30,184,136)(31,177,129)(32,178,130)(33,81,190)(34,82,191)(35,83,192)(36,84,185)(37,85,186)(38,86,187)(39,87,188)(40,88,189)(41,137,89)(42,138,90)(43,139,91)(44,140,92)(45,141,93)(46,142,94)(47,143,95)(48,144,96)(49,203,155)(50,204,156)(51,205,157)(52,206,158)(53,207,159)(54,208,160)(55,201,153)(56,202,154)(57,214,109)(58,215,110)(59,216,111)(60,209,112)(61,210,105)(62,211,106)(63,212,107)(64,213,108)(73,126,174)(74,127,175)(75,128,176)(76,121,169)(77,122,170)(78,123,171)(79,124,172)(80,125,173)(97,150,198)(98,151,199)(99,152,200)(100,145,193)(101,146,194)(102,147,195)(103,148,196)(104,149,197), (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), (2,4)(3,7)(6,8)(9,15)(11,13)(12,16)(17,23)(19,21)(20,24)(26,28)(27,31)(30,32)(33,39)(35,37)(36,40)(41,47)(43,45)(44,48)(50,52)(51,55)(54,56)(57,63)(59,61)(60,64)(65,71)(67,69)(68,72)(73,79)(75,77)(76,80)(81,87)(83,85)(84,88)(89,95)(91,93)(92,96)(97,103)(99,101)(100,104)(105,111)(107,109)(108,112)(113,119)(115,117)(116,120)(121,125)(122,128)(124,126)(129,133)(130,136)(132,134)(137,143)(139,141)(140,144)(145,149)(146,152)(148,150)(153,157)(154,160)(156,158)(161,165)(162,168)(164,166)(169,173)(170,176)(172,174)(177,181)(178,184)(180,182)(185,189)(186,192)(188,190)(193,197)(194,200)(196,198)(201,205)(202,208)(204,206)(209,213)(210,216)(212,214) );
 
G=PermutationGroup([[(1,106,38),(2,107,39),(3,108,40),(4,109,33),(5,110,34),(6,111,35),(7,112,36),(8,105,37),(9,214,190),(10,215,191),(11,216,192),(12,209,185),(13,210,186),(14,211,187),(15,212,188),(16,213,189),(17,97,89),(18,98,90),(19,99,91),(20,100,92),(21,101,93),(22,102,94),(23,103,95),(24,104,96),(25,123,155),(26,124,156),(27,125,157),(28,126,158),(29,127,159),(30,128,160),(31,121,153),(32,122,154),(41,113,150),(42,114,151),(43,115,152),(44,116,145),(45,117,146),(46,118,147),(47,119,148),(48,120,149),(49,179,171),(50,180,172),(51,181,173),(52,182,174),(53,183,175),(54,184,176),(55,177,169),(56,178,170),(57,81,166),(58,82,167),(59,83,168),(60,84,161),(61,85,162),(62,86,163),(63,87,164),(64,88,165),(65,198,137),(66,199,138),(67,200,139),(68,193,140),(69,194,141),(70,195,142),(71,196,143),(72,197,144),(73,206,134),(74,207,135),(75,208,136),(76,201,129),(77,202,130),(78,203,131),(79,204,132),(80,205,133)], [(1,171,22),(2,172,23),(3,173,24),(4,174,17),(5,175,18),(6,176,19),(7,169,20),(8,170,21),(9,126,65),(10,127,66),(11,128,67),(12,121,68),(13,122,69),(14,123,70),(15,124,71),(16,125,72),(25,142,187),(26,143,188),(27,144,189),(28,137,190),(29,138,191),(30,139,192),(31,140,185),(32,141,186),(33,182,89),(34,183,90),(35,184,91),(36,177,92),(37,178,93),(38,179,94),(39,180,95),(40,181,96),(41,81,134),(42,82,135),(43,83,136),(44,84,129),(45,85,130),(46,86,131),(47,87,132),(48,88,133),(49,102,106),(50,103,107),(51,104,108),(52,97,109),(53,98,110),(54,99,111),(55,100,112),(56,101,105),(57,206,150),(58,207,151),(59,208,152),(60,201,145),(61,202,146),(62,203,147),(63,204,148),(64,205,149),(73,113,166),(74,114,167),(75,115,168),(76,116,161),(77,117,162),(78,118,163),(79,119,164),(80,120,165),(153,193,209),(154,194,210),(155,195,211),(156,196,212),(157,197,213),(158,198,214),(159,199,215),(160,200,216)], [(1,163,14),(2,164,15),(3,165,16),(4,166,9),(5,167,10),(6,168,11),(7,161,12),(8,162,13),(17,113,65),(18,114,66),(19,115,67),(20,116,68),(21,117,69),(22,118,70),(23,119,71),(24,120,72),(25,179,131),(26,180,132),(27,181,133),(28,182,134),(29,183,135),(30,184,136),(31,177,129),(32,178,130),(33,81,190),(34,82,191),(35,83,192),(36,84,185),(37,85,186),(38,86,187),(39,87,188),(40,88,189),(41,137,89),(42,138,90),(43,139,91),(44,140,92),(45,141,93),(46,142,94),(47,143,95),(48,144,96),(49,203,155),(50,204,156),(51,205,157),(52,206,158),(53,207,159),(54,208,160),(55,201,153),(56,202,154),(57,214,109),(58,215,110),(59,216,111),(60,209,112),(61,210,105),(62,211,106),(63,212,107),(64,213,108),(73,126,174),(74,127,175),(75,128,176),(76,121,169),(77,122,170),(78,123,171),(79,124,172),(80,125,173),(97,150,198),(98,151,199),(99,152,200),(100,145,193),(101,146,194),(102,147,195),(103,148,196),(104,149,197)], [(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)], [(2,4),(3,7),(6,8),(9,15),(11,13),(12,16),(17,23),(19,21),(20,24),(26,28),(27,31),(30,32),(33,39),(35,37),(36,40),(41,47),(43,45),(44,48),(50,52),(51,55),(54,56),(57,63),(59,61),(60,64),(65,71),(67,69),(68,72),(73,79),(75,77),(76,80),(81,87),(83,85),(84,88),(89,95),(91,93),(92,96),(97,103),(99,101),(100,104),(105,111),(107,109),(108,112),(113,119),(115,117),(116,120),(121,125),(122,128),(124,126),(129,133),(130,136),(132,134),(137,143),(139,141),(140,144),(145,149),(146,152),(148,150),(153,157),(154,160),(156,158),(161,165),(162,168),(164,166),(169,173),(170,176),(172,174),(177,181),(178,184),(180,182),(185,189),(186,192),(188,190),(193,197),(194,200),(196,198),(201,205),(202,208),(204,206),(209,213),(210,216),(212,214)]])
 

189 conjugacy classes

class 1 2A2B3A···3Z4A4B6A···6Z6AA···6AZ8A8B12A···12Z12AA···12AZ24A···24AZ
order1223···3446···66···68812···1212···1224···24
size1141···1241···14···4222···24···42···2

189 irreducible representations

dim111111112222
type+++++
imageC1C2C2C2C3C6C6C6D4SD16C3×D4C3×SD16
kernelSD16×C33C32×C24D4×C33Q8×C33C32×SD16C3×C24D4×C32Q8×C32C32×C6C33C3×C6C32
# reps111126262626122652

Matrix representation of SD16×C33 ►in GL5(𝔽73)

640000
01000
00100
000640
000064
,
10000
01000
00100
00080
00008
,
80000
064000
006400
000640
000064
,
720000
017100
017200
000667
00066
,
720000
01000
017200
00010
000072

G:=sub<GL(5,GF(73))| [64,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,64,0,0,0,0,0,64],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,8,0,0,0,0,0,8],[8,0,0,0,0,0,64,0,0,0,0,0,64,0,0,0,0,0,64,0,0,0,0,0,64],[72,0,0,0,0,0,1,1,0,0,0,71,72,0,0,0,0,0,6,6,0,0,0,67,6],[72,0,0,0,0,0,1,1,0,0,0,0,72,0,0,0,0,0,1,0,0,0,0,0,72] >;
 

SD16×C33 in GAP, Magma, Sage, TeX 

{\rm SD}_{16}\times C_3^3
 
% in TeX
 
G:=Group("SD16xC3^3");
 
// GroupNames label
 
G:=SmallGroup(432,518);
 
// by ID
 
G=gap.SmallGroup(432,518);
 
# by ID
 
G:=PCGroup([7,-2,-2,-3,-3,-3,-2,-2,1512,1541,13613,6816,124]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^8=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,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=d^3>;
 
// generators/relations
 

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