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G = C3321SD16order 432 = 24·33

3rd semidirect product of C33 and SD16 acting via SD16/C8=C2

metabelian, supersoluble, monomial

Aliases: C3321SD16, C242(C3⋊S3), (C3×C24)⋊11S3, (C32×C24)⋊4C2, (C3×C6).66D12, C31(C242S3), C338Q81C2, C82(C33⋊C2), (C3×C12).197D6, (C32×C6).61D4, C6.7(C12⋊S3), C3312D4.1C2, C3211(C24⋊C2), C2.3(C3312D4), (C32×C12).75C22, C12.64(C2×C3⋊S3), C4.8(C2×C33⋊C2), SmallGroup(432,498)

Series: Derived Chief Lower central Upper central

C1C32×C12 — C3321SD16
C1C3C32C33C32×C6C32×C12C3312D4 — C3321SD16
C33C32×C6C32×C12 — C3321SD16
C1C2C4C8

Generators and relations for C3321SD16
 G = < a,b,c,d,e | a3=b3=c3=d8=e2=1, ab=ba, ac=ca, ad=da, eae=a-1, bc=cb, bd=db, ebe=b-1, cd=dc, ece=c-1, ede=d3 >

Subgroups: 2136 in 280 conjugacy classes, 115 normal (11 characteristic)
C1, C2, C2, C3 [×13], C4, C4, C22, S3 [×13], C6 [×13], C8, D4, Q8, C32 [×13], Dic3 [×13], C12 [×13], D6 [×13], SD16, C3⋊S3 [×13], C3×C6 [×13], C24 [×13], Dic6 [×13], D12 [×13], C33, C3⋊Dic3 [×13], C3×C12 [×13], C2×C3⋊S3 [×13], C24⋊C2 [×13], C33⋊C2, C32×C6, C3×C24 [×13], C324Q8 [×13], C12⋊S3 [×13], C335C4, C32×C12, C2×C33⋊C2, C242S3 [×13], C32×C24, C338Q8, C3312D4, C3321SD16
Quotients: C1, C2 [×3], C22, S3 [×13], D4, D6 [×13], SD16, C3⋊S3 [×13], D12 [×13], C2×C3⋊S3 [×13], C24⋊C2 [×13], C33⋊C2, C12⋊S3 [×13], C2×C33⋊C2, C242S3 [×13], C3312D4, C3321SD16

Smallest permutation representation of C3321SD16
On 216 points
Generators in S216
(1 81 40)(2 82 33)(3 83 34)(4 84 35)(5 85 36)(6 86 37)(7 87 38)(8 88 39)(9 127 52)(10 128 53)(11 121 54)(12 122 55)(13 123 56)(14 124 49)(15 125 50)(16 126 51)(17 112 153)(18 105 154)(19 106 155)(20 107 156)(21 108 157)(22 109 158)(23 110 159)(24 111 160)(25 67 180)(26 68 181)(27 69 182)(28 70 183)(29 71 184)(30 72 177)(31 65 178)(32 66 179)(41 129 169)(42 130 170)(43 131 171)(44 132 172)(45 133 173)(46 134 174)(47 135 175)(48 136 176)(57 198 213)(58 199 214)(59 200 215)(60 193 216)(61 194 209)(62 195 210)(63 196 211)(64 197 212)(73 165 114)(74 166 115)(75 167 116)(76 168 117)(77 161 118)(78 162 119)(79 163 120)(80 164 113)(89 208 143)(90 201 144)(91 202 137)(92 203 138)(93 204 139)(94 205 140)(95 206 141)(96 207 142)(97 189 148)(98 190 149)(99 191 150)(100 192 151)(101 185 152)(102 186 145)(103 187 146)(104 188 147)
(1 198 74)(2 199 75)(3 200 76)(4 193 77)(5 194 78)(6 195 79)(7 196 80)(8 197 73)(9 169 142)(10 170 143)(11 171 144)(12 172 137)(13 173 138)(14 174 139)(15 175 140)(16 176 141)(17 182 148)(18 183 149)(19 184 150)(20 177 151)(21 178 152)(22 179 145)(23 180 146)(24 181 147)(25 103 110)(26 104 111)(27 97 112)(28 98 105)(29 99 106)(30 100 107)(31 101 108)(32 102 109)(33 58 116)(34 59 117)(35 60 118)(36 61 119)(37 62 120)(38 63 113)(39 64 114)(40 57 115)(41 96 127)(42 89 128)(43 90 121)(44 91 122)(45 92 123)(46 93 124)(47 94 125)(48 95 126)(49 134 204)(50 135 205)(51 136 206)(52 129 207)(53 130 208)(54 131 201)(55 132 202)(56 133 203)(65 185 157)(66 186 158)(67 187 159)(68 188 160)(69 189 153)(70 190 154)(71 191 155)(72 192 156)(81 213 166)(82 214 167)(83 215 168)(84 216 161)(85 209 162)(86 210 163)(87 211 164)(88 212 165)
(1 27 175)(2 28 176)(3 29 169)(4 30 170)(5 31 171)(6 32 172)(7 25 173)(8 26 174)(9 76 106)(10 77 107)(11 78 108)(12 79 109)(13 80 110)(14 73 111)(15 74 112)(16 75 105)(17 50 115)(18 51 116)(19 52 117)(20 53 118)(21 54 119)(22 55 120)(23 56 113)(24 49 114)(33 183 136)(34 184 129)(35 177 130)(36 178 131)(37 179 132)(38 180 133)(39 181 134)(40 182 135)(41 83 71)(42 84 72)(43 85 65)(44 86 66)(45 87 67)(46 88 68)(47 81 69)(48 82 70)(57 148 205)(58 149 206)(59 150 207)(60 151 208)(61 152 201)(62 145 202)(63 146 203)(64 147 204)(89 216 192)(90 209 185)(91 210 186)(92 211 187)(93 212 188)(94 213 189)(95 214 190)(96 215 191)(97 140 198)(98 141 199)(99 142 200)(100 143 193)(101 144 194)(102 137 195)(103 138 196)(104 139 197)(121 162 157)(122 163 158)(123 164 159)(124 165 160)(125 166 153)(126 167 154)(127 168 155)(128 161 156)
(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)(9 103)(10 98)(11 101)(12 104)(13 99)(14 102)(15 97)(16 100)(17 94)(18 89)(19 92)(20 95)(21 90)(22 93)(23 96)(24 91)(25 169)(26 172)(27 175)(28 170)(29 173)(30 176)(31 171)(32 174)(33 84)(34 87)(35 82)(36 85)(37 88)(38 83)(39 86)(40 81)(41 180)(42 183)(43 178)(44 181)(45 184)(46 179)(47 182)(48 177)(49 186)(50 189)(51 192)(52 187)(53 190)(54 185)(55 188)(56 191)(57 166)(58 161)(59 164)(60 167)(61 162)(62 165)(63 168)(64 163)(65 131)(66 134)(67 129)(68 132)(69 135)(70 130)(71 133)(72 136)(73 195)(74 198)(75 193)(76 196)(77 199)(78 194)(79 197)(80 200)(105 143)(106 138)(107 141)(108 144)(109 139)(110 142)(111 137)(112 140)(113 215)(114 210)(115 213)(116 216)(117 211)(118 214)(119 209)(120 212)(121 152)(122 147)(123 150)(124 145)(125 148)(126 151)(127 146)(128 149)(153 205)(154 208)(155 203)(156 206)(157 201)(158 204)(159 207)(160 202)

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

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

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

111 conjugacy classes

class 1 2A2B3A···3M4A4B6A···6M8A8B12A···12Z24A···24AZ
order1223···3446···68812···1224···24
size111082···221082···2222···22···2

111 irreducible representations

dim1111222222
type++++++++
imageC1C2C2C2S3D4D6SD16D12C24⋊C2
kernelC3321SD16C32×C24C338Q8C3312D4C3×C24C32×C6C3×C12C33C3×C6C32
# reps11111311322652

Matrix representation of C3321SD16 in GL6(𝔽73)

1700000
1710000
0072100
0072000
000013
00007271
,
7130000
7210000
001000
000100
000010
000001
,
100000
010000
0072100
0072000
000010
000001
,
7200000
0720000
0072000
0007200
00004733
00006214
,
7200000
7210000
0072000
0072100
000010
00007272

G:=sub<GL(6,GF(73))| [1,1,0,0,0,0,70,71,0,0,0,0,0,0,72,72,0,0,0,0,1,0,0,0,0,0,0,0,1,72,0,0,0,0,3,71],[71,72,0,0,0,0,3,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,47,62,0,0,0,0,33,14],[72,72,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,1,0,0,0,0,0,0,1,72,0,0,0,0,0,72] >;

C3321SD16 in GAP, Magma, Sage, TeX

C_3^3\rtimes_{21}{\rm SD}_{16}
% in TeX

G:=Group("C3^3:21SD16");
// GroupNames label

G:=SmallGroup(432,498);
// by ID

G=gap.SmallGroup(432,498);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,85,36,254,58,1124,4037,14118]);
// 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,e*a*e=a^-1,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^3>;
// generators/relations

׿
×
𝔽