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G = SD16×C29order 464 = 24·29

Direct product of C29 and SD16

direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary

Aliases: SD16×C29, Q8⋊C58, C82C58, D4.C58, C2326C2, C58.15D4, C116.18C22, C4.2(C2×C58), (Q8×C29)⋊4C2, C2.4(D4×C29), (D4×C29).2C2, SmallGroup(464,26)

Series: Derived Chief Lower central Upper central

C1C4 — SD16×C29
C1C2C4C116Q8×C29 — SD16×C29
C1C2C4 — SD16×C29
C1C58C116 — SD16×C29

Generators and relations for SD16×C29
 G = < a,b,c | a29=b8=c2=1, ab=ba, ac=ca, cbc=b3 >

4C2
2C4
2C22
4C58
2C116
2C2×C58

Smallest permutation representation of SD16×C29
On 232 points
Generators in S232
(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)
(1 94 195 56 221 171 75 122)(2 95 196 57 222 172 76 123)(3 96 197 58 223 173 77 124)(4 97 198 30 224 174 78 125)(5 98 199 31 225 146 79 126)(6 99 200 32 226 147 80 127)(7 100 201 33 227 148 81 128)(8 101 202 34 228 149 82 129)(9 102 203 35 229 150 83 130)(10 103 175 36 230 151 84 131)(11 104 176 37 231 152 85 132)(12 105 177 38 232 153 86 133)(13 106 178 39 204 154 87 134)(14 107 179 40 205 155 59 135)(15 108 180 41 206 156 60 136)(16 109 181 42 207 157 61 137)(17 110 182 43 208 158 62 138)(18 111 183 44 209 159 63 139)(19 112 184 45 210 160 64 140)(20 113 185 46 211 161 65 141)(21 114 186 47 212 162 66 142)(22 115 187 48 213 163 67 143)(23 116 188 49 214 164 68 144)(24 88 189 50 215 165 69 145)(25 89 190 51 216 166 70 117)(26 90 191 52 217 167 71 118)(27 91 192 53 218 168 72 119)(28 92 193 54 219 169 73 120)(29 93 194 55 220 170 74 121)
(30 97)(31 98)(32 99)(33 100)(34 101)(35 102)(36 103)(37 104)(38 105)(39 106)(40 107)(41 108)(42 109)(43 110)(44 111)(45 112)(46 113)(47 114)(48 115)(49 116)(50 88)(51 89)(52 90)(53 91)(54 92)(55 93)(56 94)(57 95)(58 96)(59 179)(60 180)(61 181)(62 182)(63 183)(64 184)(65 185)(66 186)(67 187)(68 188)(69 189)(70 190)(71 191)(72 192)(73 193)(74 194)(75 195)(76 196)(77 197)(78 198)(79 199)(80 200)(81 201)(82 202)(83 203)(84 175)(85 176)(86 177)(87 178)(117 166)(118 167)(119 168)(120 169)(121 170)(122 171)(123 172)(124 173)(125 174)(126 146)(127 147)(128 148)(129 149)(130 150)(131 151)(132 152)(133 153)(134 154)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)(141 161)(142 162)(143 163)(144 164)(145 165)

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

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

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

203 conjugacy classes

class 1 2A2B4A4B8A8B29A···29AB58A···58AB58AC···58BD116A···116AB116AC···116BD232A···232BD
order122448829···2958···5858···58116···116116···116232···232
size11424221···11···14···42···24···42···2

203 irreducible representations

dim111111112222
type+++++
imageC1C2C2C2C29C58C58C58D4SD16D4×C29SD16×C29
kernelSD16×C29C232D4×C29Q8×C29SD16C8D4Q8C58C29C2C1
# reps111128282828122856

Matrix representation of SD16×C29 in GL2(𝔽233) generated by

1280
0128
,
62171
6262
,
10
0232
G:=sub<GL(2,GF(233))| [128,0,0,128],[62,62,171,62],[1,0,0,232] >;

SD16×C29 in GAP, Magma, Sage, TeX

{\rm SD}_{16}\times C_{29}
% in TeX

G:=Group("SD16xC29");
// GroupNames label

G:=SmallGroup(464,26);
// by ID

G=gap.SmallGroup(464,26);
# by ID

G:=PCGroup([5,-2,-2,-29,-2,-2,1160,1181,6963,3488,58]);
// Polycyclic

G:=Group<a,b,c|a^29=b^8=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^3>;
// generators/relations

Export

Subgroup lattice of SD16×C29 in TeX

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