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G = D202order 404 = 22·101

Dihedral group

direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: D202, C2×D101, C202⋊C2, C101⋊C22, sometimes denoted D404 or Dih202 or Dih404, SmallGroup(404,4)

Series: Derived Chief Lower central Upper central

C1C101 — D202
C1C101D101 — D202
C101 — D202
C1C2

Generators and relations for D202
 G = < a,b | a202=b2=1, bab=a-1 >

101C2
101C2
101C22

Smallest permutation representation of D202
On 202 points
Generators in S202
(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)
(1 202)(2 201)(3 200)(4 199)(5 198)(6 197)(7 196)(8 195)(9 194)(10 193)(11 192)(12 191)(13 190)(14 189)(15 188)(16 187)(17 186)(18 185)(19 184)(20 183)(21 182)(22 181)(23 180)(24 179)(25 178)(26 177)(27 176)(28 175)(29 174)(30 173)(31 172)(32 171)(33 170)(34 169)(35 168)(36 167)(37 166)(38 165)(39 164)(40 163)(41 162)(42 161)(43 160)(44 159)(45 158)(46 157)(47 156)(48 155)(49 154)(50 153)(51 152)(52 151)(53 150)(54 149)(55 148)(56 147)(57 146)(58 145)(59 144)(60 143)(61 142)(62 141)(63 140)(64 139)(65 138)(66 137)(67 136)(68 135)(69 134)(70 133)(71 132)(72 131)(73 130)(74 129)(75 128)(76 127)(77 126)(78 125)(79 124)(80 123)(81 122)(82 121)(83 120)(84 119)(85 118)(86 117)(87 116)(88 115)(89 114)(90 113)(91 112)(92 111)(93 110)(94 109)(95 108)(96 107)(97 106)(98 105)(99 104)(100 103)(101 102)

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

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

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

104 conjugacy classes

class 1 2A2B2C101A···101AX202A···202AX
order1222101···101202···202
size111011012···22···2

104 irreducible representations

dim11122
type+++++
imageC1C2C2D101D202
kernelD202D101C202C2C1
# reps1215050

Matrix representation of D202 in GL2(𝔽607) generated by

219352
2190
,
507571
126100
G:=sub<GL(2,GF(607))| [219,219,352,0],[507,126,571,100] >;

D202 in GAP, Magma, Sage, TeX

D_{202}
% in TeX

G:=Group("D202");
// GroupNames label

G:=SmallGroup(404,4);
// by ID

G=gap.SmallGroup(404,4);
# by ID

G:=PCGroup([3,-2,-2,-101,3602]);
// Polycyclic

G:=Group<a,b|a^202=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D202 in TeX

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