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G = C20×D11order 440 = 23·5·11

Direct product of C20 and D11

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

Aliases: C20×D11, C2204C2, C446C10, D22.2C10, C10.14D22, Dic115C10, C110.14C22, C558(C2×C4), C114(C2×C20), C2.1(C10×D11), C22.10(C2×C10), (C5×Dic11)⋊5C2, (C10×D11).2C2, SmallGroup(440,25)

Series: Derived Chief Lower central Upper central

C1C11 — C20×D11
C1C11C22C110C10×D11 — C20×D11
C11 — C20×D11
C1C20

Generators and relations for C20×D11
 G = < a,b,c | a20=b11=c2=1, ab=ba, ac=ca, cbc=b-1 >

11C2
11C2
11C4
11C22
11C10
11C10
11C2×C4
11C20
11C2×C10
11C2×C20

Smallest permutation representation of C20×D11
On 220 points
Generators in S220
(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)
(1 136 36 58 108 93 179 201 148 75 181)(2 137 37 59 109 94 180 202 149 76 182)(3 138 38 60 110 95 161 203 150 77 183)(4 139 39 41 111 96 162 204 151 78 184)(5 140 40 42 112 97 163 205 152 79 185)(6 121 21 43 113 98 164 206 153 80 186)(7 122 22 44 114 99 165 207 154 61 187)(8 123 23 45 115 100 166 208 155 62 188)(9 124 24 46 116 81 167 209 156 63 189)(10 125 25 47 117 82 168 210 157 64 190)(11 126 26 48 118 83 169 211 158 65 191)(12 127 27 49 119 84 170 212 159 66 192)(13 128 28 50 120 85 171 213 160 67 193)(14 129 29 51 101 86 172 214 141 68 194)(15 130 30 52 102 87 173 215 142 69 195)(16 131 31 53 103 88 174 216 143 70 196)(17 132 32 54 104 89 175 217 144 71 197)(18 133 33 55 105 90 176 218 145 72 198)(19 134 34 56 106 91 177 219 146 73 199)(20 135 35 57 107 92 178 220 147 74 200)
(1 181)(2 182)(3 183)(4 184)(5 185)(6 186)(7 187)(8 188)(9 189)(10 190)(11 191)(12 192)(13 193)(14 194)(15 195)(16 196)(17 197)(18 198)(19 199)(20 200)(21 153)(22 154)(23 155)(24 156)(25 157)(26 158)(27 159)(28 160)(29 141)(30 142)(31 143)(32 144)(33 145)(34 146)(35 147)(36 148)(37 149)(38 150)(39 151)(40 152)(41 204)(42 205)(43 206)(44 207)(45 208)(46 209)(47 210)(48 211)(49 212)(50 213)(51 214)(52 215)(53 216)(54 217)(55 218)(56 219)(57 220)(58 201)(59 202)(60 203)(61 122)(62 123)(63 124)(64 125)(65 126)(66 127)(67 128)(68 129)(69 130)(70 131)(71 132)(72 133)(73 134)(74 135)(75 136)(76 137)(77 138)(78 139)(79 140)(80 121)(101 172)(102 173)(103 174)(104 175)(105 176)(106 177)(107 178)(108 179)(109 180)(110 161)(111 162)(112 163)(113 164)(114 165)(115 166)(116 167)(117 168)(118 169)(119 170)(120 171)

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

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

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

140 conjugacy classes

class 1 2A2B2C4A4B4C4D5A5B5C5D10A10B10C10D10E···10L11A···11E20A···20H20I···20P22A···22E44A···44J55A···55T110A···110T220A···220AN
order1222444455551010101010···1011···1120···2020···2022···2244···4455···55110···110220···220
size1111111111111111111111···112···21···111···112···22···22···22···22···2

140 irreducible representations

dim1111111111222222
type++++++
imageC1C2C2C2C4C5C10C10C10C20D11D22C4×D11C5×D11C10×D11C20×D11
kernelC20×D11C5×Dic11C220C10×D11C5×D11C4×D11Dic11C44D22D11C20C10C5C4C2C1
# reps111144444165510202040

Matrix representation of C20×D11 in GL3(𝔽661) generated by

55500
04710
00471
,
100
0586587
0660660
,
66000
066074
001
G:=sub<GL(3,GF(661))| [555,0,0,0,471,0,0,0,471],[1,0,0,0,586,660,0,587,660],[660,0,0,0,660,0,0,74,1] >;

C20×D11 in GAP, Magma, Sage, TeX

C_{20}\times D_{11}
% in TeX

G:=Group("C20xD11");
// GroupNames label

G:=SmallGroup(440,25);
// by ID

G=gap.SmallGroup(440,25);
# by ID

G:=PCGroup([5,-2,-2,-5,-2,-11,106,10004]);
// Polycyclic

G:=Group<a,b,c|a^20=b^11=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C20×D11 in TeX

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