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G = C13×D11order 286 = 2·11·13

Direct product of C13 and D11

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

Aliases: C13×D11, C11⋊C26, C1433C2, SmallGroup(286,1)

Series: Derived Chief Lower central Upper central

C1C11 — C13×D11
C1C11C143 — C13×D11
C11 — C13×D11
C1C13

Generators and relations for C13×D11
 G = < a,b,c | a13=b11=c2=1, ab=ba, ac=ca, cbc=b-1 >

11C2
11C26

Smallest permutation representation of C13×D11
On 143 points
Generators in S143
(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)
(1 66 55 31 137 91 114 16 127 49 100)(2 67 56 32 138 79 115 17 128 50 101)(3 68 57 33 139 80 116 18 129 51 102)(4 69 58 34 140 81 117 19 130 52 103)(5 70 59 35 141 82 105 20 118 40 104)(6 71 60 36 142 83 106 21 119 41 92)(7 72 61 37 143 84 107 22 120 42 93)(8 73 62 38 131 85 108 23 121 43 94)(9 74 63 39 132 86 109 24 122 44 95)(10 75 64 27 133 87 110 25 123 45 96)(11 76 65 28 134 88 111 26 124 46 97)(12 77 53 29 135 89 112 14 125 47 98)(13 78 54 30 136 90 113 15 126 48 99)
(1 100)(2 101)(3 102)(4 103)(5 104)(6 92)(7 93)(8 94)(9 95)(10 96)(11 97)(12 98)(13 99)(14 29)(15 30)(16 31)(17 32)(18 33)(19 34)(20 35)(21 36)(22 37)(23 38)(24 39)(25 27)(26 28)(40 70)(41 71)(42 72)(43 73)(44 74)(45 75)(46 76)(47 77)(48 78)(49 66)(50 67)(51 68)(52 69)(53 125)(54 126)(55 127)(56 128)(57 129)(58 130)(59 118)(60 119)(61 120)(62 121)(63 122)(64 123)(65 124)(105 141)(106 142)(107 143)(108 131)(109 132)(110 133)(111 134)(112 135)(113 136)(114 137)(115 138)(116 139)(117 140)

G:=sub<Sym(143)| (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), (1,66,55,31,137,91,114,16,127,49,100)(2,67,56,32,138,79,115,17,128,50,101)(3,68,57,33,139,80,116,18,129,51,102)(4,69,58,34,140,81,117,19,130,52,103)(5,70,59,35,141,82,105,20,118,40,104)(6,71,60,36,142,83,106,21,119,41,92)(7,72,61,37,143,84,107,22,120,42,93)(8,73,62,38,131,85,108,23,121,43,94)(9,74,63,39,132,86,109,24,122,44,95)(10,75,64,27,133,87,110,25,123,45,96)(11,76,65,28,134,88,111,26,124,46,97)(12,77,53,29,135,89,112,14,125,47,98)(13,78,54,30,136,90,113,15,126,48,99), (1,100)(2,101)(3,102)(4,103)(5,104)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,29)(15,30)(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,27)(26,28)(40,70)(41,71)(42,72)(43,73)(44,74)(45,75)(46,76)(47,77)(48,78)(49,66)(50,67)(51,68)(52,69)(53,125)(54,126)(55,127)(56,128)(57,129)(58,130)(59,118)(60,119)(61,120)(62,121)(63,122)(64,123)(65,124)(105,141)(106,142)(107,143)(108,131)(109,132)(110,133)(111,134)(112,135)(113,136)(114,137)(115,138)(116,139)(117,140)>;

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), (1,66,55,31,137,91,114,16,127,49,100)(2,67,56,32,138,79,115,17,128,50,101)(3,68,57,33,139,80,116,18,129,51,102)(4,69,58,34,140,81,117,19,130,52,103)(5,70,59,35,141,82,105,20,118,40,104)(6,71,60,36,142,83,106,21,119,41,92)(7,72,61,37,143,84,107,22,120,42,93)(8,73,62,38,131,85,108,23,121,43,94)(9,74,63,39,132,86,109,24,122,44,95)(10,75,64,27,133,87,110,25,123,45,96)(11,76,65,28,134,88,111,26,124,46,97)(12,77,53,29,135,89,112,14,125,47,98)(13,78,54,30,136,90,113,15,126,48,99), (1,100)(2,101)(3,102)(4,103)(5,104)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,29)(15,30)(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,27)(26,28)(40,70)(41,71)(42,72)(43,73)(44,74)(45,75)(46,76)(47,77)(48,78)(49,66)(50,67)(51,68)(52,69)(53,125)(54,126)(55,127)(56,128)(57,129)(58,130)(59,118)(60,119)(61,120)(62,121)(63,122)(64,123)(65,124)(105,141)(106,142)(107,143)(108,131)(109,132)(110,133)(111,134)(112,135)(113,136)(114,137)(115,138)(116,139)(117,140) );

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)], [(1,66,55,31,137,91,114,16,127,49,100),(2,67,56,32,138,79,115,17,128,50,101),(3,68,57,33,139,80,116,18,129,51,102),(4,69,58,34,140,81,117,19,130,52,103),(5,70,59,35,141,82,105,20,118,40,104),(6,71,60,36,142,83,106,21,119,41,92),(7,72,61,37,143,84,107,22,120,42,93),(8,73,62,38,131,85,108,23,121,43,94),(9,74,63,39,132,86,109,24,122,44,95),(10,75,64,27,133,87,110,25,123,45,96),(11,76,65,28,134,88,111,26,124,46,97),(12,77,53,29,135,89,112,14,125,47,98),(13,78,54,30,136,90,113,15,126,48,99)], [(1,100),(2,101),(3,102),(4,103),(5,104),(6,92),(7,93),(8,94),(9,95),(10,96),(11,97),(12,98),(13,99),(14,29),(15,30),(16,31),(17,32),(18,33),(19,34),(20,35),(21,36),(22,37),(23,38),(24,39),(25,27),(26,28),(40,70),(41,71),(42,72),(43,73),(44,74),(45,75),(46,76),(47,77),(48,78),(49,66),(50,67),(51,68),(52,69),(53,125),(54,126),(55,127),(56,128),(57,129),(58,130),(59,118),(60,119),(61,120),(62,121),(63,122),(64,123),(65,124),(105,141),(106,142),(107,143),(108,131),(109,132),(110,133),(111,134),(112,135),(113,136),(114,137),(115,138),(116,139),(117,140)])

91 conjugacy classes

class 1  2 11A···11E13A···13L26A···26L143A···143BH
order1211···1113···1326···26143···143
size1112···21···111···112···2

91 irreducible representations

dim111122
type+++
imageC1C2C13C26D11C13×D11
kernelC13×D11C143D11C11C13C1
# reps111212560

Matrix representation of C13×D11 in GL2(𝔽859) generated by

4780
0478
,
01
858748
,
01
10
G:=sub<GL(2,GF(859))| [478,0,0,478],[0,858,1,748],[0,1,1,0] >;

C13×D11 in GAP, Magma, Sage, TeX

C_{13}\times D_{11}
% in TeX

G:=Group("C13xD11");
// GroupNames label

G:=SmallGroup(286,1);
// by ID

G=gap.SmallGroup(286,1);
# by ID

G:=PCGroup([3,-2,-13,-11,2342]);
// Polycyclic

G:=Group<a,b,c|a^13=b^11=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C13×D11 in TeX

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