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G = C3×D43order 258 = 2·3·43

Direct product of C3 and D43

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

Aliases: C3×D43, C433C6, C1292C2, SmallGroup(258,4)

Series: Derived Chief Lower central Upper central

C1C43 — C3×D43
C1C43C129 — C3×D43
C43 — C3×D43
C1C3

Generators and relations for C3×D43
 G = < a,b,c | a3=b43=c2=1, ab=ba, ac=ca, cbc=b-1 >

43C2
43C6

Smallest permutation representation of C3×D43
On 129 points
Generators in S129
(1 107 66)(2 108 67)(3 109 68)(4 110 69)(5 111 70)(6 112 71)(7 113 72)(8 114 73)(9 115 74)(10 116 75)(11 117 76)(12 118 77)(13 119 78)(14 120 79)(15 121 80)(16 122 81)(17 123 82)(18 124 83)(19 125 84)(20 126 85)(21 127 86)(22 128 44)(23 129 45)(24 87 46)(25 88 47)(26 89 48)(27 90 49)(28 91 50)(29 92 51)(30 93 52)(31 94 53)(32 95 54)(33 96 55)(34 97 56)(35 98 57)(36 99 58)(37 100 59)(38 101 60)(39 102 61)(40 103 62)(41 104 63)(42 105 64)(43 106 65)
(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)
(1 43)(2 42)(3 41)(4 40)(5 39)(6 38)(7 37)(8 36)(9 35)(10 34)(11 33)(12 32)(13 31)(14 30)(15 29)(16 28)(17 27)(18 26)(19 25)(20 24)(21 23)(45 86)(46 85)(47 84)(48 83)(49 82)(50 81)(51 80)(52 79)(53 78)(54 77)(55 76)(56 75)(57 74)(58 73)(59 72)(60 71)(61 70)(62 69)(63 68)(64 67)(65 66)(87 126)(88 125)(89 124)(90 123)(91 122)(92 121)(93 120)(94 119)(95 118)(96 117)(97 116)(98 115)(99 114)(100 113)(101 112)(102 111)(103 110)(104 109)(105 108)(106 107)(127 129)

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

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

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

69 conjugacy classes

class 1  2 3A3B6A6B43A···43U129A···129AP
order12336643···43129···129
size1431143432···22···2

69 irreducible representations

dim111122
type+++
imageC1C2C3C6D43C3×D43
kernelC3×D43C129D43C43C3C1
# reps11222142

Matrix representation of C3×D43 in GL2(𝔽1033) generated by

1950
0195
,
9121
759173
,
1731032
1004860
G:=sub<GL(2,GF(1033))| [195,0,0,195],[912,759,1,173],[173,1004,1032,860] >;

C3×D43 in GAP, Magma, Sage, TeX

C_3\times D_{43}
% in TeX

G:=Group("C3xD43");
// GroupNames label

G:=SmallGroup(258,4);
// by ID

G=gap.SmallGroup(258,4);
# by ID

G:=PCGroup([3,-2,-3,-43,2270]);
// Polycyclic

G:=Group<a,b,c|a^3=b^43=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C3×D43 in TeX

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