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G = C43⋊C3order 129 = 3·43

The semidirect product of C43 and C3 acting faithfully

metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary

Aliases: C43⋊C3, SmallGroup(129,1)

Series: Derived Chief Lower central Upper central

C1C43 — C43⋊C3
C1C43 — C43⋊C3
C43 — C43⋊C3
C1

Generators and relations for C43⋊C3
 G = < a,b | a43=b3=1, bab-1=a6 >

43C3

Character table of C43⋊C3

 class 13A3B43A43B43C43D43E43F43G43H43I43J43K43L43M43N
 size 1434333333333333333
ρ111111111111111111    trivial
ρ21ζ32ζ311111111111111    linear of order 3
ρ31ζ3ζ3211111111111111    linear of order 3
ρ4300ζ433443324320ζ434143314314ζ433943284319ζ43224318433ζ431743164310ζ433843354313ζ43244315434ζ433643643ζ43294312432ζ433343274326ζ43234311439ζ4330438435ζ434043254321ζ43424337437    complex faithful
ρ5300ζ43234311439ζ43294312432ζ43244315434ζ434043254321ζ433343274326ζ4330438435ζ433943284319ζ43424337437ζ434143314314ζ431743164310ζ433443324320ζ433843354313ζ43224318433ζ433643643    complex faithful
ρ6300ζ433643643ζ4330438435ζ431743164310ζ434143314314ζ43224318433ζ433443324320ζ433343274326ζ433943284319ζ433843354313ζ434043254321ζ43424337437ζ43234311439ζ43294312432ζ43244315434    complex faithful
ρ7300ζ43224318433ζ43244315434ζ4330438435ζ43424337437ζ43234311439ζ431743164310ζ433843354313ζ434143314314ζ433943284319ζ433443324320ζ434043254321ζ433343274326ζ433643643ζ43294312432    complex faithful
ρ8300ζ43424337437ζ433843354313ζ433343274326ζ43294312432ζ434043254321ζ43234311439ζ431743164310ζ43244315434ζ4330438435ζ43224318433ζ433643643ζ433443324320ζ434143314314ζ433943284319    complex faithful
ρ9300ζ434043254321ζ433943284319ζ433843354313ζ433643643ζ433443324320ζ433343274326ζ4330438435ζ43294312432ζ43244315434ζ43234311439ζ43224318433ζ431743164310ζ43424337437ζ434143314314    complex faithful
ρ10300ζ431743164310ζ43424337437ζ434143314314ζ43234311439ζ4330438435ζ433943284319ζ43294312432ζ43224318433ζ433643643ζ433843354313ζ433343274326ζ43244315434ζ433443324320ζ434043254321    complex faithful
ρ11300ζ433843354313ζ43224318433ζ433643643ζ431743164310ζ433943284319ζ43294312432ζ43424337437ζ433443324320ζ434043254321ζ43244315434ζ4330438435ζ434143314314ζ433343274326ζ43234311439    complex faithful
ρ12300ζ43294312432ζ431743164310ζ433443324320ζ433943284319ζ433643643ζ434043254321ζ43234311439ζ433843354313ζ433343274326ζ43424337437ζ434143314314ζ43224318433ζ43244315434ζ4330438435    complex faithful
ρ13300ζ4330438435ζ434043254321ζ43424337437ζ433343274326ζ43244315434ζ434143314314ζ433643643ζ43234311439ζ43224318433ζ433943284319ζ433843354313ζ43294312432ζ431743164310ζ433443324320    complex faithful
ρ14300ζ433943284319ζ43234311439ζ43224318433ζ4330438435ζ434143314314ζ433643643ζ434043254321ζ431743164310ζ433443324320ζ43294312432ζ43244315434ζ43424337437ζ433843354313ζ433343274326    complex faithful
ρ15300ζ434143314314ζ433343274326ζ43234311439ζ43244315434ζ43424337437ζ43224318433ζ433443324320ζ4330438435ζ431743164310ζ433643643ζ43294312432ζ434043254321ζ433943284319ζ433843354313    complex faithful
ρ16300ζ433343274326ζ433643643ζ43294312432ζ433443324320ζ433843354313ζ43244315434ζ434143314314ζ434043254321ζ43424337437ζ4330438435ζ431743164310ζ433943284319ζ43234311439ζ43224318433    complex faithful
ρ17300ζ43244315434ζ433443324320ζ434043254321ζ433843354313ζ43294312432ζ43424337437ζ43224318433ζ433343274326ζ43234311439ζ434143314314ζ433943284319ζ433643643ζ4330438435ζ431743164310    complex faithful

Smallest permutation representation of C43⋊C3
On 43 points: primitive
Generators in S43
(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)
(2 37 7)(3 30 13)(4 23 19)(5 16 25)(6 9 31)(8 38 43)(10 24 12)(11 17 18)(14 39 36)(15 32 42)(20 40 29)(21 33 35)(22 26 41)(27 34 28)

G:=sub<Sym(43)| (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), (2,37,7)(3,30,13)(4,23,19)(5,16,25)(6,9,31)(8,38,43)(10,24,12)(11,17,18)(14,39,36)(15,32,42)(20,40,29)(21,33,35)(22,26,41)(27,34,28)>;

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), (2,37,7)(3,30,13)(4,23,19)(5,16,25)(6,9,31)(8,38,43)(10,24,12)(11,17,18)(14,39,36)(15,32,42)(20,40,29)(21,33,35)(22,26,41)(27,34,28) );

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)], [(2,37,7),(3,30,13),(4,23,19),(5,16,25),(6,9,31),(8,38,43),(10,24,12),(11,17,18),(14,39,36),(15,32,42),(20,40,29),(21,33,35),(22,26,41),(27,34,28)])

C43⋊C3 is a maximal subgroup of   C43⋊C6
C43⋊C3 is a maximal quotient of   C43⋊C9

Matrix representation of C43⋊C3 in GL3(𝔽1033) generated by

010
001
1831476
,
100
679378614
9251654
G:=sub<GL(3,GF(1033))| [0,0,1,1,0,831,0,1,476],[1,679,92,0,378,51,0,614,654] >;

C43⋊C3 in GAP, Magma, Sage, TeX

C_{43}\rtimes C_3
% in TeX

G:=Group("C43:C3");
// GroupNames label

G:=SmallGroup(129,1);
// by ID

G=gap.SmallGroup(129,1);
# by ID

G:=PCGroup([2,-3,-43,433]);
// Polycyclic

G:=Group<a,b|a^43=b^3=1,b*a*b^-1=a^6>;
// generators/relations

Export

Subgroup lattice of C43⋊C3 in TeX
Character table of C43⋊C3 in TeX

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