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G = C29⋊C4order 116 = 22·29

The semidirect product of C29 and C4 acting faithfully

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

Aliases: C29⋊C4, D29.C2, SmallGroup(116,3)

Series: Derived Chief Lower central Upper central

C1C29 — C29⋊C4
C1C29D29 — C29⋊C4
C29 — C29⋊C4
C1

Generators and relations for C29⋊C4
 G = < a,b | a29=b4=1, bab-1=a17 >

29C2
29C4

Character table of C29⋊C4

 class 124A4B29A29B29C29D29E29F29G
 size 12929294444444
ρ111111111111    trivial
ρ211-1-11111111    linear of order 2
ρ31-1i-i1111111    linear of order 4
ρ41-1-ii1111111    linear of order 4
ρ54000ζ292529192910294ζ292329152914296ζ29212920299298ζ2918291629132911ζ29282917291229ζ29272924295292ζ29262922297293    orthogonal faithful
ρ64000ζ29262922297293ζ292529192910294ζ292329152914296ζ29282917291229ζ29212920299298ζ2918291629132911ζ29272924295292    orthogonal faithful
ρ74000ζ29282917291229ζ2918291629132911ζ29272924295292ζ292529192910294ζ29262922297293ζ292329152914296ζ29212920299298    orthogonal faithful
ρ84000ζ2918291629132911ζ29272924295292ζ29262922297293ζ292329152914296ζ292529192910294ζ29212920299298ζ29282917291229    orthogonal faithful
ρ94000ζ29212920299298ζ29282917291229ζ2918291629132911ζ29262922297293ζ29272924295292ζ292529192910294ζ292329152914296    orthogonal faithful
ρ104000ζ292329152914296ζ29212920299298ζ29282917291229ζ29272924295292ζ2918291629132911ζ29262922297293ζ292529192910294    orthogonal faithful
ρ114000ζ29272924295292ζ29262922297293ζ292529192910294ζ29212920299298ζ292329152914296ζ29282917291229ζ2918291629132911    orthogonal faithful

Permutation representations of C29⋊C4
On 29 points: primitive - transitive group 29T3
Generators in S29
(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)
(2 13 29 18)(3 25 28 6)(4 8 27 23)(5 20 26 11)(7 15 24 16)(9 10 22 21)(12 17 19 14)

G:=sub<Sym(29)| (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), (2,13,29,18)(3,25,28,6)(4,8,27,23)(5,20,26,11)(7,15,24,16)(9,10,22,21)(12,17,19,14)>;

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), (2,13,29,18)(3,25,28,6)(4,8,27,23)(5,20,26,11)(7,15,24,16)(9,10,22,21)(12,17,19,14) );

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)], [(2,13,29,18),(3,25,28,6),(4,8,27,23),(5,20,26,11),(7,15,24,16),(9,10,22,21),(12,17,19,14)])

G:=TransitiveGroup(29,3);

C29⋊C4 is a maximal subgroup of   C87⋊C4
C29⋊C4 is a maximal quotient of   C29⋊C8  C87⋊C4

Matrix representation of C29⋊C4 in GL4(𝔽233) generated by

232100
232010
232001
2162122116
,
612547222
2172122116
5716656137
14209189137
G:=sub<GL(4,GF(233))| [232,232,232,216,1,0,0,212,0,1,0,21,0,0,1,16],[61,217,57,14,25,212,166,209,47,21,56,189,222,16,137,137] >;

C29⋊C4 in GAP, Magma, Sage, TeX

C_{29}\rtimes C_4
% in TeX

G:=Group("C29:C4");
// GroupNames label

G:=SmallGroup(116,3);
// by ID

G=gap.SmallGroup(116,3);
# by ID

G:=PCGroup([3,-2,-2,-29,6,434,509]);
// Polycyclic

G:=Group<a,b|a^29=b^4=1,b*a*b^-1=a^17>;
// generators/relations

Export

Subgroup lattice of C29⋊C4 in TeX
Character table of C29⋊C4 in TeX

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