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G = C29⋊C7order 203 = 7·29

The semidirect product of C29 and C7 acting faithfully

metacyclic, supersoluble, monomial, Z-group, 7-hyperelementary

Aliases: C29⋊C7, SmallGroup(203,1)

Series: Derived Chief Lower central Upper central

C1C29 — C29⋊C7
C1C29 — C29⋊C7
C29 — C29⋊C7
C1

Generators and relations for C29⋊C7
 G = < a,b | a29=b7=1, bab-1=a20 >

29C7

Character table of C29⋊C7

 class 17A7B7C7D7E7F29A29B29C29D
 size 12929292929297777
ρ111111111111    trivial
ρ21ζ7ζ75ζ74ζ73ζ72ζ761111    linear of order 7
ρ31ζ72ζ73ζ7ζ76ζ74ζ751111    linear of order 7
ρ41ζ74ζ76ζ72ζ75ζ7ζ731111    linear of order 7
ρ51ζ76ζ72ζ73ζ74ζ75ζ71111    linear of order 7
ρ61ζ73ζ7ζ75ζ72ζ76ζ741111    linear of order 7
ρ71ζ75ζ74ζ76ζ7ζ73ζ721111    linear of order 7
ρ87000000ζ292729262918291529122910298ζ2925292429232920291629729ζ29212919291729142911293292ζ292829222913299296295294    complex faithful
ρ97000000ζ292829222913299296295294ζ292729262918291529122910298ζ2925292429232920291629729ζ29212919291729142911293292    complex faithful
ρ107000000ζ2925292429232920291629729ζ29212919291729142911293292ζ292829222913299296295294ζ292729262918291529122910298    complex faithful
ρ117000000ζ29212919291729142911293292ζ292829222913299296295294ζ292729262918291529122910298ζ2925292429232920291629729    complex faithful

Permutation representations of C29⋊C7
On 29 points: primitive - transitive group 29T4
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 17 25 8 26 24 21)(3 4 20 15 22 18 12)(5 7 10 29 14 6 23)(9 13 19 28 27 11 16)

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

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

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

G:=TransitiveGroup(29,4);

C29⋊C7 is a maximal subgroup of   C29⋊C14

Matrix representation of C29⋊C7 in GL7(𝔽2437)

0100000
0010000
0001000
0000100
0000010
0000001
1168921744811905749262
,
1000000
2356187486713481842706148
123422832360229971516521764
0010000
490161516081243146120562248
7905981991119916521615932
0000100

G:=sub<GL(7,GF(2437))| [0,0,0,0,0,0,1,1,0,0,0,0,0,1689,0,1,0,0,0,0,2174,0,0,1,0,0,0,481,0,0,0,1,0,0,1905,0,0,0,0,1,0,749,0,0,0,0,0,1,262],[1,2356,1234,0,490,790,0,0,1874,2283,0,1615,598,0,0,867,2360,1,1608,1991,0,0,1348,2299,0,1243,1199,0,0,1842,715,0,1461,1652,1,0,706,1652,0,2056,1615,0,0,148,1764,0,2248,932,0] >;

C29⋊C7 in GAP, Magma, Sage, TeX

C_{29}\rtimes C_7
% in TeX

G:=Group("C29:C7");
// GroupNames label

G:=SmallGroup(203,1);
// by ID

G=gap.SmallGroup(203,1);
# by ID

G:=PCGroup([2,-7,-29,449]);
// Polycyclic

G:=Group<a,b|a^29=b^7=1,b*a*b^-1=a^20>;
// generators/relations

Export

Subgroup lattice of C29⋊C7 in TeX
Character table of C29⋊C7 in TeX

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