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G = C29⋊C14  order 406 = 2·7·29

The semidirect product of C29 and C14 acting faithfully

metacyclic, supersoluble, monomial, Z-group

Aliases: C29⋊C14, D29⋊C7, C29⋊C7⋊C2, SmallGroup(406,1)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C29 — C29⋊C14
Chief series
C1 — C29 — C29⋊C7 — C29⋊C14
Lower central
C29 — C29⋊C14
Upper central
C1

Generators and relations for C29⋊C14
 G = < a,b | a29=b14=1, bab-1=a22 >

C1
29C2
29C7
C29
29C14
D29
C29⋊C7
C29⋊C14

Character table of C29⋊C14

 class 127A7B7C7D7E7F14A14B14C14D14E14F29A29B
 size 1292929292929292929292929291414
ρ11111111111111111    trivial
ρ21-1111111-1-1-1-1-1-111    linear of order 2
ρ31-1ζ75ζ76ζ7ζ73ζ72ζ74-ζ75-ζ72-ζ74-ζ76-ζ7-ζ7311    linear of order 14
ρ411ζ74ζ72ζ75ζ7ζ73ζ76ζ74ζ73ζ76ζ72ζ75ζ711    linear of order 7
ρ511ζ75ζ76ζ7ζ73ζ72ζ74ζ75ζ72ζ74ζ76ζ7ζ7311    linear of order 7
ρ61-1ζ74ζ72ζ75ζ7ζ73ζ76-ζ74-ζ73-ζ76-ζ72-ζ75-ζ711    linear of order 14
ρ711ζ72ζ7ζ76ζ74ζ75ζ73ζ72ζ75ζ73ζ7ζ76ζ7411    linear of order 7
ρ811ζ7ζ74ζ73ζ72ζ76ζ75ζ7ζ76ζ75ζ74ζ73ζ7211    linear of order 7
ρ911ζ76ζ73ζ74ζ75ζ7ζ72ζ76ζ7ζ72ζ73ζ74ζ7511    linear of order 7
ρ101-1ζ76ζ73ζ74ζ75ζ7ζ72-ζ76-ζ7-ζ72-ζ73-ζ74-ζ7511    linear of order 14
ρ111-1ζ7ζ74ζ73ζ72ζ76ζ75-ζ7-ζ76-ζ75-ζ74-ζ73-ζ7211    linear of order 14
ρ121-1ζ72ζ7ζ76ζ74ζ75ζ73-ζ72-ζ75-ζ73-ζ7-ζ76-ζ7411    linear of order 14
ρ1311ζ73ζ75ζ72ζ76ζ74ζ7ζ73ζ74ζ7ζ75ζ72ζ7611    linear of order 7
ρ141-1ζ73ζ75ζ72ζ76ζ74ζ7-ζ73-ζ74-ζ7-ζ75-ζ72-ζ7611    linear of order 14
ρ15140000000000000-1-√29/2-1+√29/2    orthogonal faithful
ρ16140000000000000-1+√29/2-1-√29/2    orthogonal faithful

Permutation representations of C29⋊C14
►On 29 points: primitive - transitive group 29T5
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 5 17 7 25 10 8 29 26 14 24 6 21 23)(3 9 4 13 20 19 15 28 22 27 18 11 12 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), (2,5,17,7,25,10,8,29,26,14,24,6,21,23)(3,9,4,13,20,19,15,28,22,27,18,11,12,16)>;
 
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), (2,5,17,7,25,10,8,29,26,14,24,6,21,23)(3,9,4,13,20,19,15,28,22,27,18,11,12,16) );
 
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)], [(2,5,17,7,25,10,8,29,26,14,24,6,21,23),(3,9,4,13,20,19,15,28,22,27,18,11,12,16)]])
 
G:=TransitiveGroup(29,5);
 

Matrix representation of C29⋊C14 ►in GL14(𝔽2437)

24361000000000000
24360100000000000
24360010000000000
24360001000000000
24360000100000000
24360000010000000
24360000001000000
24360000000100000
24360000000010000
24360000000001000
24360000000000100
24360000000000010
24360000000000001
1009143010054181009101332434142414282019143210071427
,
1597126216084220225921849243010048472186227220121428
1010143010054181009101332434142414282019143210071427
00000001000000
10000000000000
1007143110092436142710082210074191008212436
10041851172426243114194205962024184820078405914
00000000100000
01000000000000
418201442659114274141005510152016837201314321011
59318509971844202516091431408141842517642424311425
00000000010000
00100000000000
6100718401423202420301010409183920191019101114241425
1424101110192019183940910102030202414231840100761011

G:=sub<GL(14,GF(2437))| [2436,2436,2436,2436,2436,2436,2436,2436,2436,2436,2436,2436,2436,1009,1,0,0,0,0,0,0,0,0,0,0,0,0,1430,0,1,0,0,0,0,0,0,0,0,0,0,0,1005,0,0,1,0,0,0,0,0,0,0,0,0,0,418,0,0,0,1,0,0,0,0,0,0,0,0,0,1009,0,0,0,0,1,0,0,0,0,0,0,0,0,1013,0,0,0,0,0,1,0,0,0,0,0,0,0,3,0,0,0,0,0,0,1,0,0,0,0,0,0,2434,0,0,0,0,0,0,0,1,0,0,0,0,0,1424,0,0,0,0,0,0,0,0,1,0,0,0,0,1428,0,0,0,0,0,0,0,0,0,1,0,0,0,2019,0,0,0,0,0,0,0,0,0,0,1,0,0,1432,0,0,0,0,0,0,0,0,0,0,0,1,0,1007,0,0,0,0,0,0,0,0,0,0,0,0,1,1427],[1597,1010,0,1,1007,1004,0,0,418,593,0,0,6,1424,1262,1430,0,0,1431,1851,0,1,2014,1850,0,0,1007,1011,160,1005,0,0,1009,172,0,0,426,997,0,1,1840,1019,842,418,0,0,2436,426,0,0,591,1844,0,0,1423,2019,2022,1009,0,0,1427,2431,0,0,1427,2025,0,0,2024,1839,592,1013,0,0,1008,1419,0,0,414,1609,0,0,2030,409,1849,3,0,0,2,420,0,0,1005,1431,0,0,1010,1010,2430,2434,1,0,2,596,0,0,5,408,0,0,409,2030,1004,1424,0,0,1007,2024,1,0,1015,1418,0,0,1839,2024,847,1428,0,0,419,1848,0,0,2016,425,1,0,2019,1423,2186,2019,0,0,1008,2007,0,0,837,176,0,0,1019,1840,2272,1432,0,0,2,840,0,0,2013,424,0,0,1011,1007,2012,1007,0,0,1,591,0,0,1432,2431,0,0,1424,6,1428,1427,0,0,2436,4,0,0,1011,1425,0,0,1425,1011] >;
 

C29⋊C14 in GAP, Magma, Sage, TeX 

C_{29}\rtimes C_{14}
 
% in TeX
 
G:=Group("C29:C14");
 
// GroupNames label
 
G:=SmallGroup(406,1);
 
// by ID
 
G=gap.SmallGroup(406,1);
 
# by ID
 
G:=PCGroup([3,-2,-7,-29,3530,1013]);
 
// Polycyclic
 
G:=Group<a,b|a^29=b^14=1,b*a*b^-1=a^22>;
 
// generators/relations
 

Export

Subgroup lattice of C29⋊C14 in TeX
Character table of C29⋊C14 in TeX

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