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Properties

Label 29T5
Degree $29$
Order $406$
Cyclic no
Abelian no
Solvable yes
Primitive yes
$p$-group no
Group: $C_{29}:C_{14}$

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Show commands: Magma

magma: G := TransitiveGroup(29, 5);
 

Group action invariants

Degree $n$:  $29$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $5$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{29}:C_{14}$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (2,4,6,8,10,12,14,16,18,20,22,24,26,28)(3,5,7,9,11,13,15,17,19,21,23,25,27,29), (1,2,3,7,4,24,8,14,5,12,25,27,9,20,15,29,6,23,13,11,26,19,28,22,10,18,21,17,16)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$7$:  $C_7$
$14$:  $C_{14}$

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

LabelCycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 14, 14, 1 $ $29$ $14$ $( 2, 4, 6, 8,10,12,14,16,18,20,22,24,26,28)( 3, 5, 7, 9,11,13,15,17,19,21,23, 25,27,29)$
$ 7, 7, 7, 7, 1 $ $29$ $7$ $( 2, 6,10,14,18,22,26)( 3, 7,11,15,19,23,27)( 4, 8,12,16,20,24,28) ( 5, 9,13,17,21,25,29)$
$ 14, 14, 1 $ $29$ $14$ $( 2, 8,14,20,26, 4,10,16,22,28, 6,12,18,24)( 3, 9,15,21,27, 5,11,17,23,29, 7, 13,19,25)$
$ 7, 7, 7, 7, 1 $ $29$ $7$ $( 2,10,18,26, 6,14,22)( 3,11,19,27, 7,15,23)( 4,12,20,28, 8,16,24) ( 5,13,21,29, 9,17,25)$
$ 14, 14, 1 $ $29$ $14$ $( 2,12,22, 4,14,24, 6,16,26, 8,18,28,10,20)( 3,13,23, 5,15,25, 7,17,27, 9,19, 29,11,21)$
$ 7, 7, 7, 7, 1 $ $29$ $7$ $( 2,14,26,10,22, 6,18)( 3,15,27,11,23, 7,19)( 4,16,28,12,24, 8,20) ( 5,17,29,13,25, 9,21)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $ $29$ $2$ $( 2,16)( 3,17)( 4,18)( 5,19)( 6,20)( 7,21)( 8,22)( 9,23)(10,24)(11,25)(12,26) (13,27)(14,28)(15,29)$
$ 7, 7, 7, 7, 1 $ $29$ $7$ $( 2,18, 6,22,10,26,14)( 3,19, 7,23,11,27,15)( 4,20, 8,24,12,28,16) ( 5,21, 9,25,13,29,17)$
$ 14, 14, 1 $ $29$ $14$ $( 2,20,10,28,18, 8,26,16, 6,24,14, 4,22,12)( 3,21,11,29,19, 9,27,17, 7,25,15, 5,23,13)$
$ 7, 7, 7, 7, 1 $ $29$ $7$ $( 2,22,14, 6,26,18,10)( 3,23,15, 7,27,19,11)( 4,24,16, 8,28,20,12) ( 5,25,17, 9,29,21,13)$
$ 14, 14, 1 $ $29$ $14$ $( 2,24,18,12, 6,28,22,16,10, 4,26,20,14, 8)( 3,25,19,13, 7,29,23,17,11, 5,27, 21,15, 9)$
$ 7, 7, 7, 7, 1 $ $29$ $7$ $( 2,26,22,18,14,10, 6)( 3,27,23,19,15,11, 7)( 4,28,24,20,16,12, 8) ( 5,29,25,21,17,13, 9)$
$ 14, 14, 1 $ $29$ $14$ $( 2,28,26,24,22,20,18,16,14,12,10, 8, 6, 4)( 3,29,27,25,23,21,19,17,15,13,11, 9, 7, 5)$
$ 29 $ $14$ $29$ $( 1, 2, 3, 7, 4,24, 8,14, 5,12,25,27, 9,20,15,29, 6,23,13,11,26,19,28,22,10, 18,21,17,16)$
$ 29 $ $14$ $29$ $( 1, 3, 4, 8, 5,25, 9,15, 6,13,26,28,10,21,16, 2, 7,24,14,12,27,20,29,23,11, 19,22,18,17)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $406=2 \cdot 7 \cdot 29$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  406.1
magma: IdentifyGroup(G);
 
Character table:

1A 2A 7A1 7A-1 7A2 7A-2 7A3 7A-3 14A1 14A-1 14A3 14A-3 14A5 14A-5 29A1 29A2
Size 1 29 29 29 29 29 29 29 29 29 29 29 29 29 14 14
2 P 1A 1A 7A2 7A3 7A-2 7A-1 7A1 7A-3 7A1 7A-1 7A2 7A3 7A-2 7A-3 29A2 29A1
7 P 1A 2A 7A3 7A1 7A-3 7A2 7A-2 7A-1 14A3 14A-3 14A-1 14A-5 14A1 14A5 29A2 29A1
29 P 1A 2A 1A 1A 1A 1A 1A 1A 2A 2A 2A 2A 2A 2A 29A1 29A2
Type
406.1.1a R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
406.1.1b R 1 −1 1 1 1 1 1 1 −1 −1 −1 −1 −1 −1 1 1
406.1.1c1 C 1 1 ζ7−3 ζ73 ζ7 ζ7−1 ζ7−2 ζ72 ζ72 ζ7−2 ζ7−1 ζ7 ζ73 ζ7−3 1 1
406.1.1c2 C 1 1 ζ73 ζ7−3 ζ7−1 ζ7 ζ72 ζ7−2 ζ7−2 ζ72 ζ7 ζ7−1 ζ7−3 ζ73 1 1
406.1.1c3 C 1 1 ζ7−2 ζ72 ζ73 ζ7−3 ζ7 ζ7−1 ζ7−1 ζ7 ζ7−3 ζ73 ζ72 ζ7−2 1 1
406.1.1c4 C 1 1 ζ72 ζ7−2 ζ7−3 ζ73 ζ7−1 ζ7 ζ7 ζ7−1 ζ73 ζ7−3 ζ7−2 ζ72 1 1
406.1.1c5 C 1 1 ζ7−1 ζ7 ζ7−2 ζ72 ζ7−3 ζ73 ζ73 ζ7−3 ζ72 ζ7−2 ζ7 ζ7−1 1 1
406.1.1c6 C 1 1 ζ7 ζ7−1 ζ72 ζ7−2 ζ73 ζ7−3 ζ7−3 ζ73 ζ7−2 ζ72 ζ7−1 ζ7 1 1
406.1.1d1 C 1 −1 ζ7−3 ζ73 ζ7 ζ7−1 ζ7−2 ζ72 −ζ72 −ζ7−2 −ζ7−1 −ζ7 −ζ73 −ζ7−3 1 1
406.1.1d2 C 1 −1 ζ73 ζ7−3 ζ7−1 ζ7 ζ72 ζ7−2 −ζ7−2 −ζ72 −ζ7 −ζ7−1 −ζ7−3 −ζ73 1 1
406.1.1d3 C 1 −1 ζ7−2 ζ72 ζ73 ζ7−3 ζ7 ζ7−1 −ζ7−1 −ζ7 −ζ7−3 −ζ73 −ζ72 −ζ7−2 1 1
406.1.1d4 C 1 −1 ζ72 ζ7−2 ζ7−3 ζ73 ζ7−1 ζ7 −ζ7 −ζ7−1 −ζ73 −ζ7−3 −ζ7−2 −ζ72 1 1
406.1.1d5 C 1 −1 ζ7−1 ζ7 ζ7−2 ζ72 ζ7−3 ζ73 −ζ73 −ζ7−3 −ζ72 −ζ7−2 −ζ7 −ζ7−1 1 1
406.1.1d6 C 1 −1 ζ7 ζ7−1 ζ72 ζ7−2 ζ73 ζ7−3 −ζ7−3 −ζ73 −ζ7−2 −ζ72 −ζ7−1 −ζ7 1 1
406.1.14a1 R 14 0 0 0 0 0 0 0 0 0 0 0 0 0 ζ29−14+ζ29−12+ζ29−11+ζ29−10+ζ29−8+ζ29−3+ζ29−2+ζ292+ζ293+ζ298+ζ2910+ζ2911+ζ2912+ζ2914 −ζ29−14−ζ29−12−ζ29−11−ζ29−10−ζ29−8−ζ29−3−ζ29−2−1−ζ292−ζ293−ζ298−ζ2910−ζ2911−ζ2912−ζ2914
406.1.14a2 R 14 0 0 0 0 0 0 0 0 0 0 0 0 0 −ζ29−14−ζ29−12−ζ29−11−ζ29−10−ζ29−8−ζ29−3−ζ29−2−1−ζ292−ζ293−ζ298−ζ2910−ζ2911−ζ2912−ζ2914 ζ29−14+ζ29−12+ζ29−11+ζ29−10+ζ29−8+ζ29−3+ζ29−2+ζ292+ζ293+ζ298+ζ2910+ζ2911+ζ2912+ζ2914

magma: CharacterTable(G);