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Properties

Label 29T1
Degree $29$
Order $29$
Cyclic yes
Abelian yes
Solvable yes
Primitive yes
$p$-group yes
Group: $C_{29}$

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Show commands: Magma

magma: G := TransitiveGroup(29, 1);
 

Group action invariants

Degree $n$:  $29$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $1$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{29}$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $29$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (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

none

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

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $29$ (is prime)
magma: Order(G);
 
Cyclic:  yes
magma: IsCyclic(G);
 
Abelian:  yes
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:  $1$
Label:  29.1
magma: IdentifyGroup(G);
 
Character table:

1A 29A1 29A-1 29A2 29A-2 29A3 29A-3 29A4 29A-4 29A5 29A-5 29A6 29A-6 29A7 29A-7 29A8 29A-8 29A9 29A-9 29A10 29A-10 29A11 29A-11 29A12 29A-12 29A13 29A-13 29A14 29A-14
Size 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
29 P 1A 29A-1 29A-14 29A8 29A1 29A12 29A-10 29A-3 29A4 29A11 29A-12 29A10 29A3 29A-4 29A-11 29A-5 29A2 29A9 29A-13 29A6 29A5 29A-2 29A-9 29A13 29A-6 29A7 29A14 29A-8 29A-7
Type
29.1.1a R 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
29.1.1b1 C 1 ζ29−14 ζ2914 ζ29 ζ29−1 ζ29−13 ζ2913 ζ292 ζ29−2 ζ29−12 ζ2912 ζ293 ζ29−3 ζ29−11 ζ2911 ζ294 ζ29−4 ζ29−10 ζ2910 ζ295 ζ29−5 ζ29−9 ζ299 ζ296 ζ29−6 ζ29−8 ζ298 ζ297 ζ29−7
29.1.1b2 C 1 ζ2914 ζ29−14 ζ29−1 ζ29 ζ2913 ζ29−13 ζ29−2 ζ292 ζ2912 ζ29−12 ζ29−3 ζ293 ζ2911 ζ29−11 ζ29−4 ζ294 ζ2910 ζ29−10 ζ29−5 ζ295 ζ299 ζ29−9 ζ29−6 ζ296 ζ298 ζ29−8 ζ29−7 ζ297
29.1.1b3 C 1 ζ29−13 ζ2913 ζ293 ζ29−3 ζ29−10 ζ2910 ζ296 ζ29−6 ζ29−7 ζ297 ζ299 ζ29−9 ζ29−4 ζ294 ζ2912 ζ29−12 ζ29−1 ζ29 ζ29−14 ζ2914 ζ292 ζ29−2 ζ29−11 ζ2911 ζ295 ζ29−5 ζ29−8 ζ298
29.1.1b4 C 1 ζ2913 ζ29−13 ζ29−3 ζ293 ζ2910 ζ29−10 ζ29−6 ζ296 ζ297 ζ29−7 ζ29−9 ζ299 ζ294 ζ29−4 ζ29−12 ζ2912 ζ29 ζ29−1 ζ2914 ζ29−14 ζ29−2 ζ292 ζ2911 ζ29−11 ζ29−5 ζ295 ζ298 ζ29−8
29.1.1b5 C 1 ζ29−12 ζ2912 ζ295 ζ29−5 ζ29−7 ζ297 ζ2910 ζ29−10 ζ29−2 ζ292 ζ29−14 ζ2914 ζ293 ζ29−3 ζ29−9 ζ299 ζ298 ζ29−8 ζ29−4 ζ294 ζ2913 ζ29−13 ζ29 ζ29−1 ζ29−11 ζ2911 ζ296 ζ29−6
29.1.1b6 C 1 ζ2912 ζ29−12 ζ29−5 ζ295 ζ297 ζ29−7 ζ29−10 ζ2910 ζ292 ζ29−2 ζ2914 ζ29−14 ζ29−3 ζ293 ζ299 ζ29−9 ζ29−8 ζ298 ζ294 ζ29−4 ζ29−13 ζ2913 ζ29−1 ζ29 ζ2911 ζ29−11 ζ29−6 ζ296
29.1.1b7 C 1 ζ29−11 ζ2911 ζ297 ζ29−7 ζ29−4 ζ294 ζ2914 ζ29−14 ζ293 ζ29−3 ζ29−8 ζ298 ζ2910 ζ29−10 ζ29−1 ζ29 ζ29−12 ζ2912 ζ296 ζ29−6 ζ29−5 ζ295 ζ2913 ζ29−13 ζ292 ζ29−2 ζ29−9 ζ299
29.1.1b8 C 1 ζ2911 ζ29−11 ζ29−7 ζ297 ζ294 ζ29−4 ζ29−14 ζ2914 ζ29−3 ζ293 ζ298 ζ29−8 ζ29−10 ζ2910 ζ29 ζ29−1 ζ2912 ζ29−12 ζ29−6 ζ296 ζ295 ζ29−5 ζ29−13 ζ2913 ζ29−2 ζ292 ζ299 ζ29−9
29.1.1b9 C 1 ζ29−10 ζ2910 ζ299 ζ29−9 ζ29−1 ζ29 ζ29−11 ζ2911 ζ298 ζ29−8 ζ29−2 ζ292 ζ29−12 ζ2912 ζ297 ζ29−7 ζ29−3 ζ293 ζ29−13 ζ2913 ζ296 ζ29−6 ζ29−4 ζ294 ζ29−14 ζ2914 ζ295 ζ29−5
29.1.1b10 C 1 ζ2910 ζ29−10 ζ29−9 ζ299 ζ29 ζ29−1 ζ2911 ζ29−11 ζ29−8 ζ298 ζ292 ζ29−2 ζ2912 ζ29−12 ζ29−7 ζ297 ζ293 ζ29−3 ζ2913 ζ29−13 ζ29−6 ζ296 ζ294 ζ29−4 ζ2914 ζ29−14 ζ29−5 ζ295
29.1.1b11 C 1 ζ29−9 ζ299 ζ2911 ζ29−11 ζ292 ζ29−2 ζ29−7 ζ297 ζ2913 ζ29−13 ζ294 ζ29−4 ζ29−5 ζ295 ζ29−14 ζ2914 ζ296 ζ29−6 ζ29−3 ζ293 ζ29−12 ζ2912 ζ298 ζ29−8 ζ29−1 ζ29 ζ29−10 ζ2910
29.1.1b12 C 1 ζ299 ζ29−9 ζ29−11 ζ2911 ζ29−2 ζ292 ζ297 ζ29−7 ζ29−13 ζ2913 ζ29−4 ζ294 ζ295 ζ29−5 ζ2914 ζ29−14 ζ29−6 ζ296 ζ293 ζ29−3 ζ2912 ζ29−12 ζ29−8 ζ298 ζ29 ζ29−1 ζ2910 ζ29−10
29.1.1b13 C 1 ζ29−8 ζ298 ζ2913 ζ29−13 ζ295 ζ29−5 ζ29−3 ζ293 ζ29−11 ζ2911 ζ2910 ζ29−10 ζ292 ζ29−2 ζ29−6 ζ296 ζ29−14 ζ2914 ζ297 ζ29−7 ζ29−1 ζ29 ζ29−9 ζ299 ζ2912 ζ29−12 ζ294 ζ29−4
29.1.1b14 C 1 ζ298 ζ29−8 ζ29−13 ζ2913 ζ29−5 ζ295 ζ293 ζ29−3 ζ2911 ζ29−11 ζ29−10 ζ2910 ζ29−2 ζ292 ζ296 ζ29−6 ζ2914 ζ29−14 ζ29−7 ζ297 ζ29 ζ29−1 ζ299 ζ29−9 ζ29−12 ζ2912 ζ29−4 ζ294
29.1.1b15 C 1 ζ29−7 ζ297 ζ29−14 ζ2914 ζ298 ζ29−8 ζ29 ζ29−1 ζ29−6 ζ296 ζ29−13 ζ2913 ζ299 ζ29−9 ζ292 ζ29−2 ζ29−5 ζ295 ζ29−12 ζ2912 ζ2910 ζ29−10 ζ293 ζ29−3 ζ29−4 ζ294 ζ29−11 ζ2911
29.1.1b16 C 1 ζ297 ζ29−7 ζ2914 ζ29−14 ζ29−8 ζ298 ζ29−1 ζ29 ζ296 ζ29−6 ζ2913 ζ29−13 ζ29−9 ζ299 ζ29−2 ζ292 ζ295 ζ29−5 ζ2912 ζ29−12 ζ29−10 ζ2910 ζ29−3 ζ293 ζ294 ζ29−4 ζ2911 ζ29−11
29.1.1b17 C 1 ζ29−6 ζ296 ζ29−12 ζ2912 ζ2911 ζ29−11 ζ295 ζ29−5 ζ29−1 ζ29 ζ29−7 ζ297 ζ29−13 ζ2913 ζ2910 ζ29−10 ζ294 ζ29−4 ζ29−2 ζ292 ζ29−8 ζ298 ζ29−14 ζ2914 ζ299 ζ29−9 ζ293 ζ29−3
29.1.1b18 C 1 ζ296 ζ29−6 ζ2912 ζ29−12 ζ29−11 ζ2911 ζ29−5 ζ295 ζ29 ζ29−1 ζ297 ζ29−7 ζ2913 ζ29−13 ζ29−10 ζ2910 ζ29−4 ζ294 ζ292 ζ29−2 ζ298 ζ29−8 ζ2914 ζ29−14 ζ29−9 ζ299 ζ29−3 ζ293
29.1.1b19 C 1 ζ29−5 ζ295 ζ29−10 ζ2910 ζ2914 ζ29−14 ζ299 ζ29−9 ζ294 ζ29−4 ζ29−1 ζ29 ζ29−6 ζ296 ζ29−11 ζ2911 ζ2913 ζ29−13 ζ298 ζ29−8 ζ293 ζ29−3 ζ29−2 ζ292 ζ29−7 ζ297 ζ29−12 ζ2912
29.1.1b20 C 1 ζ295 ζ29−5 ζ2910 ζ29−10 ζ29−14 ζ2914 ζ29−9 ζ299 ζ29−4 ζ294 ζ29 ζ29−1 ζ296 ζ29−6 ζ2911 ζ29−11 ζ29−13 ζ2913 ζ29−8 ζ298 ζ29−3 ζ293 ζ292 ζ29−2 ζ297 ζ29−7 ζ2912 ζ29−12
29.1.1b21 C 1 ζ29−4 ζ294 ζ29−8 ζ298 ζ29−12 ζ2912 ζ2913 ζ29−13 ζ299 ζ29−9 ζ295 ζ29−5 ζ29 ζ29−1 ζ29−3 ζ293 ζ29−7 ζ297 ζ29−11 ζ2911 ζ2914 ζ29−14 ζ2910 ζ29−10 ζ296 ζ29−6 ζ292 ζ29−2
29.1.1b22 C 1 ζ294 ζ29−4 ζ298 ζ29−8 ζ2912 ζ29−12 ζ29−13 ζ2913 ζ29−9 ζ299 ζ29−5 ζ295 ζ29−1 ζ29 ζ293 ζ29−3 ζ297 ζ29−7 ζ2911 ζ29−11 ζ29−14 ζ2914 ζ29−10 ζ2910 ζ29−6 ζ296 ζ29−2 ζ292
29.1.1b23 C 1 ζ29−3 ζ293 ζ29−6 ζ296 ζ29−9 ζ299 ζ29−12 ζ2912 ζ2914 ζ29−14 ζ2911 ζ29−11 ζ298 ζ29−8 ζ295 ζ29−5 ζ292 ζ29−2 ζ29−1 ζ29 ζ29−4 ζ294 ζ29−7 ζ297 ζ29−10 ζ2910 ζ29−13 ζ2913
29.1.1b24 C 1 ζ293 ζ29−3 ζ296 ζ29−6 ζ299 ζ29−9 ζ2912 ζ29−12 ζ29−14 ζ2914 ζ29−11 ζ2911 ζ29−8 ζ298 ζ29−5 ζ295 ζ29−2 ζ292 ζ29 ζ29−1 ζ294 ζ29−4 ζ297 ζ29−7 ζ2910 ζ29−10 ζ2913 ζ29−13
29.1.1b25 C 1 ζ29−2 ζ292 ζ29−4 ζ294 ζ29−6 ζ296 ζ29−8 ζ298 ζ29−10 ζ2910 ζ29−12 ζ2912 ζ29−14 ζ2914 ζ2913 ζ29−13 ζ2911 ζ29−11 ζ299 ζ29−9 ζ297 ζ29−7 ζ295 ζ29−5 ζ293 ζ29−3 ζ29 ζ29−1
29.1.1b26 C 1 ζ292 ζ29−2 ζ294 ζ29−4 ζ296 ζ29−6 ζ298 ζ29−8 ζ2910 ζ29−10 ζ2912 ζ29−12 ζ2914 ζ29−14 ζ29−13 ζ2913 ζ29−11 ζ2911 ζ29−9 ζ299 ζ29−7 ζ297 ζ29−5 ζ295 ζ29−3 ζ293 ζ29−1 ζ29
29.1.1b27 C 1 ζ29−1 ζ29 ζ29−2 ζ292 ζ29−3 ζ293 ζ29−4 ζ294 ζ29−5 ζ295 ζ29−6 ζ296 ζ29−7 ζ297 ζ29−8 ζ298 ζ29−9 ζ299 ζ29−10 ζ2910 ζ29−11 ζ2911 ζ29−12 ζ2912 ζ29−13 ζ2913 ζ29−14 ζ2914
29.1.1b28 C 1 ζ29 ζ29−1 ζ292 ζ29−2 ζ293 ζ29−3 ζ294 ζ29−4 ζ295 ζ29−5 ζ296 ζ29−6 ζ297 ζ29−7 ζ298 ζ29−8 ζ299 ζ29−9 ζ2910 ζ29−10 ζ2911 ζ29−11 ζ2912 ζ29−12 ζ2913 ζ29−13 ζ2914 ζ29−14

magma: CharacterTable(G);