Show commands:
Magma
magma: G := TransitiveGroup(29, 2);
Group action invariants
Degree $n$: | $29$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
Transitive number $t$: | $2$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
Group: | $D_{29}$ | ||
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: | (2,16)(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), (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) $2$: $C_2$ 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
Cycle Type | Size | Order | Representative |
$ 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 $ | $1$ | $1$ | $()$ |
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $ | $29$ | $2$ | $( 2,16)( 3,17)( 4,18)( 5,19)( 6,20)( 7,21)( 8,22)( 9,23)(10,24)(11,25)(12,26) (13,27)(14,28)(15,29)$ |
$ 29 $ | $2$ | $29$ | $( 1, 2, 3, 7, 4,24, 8,14, 5,12,25,27, 9,20,15,29, 6,23,13,11,26,19,28,22,10, 18,21,17,16)$ |
$ 29 $ | $2$ | $29$ | $( 1, 3, 4, 8, 5,25, 9,15, 6,13,26,28,10,21,16, 2, 7,24,14,12,27,20,29,23,11, 19,22,18,17)$ |
$ 29 $ | $2$ | $29$ | $( 1, 4, 5, 9, 6,26,10,16, 7,14,27,29,11,22,17, 3, 8,25,15,13,28,21, 2,24,12, 20,23,19,18)$ |
$ 29 $ | $2$ | $29$ | $( 1, 5, 6,10, 7,27,11,17, 8,15,28, 2,12,23,18, 4, 9,26,16,14,29,22, 3,25,13, 21,24,20,19)$ |
$ 29 $ | $2$ | $29$ | $( 1, 6, 7,11, 8,28,12,18, 9,16,29, 3,13,24,19, 5,10,27,17,15, 2,23, 4,26,14, 22,25,21,20)$ |
$ 29 $ | $2$ | $29$ | $( 1, 7, 8,12, 9,29,13,19,10,17, 2, 4,14,25,20, 6,11,28,18,16, 3,24, 5,27,15, 23,26,22,21)$ |
$ 29 $ | $2$ | $29$ | $( 1, 8, 9,13,10, 2,14,20,11,18, 3, 5,15,26,21, 7,12,29,19,17, 4,25, 6,28,16, 24,27,23,22)$ |
$ 29 $ | $2$ | $29$ | $( 1, 9,10,14,11, 3,15,21,12,19, 4, 6,16,27,22, 8,13, 2,20,18, 5,26, 7,29,17, 25,28,24,23)$ |
$ 29 $ | $2$ | $29$ | $( 1,10,11,15,12, 4,16,22,13,20, 5, 7,17,28,23, 9,14, 3,21,19, 6,27, 8, 2,18, 26,29,25,24)$ |
$ 29 $ | $2$ | $29$ | $( 1,11,12,16,13, 5,17,23,14,21, 6, 8,18,29,24,10,15, 4,22,20, 7,28, 9, 3,19, 27, 2,26,25)$ |
$ 29 $ | $2$ | $29$ | $( 1,12,13,17,14, 6,18,24,15,22, 7, 9,19, 2,25,11,16, 5,23,21, 8,29,10, 4,20, 28, 3,27,26)$ |
$ 29 $ | $2$ | $29$ | $( 1,13,14,18,15, 7,19,25,16,23, 8,10,20, 3,26,12,17, 6,24,22, 9, 2,11, 5,21, 29, 4,28,27)$ |
$ 29 $ | $2$ | $29$ | $( 1,14,15,19,16, 8,20,26,17,24, 9,11,21, 4,27,13,18, 7,25,23,10, 3,12, 6,22, 2, 5,29,28)$ |
$ 29 $ | $2$ | $29$ | $( 1,15,16,20,17, 9,21,27,18,25,10,12,22, 5,28,14,19, 8,26,24,11, 4,13, 7,23, 3, 6, 2,29)$ |
magma: ConjugacyClasses(G);
Group invariants
Order: | $58=2 \cdot 29$ | magma: Order(G);
| |
Cyclic: | no | magma: IsCyclic(G);
| |
Abelian: | no | magma: IsAbelian(G);
| |
Solvable: | yes | magma: IsSolvable(G);
| |
Nilpotency class: | not nilpotent | ||
Label: | 58.1 | magma: IdentifyGroup(G);
|
Character table: |
2 1 1 . . . . . . . . . . . . . . 29 1 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1a 2a 29a 29b 29c 29d 29e 29f 29g 29h 29i 29j 29k 29l 29m 29n 2P 1a 1a 29b 29c 29d 29e 29f 29g 29h 29i 29j 29k 29l 29m 29n 29a 3P 1a 2a 29f 29g 29h 29i 29j 29k 29l 29m 29n 29a 29b 29c 29d 29e 5P 1a 2a 29i 29j 29k 29l 29m 29n 29a 29b 29c 29d 29e 29f 29g 29h 7P 1a 2a 29m 29n 29a 29b 29c 29d 29e 29f 29g 29h 29i 29j 29k 29l 11P 1a 2a 29l 29m 29n 29a 29b 29c 29d 29e 29f 29g 29h 29i 29j 29k 13P 1a 2a 29e 29f 29g 29h 29i 29j 29k 29l 29m 29n 29a 29b 29c 29d 17P 1a 2a 29h 29i 29j 29k 29l 29m 29n 29a 29b 29c 29d 29e 29f 29g 19P 1a 2a 29j 29k 29l 29m 29n 29a 29b 29c 29d 29e 29f 29g 29h 29i 23P 1a 2a 29g 29h 29i 29j 29k 29l 29m 29n 29a 29b 29c 29d 29e 29f 29P 1a 2a 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.3 2 . A H L K I C E M J D G B N F X.4 2 . B N F A H L K I C E M J D G X.5 2 . C E M J D G B N F A H L K I X.6 2 . D G B N F A H L K I C E M J X.7 2 . E M J D G B N F A H L K I C X.8 2 . F A H L K I C E M J D G B N X.9 2 . G B N F A H L K I C E M J D X.10 2 . H L K I C E M J D G B N F A X.11 2 . I C E M J D G B N F A H L K X.12 2 . J D G B N F A H L K I C E M X.13 2 . K I C E M J D G B N F A H L X.14 2 . L K I C E M J D G B N F A H X.15 2 . M J D G B N F A H L K I C E X.16 2 . N F A H L K I C E M J D G B A = E(29)+E(29)^28 B = E(29)^11+E(29)^18 C = E(29)^3+E(29)^26 D = E(29)^10+E(29)^19 E = E(29)^6+E(29)^23 F = E(29)^14+E(29)^15 G = E(29)^9+E(29)^20 H = E(29)^2+E(29)^27 I = E(29)^13+E(29)^16 J = E(29)^5+E(29)^24 K = E(29)^8+E(29)^21 L = E(29)^4+E(29)^25 M = E(29)^12+E(29)^17 N = E(29)^7+E(29)^22 |
magma: CharacterTable(G);