Group action invariants
| Degree $n$ : | $29$ | |
| Transitive number $t$ : | $2$ | |
| Group : | $D_{29}$ | |
| Parity: | $1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| 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) | |
| $|\Aut(F/K)|$: | $1$ |
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 $ | $2$ | $29$ | $( 1,15,16,20,17, 9,21,27,18,25,10,12,22, 5,28,14,19, 8,26,24,11, 4,13, 7,23, 3, 6, 2,29)$ |
Group invariants
| Order: | $58=2 \cdot 29$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [58, 1] |
| 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
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