Properties

Label 29T2
Order \(58\)
n \(29\)
Cyclic No
Abelian No
Solvable Yes
Primitive Yes
$p$-group No
Group: $D_{29}$

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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 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 $ $1$ $1$ $()$
$ 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