Properties

Label 29T6
Order \(812\)
n \(29\)
Cyclic No
Abelian No
Solvable Yes
Primitive Yes
$p$-group No
Group: $F_{29}$

Related objects

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Group action invariants

Degree $n$ :  $29$
Transitive number $t$ :  $6$
Group :  $F_{29}$
Parity:  $-1$
Primitive:  Yes
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29), (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:  $C_2$
4:  $C_4$
7:  $C_7$
14:  $C_{14}$
28:  $C_{28}$

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

Group invariants

Order:  $812=2^{2} \cdot 7 \cdot 29$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [812, 7]
Character table: Data not available.