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Properties

Label 14T53
Order \(161280\)
n \(14\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $14$
Transitive number $t$ :  $53$
CHM label :  $[2^{6}]A(7)$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (3,13,5)(6,12,10), (2,9)(7,14), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2520:  $A_7$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 7: $A_7$

Low degree siblings

42T1346, 42T1347

Siblings are shown 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 $ $1$ $1$ $()$
$ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $21$ $2$ $( 6,13)( 7,14)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $35$ $2$ $( 3,10)( 5,12)( 6,13)( 7,14)$
$ 2, 2, 2, 2, 2, 2, 1, 1 $ $7$ $2$ $( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)$
$ 4, 4, 1, 1, 1, 1, 1, 1 $ $420$ $4$ $( 1, 2, 8, 9)( 3,11,10, 4)$
$ 4, 4, 2, 2, 1, 1 $ $1260$ $4$ $( 1, 2, 8, 9)( 3,11,10, 4)( 6,13)( 7,14)$
$ 4, 2, 2, 2, 1, 1, 1, 1 $ $2520$ $4$ $( 1, 2, 8, 9)( 3,11)( 4,10)( 7,14)$
$ 4, 2, 2, 2, 2, 2 $ $840$ $4$ $( 1, 2, 8, 9)( 3,11)( 4,10)( 5,12)( 6,13)( 7,14)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $420$ $2$ $( 1, 9)( 2, 8)( 3,11)( 4,10)$
$ 2, 2, 2, 2, 2, 2, 1, 1 $ $1260$ $2$ $( 1, 9)( 2, 8)( 3,11)( 4,10)( 6,13)( 7,14)$
$ 3, 3, 2, 2, 2, 2 $ $280$ $6$ $( 1, 2, 3)( 4,11)( 5,12)( 6,13)( 7,14)( 8, 9,10)$
$ 3, 3, 2, 2, 1, 1, 1, 1 $ $1680$ $6$ $( 1, 2, 3)( 4,11)( 5,12)( 8, 9,10)$
$ 6, 2, 2, 2, 1, 1 $ $1120$ $6$ $( 1, 2,10, 8, 9, 3)( 4,11)( 5,12)( 6,13)$
$ 6, 2, 1, 1, 1, 1, 1, 1 $ $1120$ $6$ $( 1, 2,10, 8, 9, 3)( 4,11)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ $280$ $3$ $( 1, 2, 3)( 8, 9,10)$
$ 4, 4, 3, 3 $ $3360$ $12$ $( 1, 2, 3)( 4,12,11, 5)( 6,14,13, 7)( 8, 9,10)$
$ 3, 3, 2, 2, 2, 2 $ $3360$ $6$ $( 1, 2, 3)( 4, 5)( 6, 7)( 8, 9,10)(11,12)(13,14)$
$ 6, 4, 2, 2 $ $6720$ $12$ $( 1, 2,10, 8, 9, 3)( 4,12,11, 5)( 6, 7)(13,14)$
$ 6, 3, 3, 2 $ $4480$ $6$ $( 1, 2, 3)( 4,12,13,11, 5, 6)( 7,14)( 8, 9,10)$
$ 3, 3, 3, 3, 1, 1 $ $4480$ $3$ $( 1, 2, 3)( 4,12, 6)( 5,13,11)( 8, 9,10)$
$ 6, 6, 1, 1 $ $4480$ $6$ $( 1, 2,10, 8, 9, 3)( 4,12,13,11, 5, 6)$
$ 6, 3, 3, 2 $ $4480$ $6$ $( 1, 2,10, 8, 9, 3)( 4,12, 6)( 5,13,11)( 7,14)$
$ 8, 2, 2, 2 $ $10080$ $8$ $( 1, 2, 3, 4, 8, 9,10,11)( 5,13)( 6,12)( 7,14)$
$ 8, 4, 1, 1 $ $10080$ $8$ $( 1, 2, 3, 4, 8, 9,10,11)( 5, 6,12,13)$
$ 4, 4, 2, 2, 1, 1 $ $10080$ $4$ $( 1, 2,10,11)( 3, 4, 8, 9)( 5,13)( 6,12)$
$ 4, 4, 4, 2 $ $10080$ $4$ $( 1, 2,10,11)( 3, 4, 8, 9)( 5, 6,12,13)( 7,14)$
$ 5, 5, 1, 1, 1, 1 $ $8064$ $5$ $( 1, 2, 3, 4, 5)( 8, 9,10,11,12)$
$ 5, 5, 2, 2 $ $8064$ $10$ $( 1, 2, 3, 4, 5)( 6,13)( 7,14)( 8, 9,10,11,12)$
$ 10, 2, 1, 1 $ $8064$ $10$ $( 1, 2, 3, 4,12, 8, 9,10,11, 5)( 7,14)$
$ 10, 2, 1, 1 $ $8064$ $10$ $( 1, 2, 3, 4,12, 8, 9,10,11, 5)( 6,13)$
$ 7, 7 $ $23040$ $7$ $( 1, 2, 3, 4, 5, 6, 7)( 8, 9,10,11,12,13,14)$
$ 7, 7 $ $23040$ $7$ $( 1, 2, 3, 4, 5, 7, 6)( 8, 9,10,11,12,14,13)$

Group invariants

Order:  $161280=2^{9} \cdot 3^{2} \cdot 5 \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.