Properties

Label 14T57
Degree $14$
Order $645120$
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 $t$:  $57$
CHM label:  $[2^{7}]S(7)$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (3,13,5)(6,12,10), (3,5)(10,12), (7,14), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$5040$:  $S_7$
$10080$:  $S_7\times C_2$
$322560$:  14T54

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 7: $S_7$

Low degree siblings

14T57, 28T1097 x 2, 28T1098, 28T1099 x 2, 42T1778 x 2, 42T1779 x 2

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 110 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $645120=2^{11} \cdot 3^{2} \cdot 5 \cdot 7$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.