Properties

Label 12T293
Degree $12$
Order $46080$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $12$
Transitive number $t$:  $293$
CHM label:  $[2^{6}]S(6)=2wrS(6)$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,12), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,3)(2,12)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$720$:  $S_6$
$1440$:  $S_6\times C_2$
$23040$:  30T937

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: None

Degree 4: None

Degree 6: $S_6$

Low degree siblings

12T293 x 3, 24T14632 x 2, 24T14633 x 2, 24T14634 x 2, 40T18563 x 2, 40T18564 x 2, 40T18573 x 2, 40T18579 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 65 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $46080=2^{10} \cdot 3^{2} \cdot 5$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.