Properties

Label 16T1852
Order \(49152\)
n \(16\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $16$
Transitive number $t$ :  $1852$
Parity:  $1$
Primitive:  No
Generators:  (1,6,3,15,10,14,11,8)(2,5,4,16,9,13,12,7), (1,9)(2,10)(3,5,15)(4,6,16)(7,11,13)(8,12,14)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $V_4$
6:  $S_3$
12:  $D_{6}$
24:  $S_4$ x 3
48:  $S_4\times C_2$ x 3
96:  $V_4^2:S_3$
192:  $C_2^3:S_4$ x 2, $V_4^2:(S_3\times C_2)$ x 2, 12T100
384:  $C_2 \wr S_4$ x 2, 16T747
768:  16T1068
1536:  24T3293, 24T3382 x 2
3072:  16T1521 x 2, 16T1538
6144:  32T397650
24576:  48T?

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: $S_4$

Degree 8: $C_2 \wr S_4$

Low degree siblings

16T1848 x 4, 16T1852 x 3, 32T1515637 x 2, 32T1515638 x 2, 32T1515639 x 4, 32T1515640 x 2, 32T1515641 x 2, 32T1515642 x 2, 32T1515643 x 2, 32T1515664 x 2, 32T1515665 x 2, 32T1515666 x 2, 32T1515667 x 2, 32T1515668 x 2, 32T1515669 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 116 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $49152=2^{14} \cdot 3$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.