Properties

Label 16T1851
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 $t$ :  $1851$
Parity:  $-1$
Primitive:  No
Generators:  (1,11,14)(2,12,13)(3,5,9)(4,6,10), (1,14,8,10,5,16)(2,13,7,9,6,15)(11,12), (3,6,4,5)(9,10)(11,13,12,14)(15,16)
$|\Aut(F/K)|$:  $2$

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

16T1851 x 7, 32T1515657 x 4, 32T1515658 x 4, 32T1515659 x 4, 32T1515660 x 4, 32T1515661 x 4, 32T1515662 x 4, 32T1515663 x 4

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.