Galois Group: 16T1879

• Label: 16T1879
• Order: \(98304\)
• n: \(16\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: No

Group action invariants

Degree $n$ :		$16$
Transitive number $t$ :		$1879$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(1,6,7,3,10,13,16,12,2,5,8,4,9,14,15,11), (1,15,10,7)(2,16,9,8)(3,6)(4,5)(11,14,12,13), (1,16,12)(2,15,11)(3,9,8)(4,10,7)(5,13)(6,14)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 7
4:	$C_2^2$ x 7
6:	$S_3$
8:	$C_2^3$
12:	$D_{6}$ x 3
24:	$S_4$, $S_3 \times C_2^2$
48:	$S_4\times C_2$ x 3
96:	12T48
192:	$V_4^2:(S_3\times C_2)$ x 3
384:	$C_2 \wr S_4$ x 6, 12T136 x 3
768:	16T1045 x 3
1536:	24T4591
3072:	24T5576 x 3
6144:	16T1664
12288:	32T722139
49152:	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

16T1879 x 15, 32T1832455 x 8, 32T1832456 x 8, 32T1832457 x 8, 32T1832458 x 8, 32T1832459 x 8, 32T1832460 x 8, 32T1832461 x 8, 32T1832462 x 8, 32T1832463 x 8, 32T1832464 x 8, 32T1832465 x 8, 32T1832466 x 8, 32T1832467 x 8, 32T1832468 x 8, 32T1832469 x 8

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 190 conjugacy classes of elements. Data not shown.

Group invariants

Order:		$98304=2^{15} \cdot 3$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		Data not available

Character table: Data not available.