Galois Group: 16T1741

• Label: 16T1741
• Order: \(8192\)
• n: \(16\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: Yes

Group action invariants

Degree $n$ :		$16$
Transitive number $t$ :		$1741$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$7$
Generators:		(1,3,2,4)(5,7)(6,8)(9,11,14,16)(10,12,13,15), (1,9,4,12,6,13,8,15,2,10,3,11,5,14,7,16), (1,11)(2,12)(3,13,8,10)(4,14,7,9)(5,16,6,15)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 7
4:	$C_2^2$ x 7
8:	$D_{4}$ x 12, $C_2^3$
16:	$D_4\times C_2$ x 6, $Q_8:C_2$
32:	$C_2^2 \wr C_2$ x 3, 16T34 x 3, $C_4^2:C_2$
64:	$(((C_4 \times C_2): C_2):C_2):C_2$ x 6, 32T320
128:	$C_2 \wr C_2\wr C_2$ x 4, 16T342 x 4, 16T350 x 3
256:	32T5807 x 4, 32T6030
512:	16T956, 16T969 x 2
1024:	32T41928
2048:	16T1439
4096:	32T316849

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

Degree 8: $C_2 \wr C_2\wr C_2$

Low degree siblings

16T1741 x 15, 32T400458 x 8, 32T400459 x 8, 32T400460 x 8, 32T400461 x 8, 32T400462 x 8, 32T400463 x 8, 32T400464 x 8, 32T400465 x 8, 32T400466 x 8, 32T400467 x 8, 32T400468 x 8, 32T400469 x 8, 32T400470 x 8, 32T400471 x 8, 32T400472 x 8, 32T408442 x 8, 32T408452 x 8, 32T430886 x 4, 32T430929 x 4, 32T431002 x 4, 32T549304 x 4, 32T549376 x 4, 32T549457 x 4, 32T549561 x 4, 32T549564 x 4, 32T549606 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 95 conjugacy classes of elements. Data not shown.

Group invariants

Order:		$8192=2^{13}$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		Data not available

Character table: Data not available.