Galois Group: 16T1771

• Label: 16T1771
• Order: \(16384\)
• n: \(16\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: Yes

Group action invariants

Degree $n$ :		$16$
Transitive number $t$ :		$1771$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$8$
Generators:		(1,6,10,14,2,5,9,13)(3,15)(4,16)(7,11,8,12), (1,4,14,7,2,3,13,8)(5,16,10,12,6,15,9,11), (1,8,14,3,9,16,5,12,2,7,13,4,10,15,6,11)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 7
4:	$C_4$ x 4, $C_2^2$ x 7
8:	$D_{4}$ x 12, $C_4\times C_2$ x 6, $C_2^3$
16:	$D_4\times C_2$ x 6, $C_2^2:C_4$ x 12, $C_4\times C_2^2$
32:	$C_2^2 \wr C_2$ x 4, $C_2^3 : C_4 $ x 12, $C_2 \times (C_2^2:C_4)$ x 3
64:	$((C_8 : C_2):C_2):C_2$ x 24, 16T76 x 6, 16T79
128:	16T227 x 12, 16T240 x 3
256:	16T502 x 6, 16T581
512:	16T911 x 3
1024:	16T1224
2048:	32T185988
4096:	16T1565
8192:	32T409911

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 8: $((C_8 : C_2):C_2):C_2$

Low degree siblings

16T1771 x 127, 32T723692 x 128, 32T723693 x 128, 32T723694 x 64, 32T723695 x 128, 32T723696 x 128, 32T723697 x 128, 32T723698 x 128, 32T723699 x 128, 32T723700 x 64, 32T723701 x 128, 32T723702 x 128, 32T723703 x 128, 32T723704 x 128, 32T723705 x 128, 32T723706 x 128, 32T723707 x 64, 32T723708 x 64, 32T723709 x 128, 32T723710 x 128, 32T723711 x 128, 32T723712 x 128, 32T723713 x 128, 32T723714 x 128, 32T723715 x 64, 32T723716 x 128, 32T723717 x 64, 32T723718 x 128, 32T723719 x 128, 32T723720 x 128, 32T723721 x 128, 32T723722 x 64, 32T723723 x 128, 32T723724 x 128, 32T723725 x 64, 32T723726 x 128, 32T723727 x 128, 32T723728 x 64, 32T723729 x 128, 32T723730 x 64, 32T723731 x 128, 32T723732 x 128, 32T723733 x 128, 32T723734 x 64, 32T723735 x 64, 32T723736 x 64, 32T723737 x 128, 32T723738 x 128, 32T723739 x 128, 32T723740 x 128, 32T723741 x 64, 32T723742 x 128, 32T723743 x 64, 32T723744 x 128, 32T723745 x 128, 32T723746 x 64, 32T723747 x 64, 32T723748 x 64, 32T723749 x 128, 32T723750 x 128, 32T723751 x 64, 32T723752 x 64, 32T723753 x 128, 32T723754 x 128, 32T723755 x 64, 32T723756 x 64, 32T723757 x 128, 32T723758 x 128, 32T723759 x 128, 32T723760 x 64, 32T723761 x 128, 32T723762 x 128, 32T723763 x 64, 32T723764 x 64, 32T723765 x 64, 32T723766 x 64, 32T723767 x 64, 32T723768 x 64, 32T723769 x 64, 32T723770 x 64, 32T727447 x 64

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:		$16384=2^{14}$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		Data not available

Character table: Data not available.