Galois Group: 16T1351

• Label: 16T1351
• Order: \(2048\)
• n: \(16\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: Yes

Group action invariants

Degree $n$ :		$16$
Transitive number $t$ :		$1351$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$8$
Generators:		(1,12,5,16,10,3,14,8)(2,11,6,15,9,4,13,7), (3,4)(5,6)(9,10)(11,12)(13,14)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 3
4:	$C_4$ x 2, $C_2^2$
8:	$D_{4}$ x 2, $C_8$ x 2, $C_4\times C_2$
16:	$C_8:C_2$, $C_2^2:C_4$, $C_8\times C_2$
32:	$(C_8:C_2):C_2$, $C_2^3 : C_4 $, $C_2^2 : C_8$
64:	$((C_8 : C_2):C_2):C_2$ x 2, 16T84
128:	16T228
256:	16T565
512:	16T817
1024:	16T1194

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 8: $C_8$

Low degree siblings

16T1351 x 15, 16T1422 x 16, 32T97990 x 16, 32T97991 x 32, 32T97992 x 32, 32T97993 x 64, 32T97994 x 64, 32T97995 x 64, 32T97996 x 32, 32T97997 x 64, 32T97998 x 64, 32T97999 x 64, 32T98000 x 32, 32T98001 x 16, 32T98002 x 32, 32T98003 x 64, 32T98004 x 16, 32T98005 x 32, 32T98006 x 64, 32T98007 x 32, 32T98008 x 8, 32T98009 x 16, 32T98010 x 16, 32T98011 x 32, 32T98012 x 8, 32T98013 x 32, 32T98014 x 16, 32T98015 x 32, 32T98016 x 8, 32T98017 x 8, 32T98018 x 16, 32T98019 x 8, 32T98020 x 16, 32T98021 x 8, 32T98022 x 16, 32T98824 x 8, 32T98825 x 8, 32T98826 x 16, 32T98827 x 16, 32T98828 x 16, 32T98829 x 8, 32T98830 x 8, 32T98831 x 8, 32T98832 x 16, 32T98833 x 8, 32T116544 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 56 conjugacy classes of elements. Data not shown.

Group invariants

Order:		$2048=2^{11}$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		Data not available

Character table: Data not available.