Galois Group: 16T1775

• Label: 16T1775
• Order: \(16384\)
• n: \(16\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: Yes

Group action invariants

Degree $n$ :		$16$
Transitive number $t$ :		$1775$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$8$
Generators:		(1,14,2,13)(3,4)(5,9)(6,10)(7,15,8,16), (15,16), (1,3,6,7,9,11,13,15,2,4,5,8,10,12,14,16), (1,10,2,9)(7,16,8,15)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 15
4:	$C_2^2$ x 35
8:	$D_{4}$ x 20, $C_2^3$ x 15
16:	$D_4\times C_2$ x 30, $C_2^4$
32:	$C_2^2 \wr C_2$ x 8, $C_2^3 : D_4 $ x 2, $C_2^2 \times D_4$ x 5
64:	$(C_4^2 : C_2):C_2$ x 4, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, 16T87, 16T105 x 2, 16T109 x 4
128:	$C_2 \wr C_2\wr C_2$ x 4, 16T245 x 2, 16T265 x 2, 32T1237
256:	16T477 x 2, 16T509 x 2, 16T511, 16T531, 16T538
512:	32T12264 x 2, 32T12969
1024:	16T1177
2048:	32T128074
4096:	16T1556
8192:	32T519843

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

Degree 8: $(C_4^2 : C_2):C_2$

Low degree siblings

16T1775 x 15, 16T1779 x 16, 32T723864 x 8, 32T723865 x 8, 32T723866 x 8, 32T723867 x 8, 32T723868 x 8, 32T723869 x 8, 32T723870 x 8, 32T723871 x 8, 32T723872 x 8, 32T723873 x 8, 32T723874 x 8, 32T723875 x 16, 32T723876 x 8, 32T723877 x 8, 32T723878 x 8, 32T723879 x 8, 32T723880 x 8, 32T723881 x 8, 32T723882 x 8, 32T723883 x 8, 32T723884 x 8, 32T723885 x 8, 32T723886 x 8, 32T723887 x 8, 32T723888 x 8, 32T723889 x 8, 32T723890 x 8, 32T723891 x 8, 32T723892 x 8, 32T723893 x 8, 32T723894 x 8, 32T723986 x 8, 32T723987 x 8, 32T723988 x 8, 32T723989 x 8, 32T723990 x 8, 32T723991 x 8, 32T723992 x 8, 32T723993 x 8, 32T723994 x 8, 32T723995 x 8, 32T723996 x 8, 32T723997 x 8, 32T723998 x 8, 32T723999 x 8, 32T724000 x 8, 32T724001 x 8, 32T724002 x 8, 32T724003 x 8, 32T724004 x 8, 32T724005 x 8, 32T724006 x 8, 32T724007 x 8, 32T724008 x 8, 32T724009 x 8, 32T724010 x 8, 32T724011 x 8, 32T724012 x 8, 32T724013 x 8, 32T724014 x 8, 32T724015 x 8, 32T727404 x 8, 32T728417 x 8, 32T743356 x 4, 32T743433 x 4, 32T743528 x 4, 32T743568 x 4, 32T743678 x 4, 32T743789 x 4, 32T862501 x 4, 32T862596 x 4, 32T873083 x 4, 32T873832 x 4, 32T968027 x 4, 32T968141 x 4, 32T1037995 x 4, 32T1038046 x 4, 32T1061662 x 4, 32T1061665 x 4, 32T1099771 x 4, 32T1099774 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 136 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.