Galois Group: 16T1772

• Label: 16T1772
• Order: \(16384\)
• n: \(16\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: Yes

Group action invariants

Degree $n$ :		$16$
Transitive number $t$ :		$1772$
Parity:		$1$
Primitive:		No
Nilpotency class:		$7$
Generators:		(3,11)(4,12)(9,10)(15,16), (1,3,5,16)(2,4,6,15)(7,9,11,14)(8,10,12,13), (1,10)(2,9)(5,6)(11,12), (1,2)(3,4)(5,14,6,13)(15,16), (1,6)(2,5)(3,12)(4,11)(9,13,10,14)(15,16)
$|\Aut(F/K)|$:		$2$

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:	$(((C_4 \times C_2): C_2):C_2):C_2$ x 8, 16T87, 16T105 x 2, 16T109 x 4
128:	$C_2 \wr C_2\wr C_2$ x 4, 16T245 x 4, 32T1237
256:	16T477 x 2, 16T509 x 2, 16T531 x 2, 16T536
512:	32T12264 x 2, 32T13404
1024:	16T1116, 16T1124 x 2
2048:	32T101073
4096:	16T1553
8192:	32T520951

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

16T1772 x 15, 16T1778 x 16, 32T723771 x 8, 32T723772 x 8, 32T723773 x 16, 32T723774 x 8, 32T723775 x 8, 32T723776 x 8, 32T723777 x 8, 32T723778 x 8, 32T723779 x 8, 32T723780 x 8, 32T723781 x 8, 32T723782 x 8, 32T723783 x 8, 32T723784 x 8, 32T723785 x 8, 32T723786 x 8, 32T723787 x 8, 32T723788 x 8, 32T723789 x 8, 32T723790 x 8, 32T723791 x 8, 32T723792 x 8, 32T723793 x 8, 32T723794 x 8, 32T723795 x 8, 32T723796 x 8, 32T723797 x 8, 32T723798 x 8, 32T723799 x 8, 32T723800 x 8, 32T723801 x 8, 32T723956 x 8, 32T723957 x 8, 32T723958 x 8, 32T723959 x 8, 32T723960 x 8, 32T723961 x 8, 32T723962 x 8, 32T723963 x 8, 32T723964 x 8, 32T723965 x 8, 32T723966 x 8, 32T723967 x 8, 32T723968 x 8, 32T723969 x 8, 32T723970 x 8, 32T723971 x 8, 32T723972 x 8, 32T723973 x 8, 32T723974 x 8, 32T723975 x 8, 32T723976 x 8, 32T723977 x 8, 32T723978 x 8, 32T723979 x 8, 32T723980 x 8, 32T723981 x 8, 32T723982 x 8, 32T723983 x 8, 32T723984 x 8, 32T723985 x 8, 32T726862 x 8, 32T726869 x 8, 32T728312 x 8, 32T742372 x 4, 32T742657 x 4, 32T742659 x 4, 32T742677 x 4, 32T742692 x 4, 32T742879 x 4, 32T861570 x 4, 32T861571 x 4, 32T873285 x 4, 32T873590 x 4, 32T968026 x 4, 32T968145 x 4, 32T1037989 x 4, 32T1038052 x 4, 32T1061671 x 4, 32T1061677 x 4, 32T1098185 x 4, 32T1098187 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 148 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.