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Properties

Label 16T1778
Order \(16384\)
n \(16\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group Yes

Related objects

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Group action invariants

Degree $n$ :  $16$
Transitive number $t$ :  $1778$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $7$
Generators:  (1,10,2,9)(3,11)(4,12)(5,13)(6,14)(7,15,8,16), (1,15,2,16)(3,5,4,6)(7,9)(8,10)(11,13)(12,14), (15,16), (1,5,2,6)(9,13)(10,14), (1,5)(2,6)(7,9,11,13)(8,10,12,14)(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: $(((C_4 \times C_2): C_2):C_2):C_2$

Low degree siblings

16T1772 x 16, 16T1778 x 15, 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.