↑

Properties

Label 16T1581
Order \(4096\)
n \(16\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group Yes

Related objects

Learn more about

Group action invariants

Degree $n$ :  $16$
Transitive number $t$ :  $1581$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $6$
Generators:  (1,2)(7,8), (1,15)(2,16)(3,5,4,6)(7,12)(8,11)(9,14)(10,13), (1,10)(2,9)(3,12,4,11)(5,13,6,14)(7,15)(8,16), (7,9,8,10)(11,14)(12,13)
$|\Aut(F/K)|$:  $2$

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$ x 3

Degree 8: $C_2^2 \wr C_2$

Low degree siblings

16T1556 x 8, 16T1581 x 7, 16T1624 x 16, 32T206997 x 4, 32T206998 x 8, 32T206999 x 4, 32T207000 x 4, 32T207001 x 8, 32T207002 x 4, 32T207003 x 8, 32T207004 x 8, 32T207005 x 4, 32T207006 x 8, 32T207007 x 4, 32T207354 x 16, 32T207355 x 8, 32T207356 x 8, 32T207357 x 8, 32T207358 x 4, 32T207359 x 4, 32T207360 x 8, 32T207361 x 8, 32T207362 x 8, 32T207363 x 4, 32T207364 x 8, 32T207365 x 8, 32T207366 x 8, 32T207367 x 8, 32T207368 x 8, 32T207369 x 4, 32T207370 x 4, 32T207371 x 4, 32T207976 x 8, 32T207977 x 8, 32T207978 x 8, 32T207979 x 8, 32T207980 x 8, 32T207981 x 8, 32T207982 x 8, 32T207983 x 8, 32T207984 x 8, 32T207985 x 8, 32T207986 x 8, 32T207987 x 8, 32T207988 x 8, 32T207989 x 8, 32T220700 x 4, 32T245907 x 2, 32T245925 x 2, 32T245963 x 4, 32T246016 x 4, 32T248524 x 4, 32T248666 x 4, 32T248687 x 4, 32T249553 x 4, 32T249556 x 4, 32T249583 x 4, 32T303602 x 4, 32T311747 x 4, 32T313917 x 4, 32T313946 x 4, 32T313947 x 4, 32T314049 x 4, 32T314144 x 4, 32T321570 x 2, 32T321593 x 4, 32T327812 x 2, 32T327831 x 2, 32T375035 x 4, 32T389465 x 2, 32T389475 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 94 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4096=2^{12}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.