Properties

Label 16T1905
Order \(294912\)
n \(16\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $16$
Transitive number $t$ :  $1905$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,11,3,13,16,9,2,12,4,14,15,10)(5,8)(6,7), (1,16,3)(2,15,4)(7,12,13,9,8,11,14,10), (1,3)(2,4)(5,16,6,15)(7,12,13,9,8,11,14,10)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 7
4:  $C_2^2$ x 7
8:  $D_{4}$ x 6, $C_2^3$
16:  $D_4\times C_2$ x 3
32:  $C_2^2 \wr C_2$
72:  $C_3^2:D_4$
144:  12T77
288:  12T125
1152:  $S_4\wr C_2$
2304:  12T235
4608:  12T260
73728:  16T1864
147456:  32T2077237

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 8: $S_4\wr C_2$

Low degree siblings

16T1905 x 15, 32T2265666 x 8, 32T2265667 x 8, 32T2265668 x 8, 32T2265669 x 8, 32T2265670 x 8, 32T2265671 x 8, 32T2265672 x 8, 32T2265673 x 8, 32T2265674 x 8, 32T2265675 x 8, 32T2265676 x 8, 32T2265677 x 8, 32T2265678 x 8, 32T2265679 x 8, 32T2265680 x 8, 32T2265730 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 230 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $294912=2^{15} \cdot 3^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.