Properties

Label 20T656
Degree $20$
Order $57600$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $20$
Transitive number $t$:  $656$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,15,9,4,13,20,5,7,17,12)(2,16,10,3,14,19,6,8,18,11), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20), (1,11)(2,12)(3,13,16,9,8,17,19,5)(4,14,15,10,7,18,20,6)

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 2, $C_2^3$
$16$:  $D_4\times C_2$
$28800$:  $S_5^2 \wr C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

Degree 5: None

Degree 10: $S_5^2 \wr C_2$

Low degree siblings

20T655 x 2, 20T656, 24T16043 x 2, 24T16044 x 2, 40T18814 x 2, 40T18815 x 2, 40T18817 x 2, 40T18820 x 2, 40T18822 x 2, 40T18830 x 2, 40T18839, 40T18840

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 70 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $57600=2^{8} \cdot 3^{2} \cdot 5^{2}$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.