Properties

Label 20T654
Order \(57600\)
n \(20\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $20$
Transitive number $t$ :  $654$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,15,9,4)(2,16,10,3)(5,7,6,8)(11,13,12,14)(17,20,18,19), (1,13,10,17)(2,14,9,18)(3,8,15,20,12)(4,7,16,19,11)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_4$ x 2, $C_2^2$
8:  $D_{4}$ x 2, $C_4\times C_2$
16:  $C_2^2:C_4$
28800:  $S_5^2 \wr C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 5: None

Degree 10: $S_5^2 \wr C_2$

Low degree siblings

20T654, 20T657 x 2, 24T16045 x 2, 24T16046 x 2, 40T18813 x 2, 40T18816 x 2, 40T18818 x 2, 40T18819 x 2, 40T18821 x 2, 40T18829 x 2, 40T18841, 40T18842

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:  Data not available
Character table: Data not available.