Properties

Label 20T993
Order \(1966080\)
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 $t$ :  $993$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,20,12,9)(2,19,11,10)(3,15,18,14,5,7,4,16,17,13,6,8), (1,2)(3,9,15,13,19,5)(4,10,16,14,20,6)(7,8)(17,18)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
120:  $S_5$
240:  $S_5\times C_2$
1920:  $(C_2^4:A_5) : C_2$ x 3
3840:  $C_2 \wr S_5$ x 3
30720:  20T555
61440:  20T664

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $S_5$

Degree 10: $C_2 \wr S_5$

Low degree siblings

20T993 x 7, 40T153177 x 4, 40T153268 x 4, 40T153392 x 4, 40T153697 x 4, 40T153710 x 4, 40T153804 x 4, 40T153808 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 265 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1966080=2^{17} \cdot 3 \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.