Properties

Label 20T1030
Order \(7372800\)
n \(20\)
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 $t$ :  $1030$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,16,9,19)(2,15,10,20)(3,18)(4,17)(5,12,8,13)(6,11,7,14), (1,19)(2,20)(3,17,10,14,8,16,5,11)(4,18,9,13,7,15,6,12)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: None

Degree 10: $S_5^2 \wr C_2$

Low degree siblings

20T1022, 20T1026, 20T1031, 32T2713780, 40T171517, 40T171518, 40T171519, 40T171520, 40T171521, 40T171522, 40T171523, 40T171524, 40T171525, 40T171526, 40T171529, 40T171530, 40T171533, 40T171534

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 189 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $7372800=2^{15} \cdot 3^{2} \cdot 5^{2}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.