Properties

Label 20T538
Order \(25600\)
n \(20\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $20$
Transitive number $t$ :  $538$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,6,10,13,18,2,5,9,14,17)(3,11,19,8,16,4,12,20,7,15), (1,19,17,15,14,11,9,7,6,4)(2,20,18,16,13,12,10,8,5,3)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
5:  $C_5$
10:  $D_{5}$, $C_{10}$ x 3
20:  $D_{10}$, 20T3
50:  $D_5\times C_5$
100:  20T24
12800:  20T455

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: None

Degree 10: $D_5\times C_5$

Low degree siblings

20T538 x 2, 40T14314 x 3, 40T14332 x 3, 40T14334 x 6, 40T14336 x 12

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 88 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $25600=2^{10} \cdot 5^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.