Properties

Label 20T887
Degree $20$
Order $245760$
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 $t$:  $887$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,18,5,14,10,2,17,6,13,9)(3,19,12,8,16)(4,20,11,7,15), (1,16,13,7,2,15,14,8)(3,18,11,6)(4,17,12,5)(9,20)(10,19), (1,9,17,13,2,10,18,14)(3,12,20,8)(4,11,19,7)(5,6)

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, $C_2^3$
$16$:  $D_4\times C_2$
$120$:  $S_5$
$240$:  $S_5\times C_2$ x 3
$480$:  20T117
$960$:  20T174
$1920$:  $(C_2^4:A_5) : C_2$
$3840$:  $C_2 \wr S_5$ x 3
$7680$:  20T368
$15360$:  20T466
$61440$:  20T667
$122880$:  20T794

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: $S_5$

Degree 10: $S_5\times C_2$

Low degree siblings

20T886 x 4, 20T887 x 3, 40T106464 x 4, 40T106465 x 4, 40T106491 x 2, 40T106516 x 2, 40T106517 x 2, 40T106549 x 4, 40T106550 x 4, 40T106551 x 4, 40T106552 x 4, 40T106571 x 2, 40T106600 x 2, 40T106608 x 2, 40T106662 x 2, 40T106669 x 2, 40T106672 x 4, 40T106674 x 4, 40T106757 x 2, 40T106759 x 2, 40T106762 x 2, 40T106766 x 2, 40T106771 x 4, 40T106826 x 4, 40T106827 x 4, 40T106828 x 4, 40T106829 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 201 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $245760=2^{14} \cdot 3 \cdot 5$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.