Properties

Label 20T799
Degree $20$
Order $122880$
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 $t$:  $799$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $4$
Generators:  (1,2)(3,4)(5,16,6,15)(7,14,8,13)(9,18,12,20)(10,17,11,19), (1,3)(2,4)(5,10)(6,9)(7,11)(8,12)(13,17,14,18)(15,19,16,20), (1,12,8,2,11,7)(3,9,6,4,10,5)(13,18,15,20)(14,17,16,19)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_2^2$ x 7
$8$:  $C_2^3$
$120$:  $S_5$
$240$:  $S_5\times C_2$ x 3
$480$:  20T117
$1920$:  $(C_2^4:A_5) : C_2$ x 3
$3840$:  $C_2 \wr S_5$ x 9
$7680$:  20T368 x 3
$30720$:  20T555
$61440$:  20T664 x 3

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $S_5$

Degree 10: $C_2 \wr S_5$ x 3

Low degree siblings

20T799 x 23, 40T45858 x 6, 40T45918 x 36, 40T45949 x 72, 40T46012 x 36, 40T46027 x 24

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 252 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $122880=2^{13} \cdot 3 \cdot 5$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.