Properties

Label 20T1015
Degree $20$
Order $3932160$
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 $t$:  $1015$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,4,15)(2,3,16)(5,12,13)(6,11,14)(7,20,17,10)(8,19,18,9), (1,12)(2,11)(3,14)(4,13)(5,16)(6,15)(7,19,8,20)(9,18)(10,17), (1,8,4,12,18,13,2,7,3,11,17,14)(5,15)(6,16)(9,19)(10,20)

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
$122880$:  20T799

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

20T1015 x 15, 40T162300 x 8, 40T162378 x 8, 40T162506 x 8, 40T162681 x 8, 40T162682 x 8, 40T162685 x 8, 40T162686 x 8, 40T162820 x 8, 40T162822 x 8, 40T162888 x 8, 40T162890 x 8, 40T163186 x 8, 40T163188 x 8, 40T163195 x 8, 40T163198 x 8

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 506 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $3932160=2^{18} \cdot 3 \cdot 5$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.