Galois group: 20T514

• Label: 20T514
• Degree: $20$
• Order: $20480$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2^9.(C_2\times F_5)$

Group invariants

Abstract group:		$C_2^9.(C_2\times F_5)$
Order:		$20480=2^{12} \cdot 5$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$20$
Transitive number $t$:		$514$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,19,13,16,2,20,14,15)(3,6,12,9)(4,5,11,10)(7,17)(8,18)$, $(1,16,9,3,17,11,6,19,14,7)(2,15,10,4,18,12,5,20,13,8)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_4$ x 2, $C_2^2$
$8$:	$D_{4}$ x 2, $C_4\times C_2$
$16$:	$C_2^2:C_4$
$20$:	$F_5$
$40$:	$F_{5}\times C_2$
$80$:	20T19
$320$:	$(C_2^4 : C_5):C_4$
$640$:	$((C_2^4 : C_5):C_4)\times C_2$
$1280$:	20T191
$10240$:	20T416

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: $F_5$

Degree 10: $F_{5}\times C_2$

Low degree siblings

20T514 x 3, 20T530 x 4, 40T11336 x 4, 40T11339 x 2, 40T11360 x 2, 40T11364 x 2, 40T11373 x 2, 40T11378 x 2, 40T11390 x 4, 40T11391 x 4, 40T12858 x 2, 40T12860 x 4, 40T12876 x 2, 40T12878 x 2, 40T12880 x 2, 40T12988 x 2, 40T12991 x 2, 40T12992 x 4, 40T13368 x 2, 40T13429 x 2, 40T13440 x 4, 40T13454 x 4, 40T13593 x 2, 40T13608 x 2, 40T14049 x 4, 40T14050 x 4, 40T14163 x 2, 40T14167 x 2, 40T14170 x 2, 40T14175 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Conjugacy classes not computed

Character table

74 x 74 character table

Regular extensions

Data not computed