Galois group: 5T3

• Label: 5T3
• Degree: $5$
• Order: $20$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: yes
• $p$-group: no
• Group: $F_5$

Group action invariants

Degree $n$:		$5$
Transitive number $t$:		$3$
Group:		$F_5$
CHM label:		$F(5) = 5:4$
Parity:		$-1$
Primitive:		yes
$\card{\Aut(F/K)}$:		$1$
Generators:		(1,2,3,4,5), (1,2,4,3)

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$
$4$:	$C_4$

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

10T4, 20T5

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Label	Cycle Type	Size	Order	Index	Representative
1A	$1^{5}$	$1$	$1$	$0$	$()$
2A	$2^{2},1$	$5$	$2$	$2$	$(2,5)(3,4)$
4A1	$4,1$	$5$	$4$	$3$	$(2,3,5,4)$
4A-1	$4,1$	$5$	$4$	$3$	$(2,4,5,3)$
5A	$5$	$4$	$5$	$4$	$(1,2,3,4,5)$

Malle's constant $a(G)$:     $1/2$

Group invariants

Order:		$20=2^{2} \cdot 5$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent
Label:		20.3
Character table:

		1A	2A	4A1	4A-1	5A
	Size	1	5	5	5	4
	2 P	1A	1A	2A	2A	5A
	5 P	1A	2A	4A1	4A-1	1A
	Type
20.3.1a	R	$1$	$1$	$1$	$1$	$1$
20.3.1b	R	$1$	$1$	$-1$	$-1$	$1$
20.3.1c1	C	$1$	$-1$	$-i$	$i$	$1$
20.3.1c2	C	$1$	$-1$	$i$	$-i$	$1$
20.3.4a	R	$4$	$0$	$0$	$0$	$-1$