Galois group: 36T3430

• Label: 36T3430
• Degree: $36$
• Order: $2304$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• pp-group: no
• Group: $C_2^4:A_4^2$

Group action invariants

Degree $n$:		$36$
Transitive number $t$:		$3430$
Group:		$C_2^4:A_4^2$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$4$
Generators:		(1,22,28)(2,21,27)(3,24,25)(4,23,26)(5,16,32,7,13,29)(6,15,31,8,14,30)(9,20,36,10,19,35)(11,18,34,12,17,33), (1,17,30,2,18,29)(3,19,31,4,20,32)(5,24,34)(6,23,33)(7,22,36)(8,21,35)(9,16,27,12,14,25)(10,15,28,11,13,26)

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$3$:	$C_3$ x 4
$4$:	$C_2^2$
$6$:	$C_6$ x 12
$9$:	$C_3^2$
$12$:	$A_4$ x 3, $C_6\times C_2$ x 4
$18$:	$C_6 \times C_3$ x 3
$24$:	$A_4\times C_2$ x 9
$36$:	$C_3\times A_4$ x 3, 36T4
$48$:	$C_2^2 \times A_4$ x 3
$72$:	18T25 x 9
$144$:	12T85 x 3, 36T103 x 3
$288$:	18T109 x 9
$576$:	12T164, 36T718 x 3
$1152$:	18T263 x 3

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $C_3$ x 4

Degree 4: None

Degree 6: None

Degree 9: $C_3^2$

Degree 12: None

Degree 18: 18T263 x 3

Low degree siblings

36T3047 x 9, 36T3140 x 54, 36T3141 x 54, 36T3358 x 54, 36T3359 x 18, 36T3360 x 54, 36T3361 x 108, 36T3429 x 6, 36T3430 x 17

Siblings are shown with degree $\leq 47$

A number field with this Galois group has 2 arithmetically equivalent fields.

Conjugacy classes

Conjugacy classes not computed

Group invariants

Order:		$2304=2^{8} \cdot 3^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent
Label:		2304.ii
Character table:		96 x 96 character table