Galois group: 18T241

• Label: 18T241
• Degree: $18$
• Order: $972$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_3^3:S_3^2$

Group invariants

Abstract group:		$C_3^3:S_3^2$
Order:		$972=2^{2} \cdot 3^{5}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$18$
Transitive number $t$:		$241$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$3$
Generators:		$(1,18,2,16,3,17)(4,14,6,15,5,13)(7,10,8,11,9,12)$, $(1,17,10,6,15,9,2,18,12,5,13,8,3,16,11,4,14,7)$, $(1,12,14,3,10,13,2,11,15)(4,8,18,5,9,17,6,7,16)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$3$:	$C_3$
$4$:	$C_2^2$
$6$:	$S_3$ x 2, $C_6$ x 3
$12$:	$D_{6}$ x 2, $C_6\times C_2$
$18$:	$S_3\times C_3$ x 2
$36$:	$S_3^2$, $C_6\times S_3$ x 2
$54$:	$C_3^2 : C_6$
$108$:	12T70, 18T41
$162$:	$C_3 \wr S_3 $
$324$:	18T119, 18T121

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $S_3$

Degree 6: $D_{6}$

Degree 9: None

Low degree siblings

18T241 x 2, 27T290 x 3, 36T1501 x 3

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

66 x 66 character table

Regular extensions

Data not computed