Galois group: 24T7644

• Label: 24T7644
• Degree: $24$
• Order: $5184$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_3^4:C_4^2:C_2^2$

Group invariants

Abstract group:		$C_3^4:C_4^2:C_2^2$
Order:		$5184=2^{6} \cdot 3^{4}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$24$
Transitive number $t$:		$7644$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,20)(2,19)(3,9)(4,10)(5,24)(6,23)(7,13)(8,14)(11,18)(12,17)(15,21)(16,22)$, $(1,24,2,23)(3,21,4,22)(5,11,6,12)(7,9,8,10)(13,19,14,20)(15,17,16,18)$, $(9,18)(10,17)(11,19)(12,20)$, $(1,2)(3,4)(5,6)(7,8)(9,10)(11,20)(12,19)(13,21)(14,22)(15,16)(17,18)(23,24)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 15
$4$:	$C_4$ x 8, $C_2^2$ x 35
$8$:	$C_4\times C_2$ x 28, $C_2^3$ x 15
$16$:	$C_4\times C_2^2$ x 14, $C_2^4$
$32$:	$Q_8:C_2^2$ x 2, 32T34
$64$:	16T68
$2592$:	12T242

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 3

Degree 3: None

Degree 4: $C_4$ x 2, $C_2^2$

Degree 6: None

Degree 8: $C_4\times C_2$

Degree 12: 12T242

Low degree siblings

24T7644 x 7, 24T7650 x 8, 36T6055 x 8

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

84 x 84 character table

Regular extensions

Data not computed