Galois group: 24T2864

• Label: 24T2864
• Degree: $24$
• Order: $1296$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2\times C_3^4:D_4$

Group invariants

Abstract group:		$C_2\times C_3^4:D_4$
Order:		$1296=2^{4} \cdot 3^{4}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$24$
Transitive number $t$:		$2864$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,8)(2,7)(3,22,19,5)(4,21,20,6)(9,16,17,24)(10,15,18,23)(11,14)(12,13)$, $(1,22)(2,21)(3,23,19,15,12,8)(4,24,20,16,11,7)(5,18)(6,17)(9,14)(10,13)$, $(1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,23)(8,24)(15,16)(17,18)(19,20)(21,22)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 7
$4$:	$C_2^2$ x 7
$8$:	$D_{4}$ x 2, $C_2^3$
$16$:	$D_4\times C_2$
$72$:	$C_3^2:D_4$ x 4
$144$:	12T77 x 4
$648$:	12T172

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 7

Degree 3: None

Degree 4: $C_2^2$ x 7

Degree 6: None

Degree 8: $C_2^3$

Degree 12: 12T172

Low degree siblings

24T2862 x 6, 24T2864 x 5, 36T2116 x 4, 36T2119 x 4, 36T2121 x 6, 36T2129 x 24, 36T2130 x 24

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

54 x 54 character table

Regular extensions

Data not computed