Galois group: 24T2471

• Label: 24T2471
• Degree: $24$
• Order: $768$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2^3:\GL(2,\mathbb{Z}/4)$

Group invariants

Abstract group:		$C_2^3:\GL(2,\mathbb{Z}/4)$
Order:		$768=2^{8} \cdot 3$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$24$
Transitive number $t$:		$2471$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$4$
Generators:		$(1,21,23,19)(2,22,24,20)(3,18,5,16)(4,17,6,15)(7,12,8,11)(9,13,10,14)$, $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$, $(1,9,17)(2,10,18)(3,13,19,6,11,21)(4,14,20,5,12,22)(7,15,24)(8,16,23)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 7
$4$:	$C_2^2$ x 7
$6$:	$S_3$
$8$:	$D_{4}$ x 2, $C_2^3$
$12$:	$D_{6}$ x 3
$16$:	$D_4\times C_2$
$24$:	$S_4$ x 3, $S_3 \times C_2^2$, $(C_6\times C_2):C_2$ x 2
$48$:	$S_4\times C_2$ x 9, 24T25
$96$:	$V_4^2:S_3$, 12T48 x 3, 12T49 x 6
$192$:	12T100 x 3, 24T398 x 3
$384$:	12T135 x 2, 12T139

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $S_3$

Degree 4: None

Degree 6: $S_3$

Degree 8: None

Degree 12: 12T106, 12T135 x 2

Low degree siblings

24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 7, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

Conjugacy classes

Conjugacy classes not computed

Character table

56 x 56 character table

Regular extensions

Data not computed