Galois group: 16T1672

• Label: 16T1672
• Degree: $16$
• Order: $6144$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• pp-group: no
• Group: $C_4^4:\SL(2,3)$

Group invariants

Abstract group:		$C_4^4:\SL(2,3)$
Order:		$6144=2^{11} \cdot 3$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$16$
Transitive number $t$:		$1672$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,3)(2,4)(5,16,12,6,15,11)(7,14,10)(8,13,9)$, $(1,15,8,4,13,5,2,16,7,3,14,6)(9,11,10,12)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$
$3$:	$C_3$
$6$:	$C_6$
$12$:	$A_4$
$24$:	$A_4\times C_2$, $\SL(2,3)$ x 2
$48$:	16T59
$96$:	$C_2^4:C_6$
$192$:	$C_2\wr A_4$ x 2, 24T291
$384$:	16T726 x 2, 16T729
$768$:	32T34813
$3072$:	48T?

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: $A_4$

Degree 8: $C_2\wr A_4$

Low degree siblings

16T1672 x 7, 32T397446 x 4, 32T397447 x 4, 32T397448 x 4

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

56 x 56 character table

Regular extensions

Data not computed