Galois group: 45T383

• Label: 45T383
• Degree: $45$
• Order: $5400$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_{15}^2:(C_2\times D_6)$

Group invariants

Abstract group:		$C_{15}^2:(C_2\times D_6)$
Order:		$5400=2^{3} \cdot 3^{3} \cdot 5^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$45$
Transitive number $t$:		$383$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$1$
Generators:		$(1,7,19,36,37,17,10,44,28,26)(2,8,20,34,38,18,11,45,29,27)(3,9,21,35,39,16,12,43,30,25)(4,42)(5,40)(6,41)(13,32)(14,33)(15,31)$, $(1,22,11,15,21,4,28,41,38,31,3,23,10,13,20,5,30,42,37,32,2,24,12,14,19,6,29,40,39,33)(7,16)(8,18)(9,17)(25,44)(26,43)(27,45)(35,36)$, $(4,45)(5,43)(6,44)(7,13)(8,14)(9,15)(16,24)(17,22)(18,23)(25,31)(26,32)(27,33)(34,42)(35,40)(36,41)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 7
$4$:	$C_2^2$ x 7
$6$:	$S_3$ x 2
$8$:	$C_2^3$
$12$:	$D_{6}$ x 6
$24$:	$S_3 \times C_2^2$ x 2
$36$:	$S_3^2$
$72$:	12T37
$108$:	$C_3^2 : D_{6} $
$216$:	18T94
$300$:	$((C_5^2 : C_3):C_2):C_2$
$600$:	30T127
$1800$:	45T212

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 5: None

Degree 9: $C_3^2 : D_{6} $

Degree 15: $((C_5^2 : C_3):C_2):C_2$

Low degree siblings

45T383

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

58 x 58 character table

Regular extensions

Data not computed