Galois Group: 15T26

• Label: 15T26
• Order: \(405\)
• n: \(15\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: No
• Group: $C_3^4:C_5$

Group action invariants

Degree $n$ :		$15$
Transitive number $t$ :		$26$
Group :		$C_3^4:C_5$
CHM label :		$[3^{4}]5$
Parity:		$1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(1,6,11)(4,14,9), (1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15)
$|\Aut(F/K)|$:		$3$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
5:	$C_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 5: $C_5$

Low degree siblings

15T26 x 7, 45T61 x 2, 45T62 x 16, 45T63 x 8

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

Cycle Type	Size	Order	Representative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$1$	$1$	$()$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$5$	$3$	$( 4, 9,14)( 5,15,10)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$5$	$3$	$( 4,14, 9)( 5,10,15)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$5$	$3$	$( 3, 8,13)( 5,15,10)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $	$5$	$3$	$( 3, 8,13)( 4, 9,14)( 5,10,15)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$5$	$3$	$( 3,13, 8)( 5,10,15)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $	$5$	$3$	$( 3,13, 8)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $	$5$	$3$	$( 2, 7,12)( 4, 9,14)( 5,10,15)$
$ 3, 3, 3, 3, 1, 1, 1 $	$5$	$3$	$( 2, 7,12)( 3, 8,13)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 3, 1, 1, 1 $	$5$	$3$	$( 2, 7,12)( 3,13, 8)( 4, 9,14)( 5,15,10)$
$ 3, 3, 3, 3, 1, 1, 1 $	$5$	$3$	$( 2, 7,12)( 3,13, 8)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $	$5$	$3$	$( 2,12, 7)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 3, 1, 1, 1 $	$5$	$3$	$( 2,12, 7)( 3, 8,13)( 4, 9,14)( 5,15,10)$
$ 3, 3, 3, 3, 1, 1, 1 $	$5$	$3$	$( 2,12, 7)( 3, 8,13)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 3, 1, 1, 1 $	$5$	$3$	$( 2,12, 7)( 3,13, 8)( 4, 9,14)( 5,10,15)$
$ 5, 5, 5 $	$81$	$5$	$( 1, 2, 3, 4, 5)( 6, 7, 8, 9,10)(11,12,13,14,15)$
$ 5, 5, 5 $	$81$	$5$	$( 1, 3, 5, 2, 4)( 6, 8,10, 7, 9)(11,13,15,12,14)$
$ 5, 5, 5 $	$81$	$5$	$( 1, 4, 2, 5, 3)( 6, 9, 7,10, 8)(11,14,12,15,13)$
$ 5, 5, 5 $	$81$	$5$	$( 1, 5, 4, 3, 2)( 6,10, 9, 8, 7)(11,15,14,13,12)$
$ 3, 3, 3, 3, 3 $	$5$	$3$	$( 1, 6,11)( 2, 7,12)( 3, 8,13)( 4, 9,14)( 5,15,10)$
$ 3, 3, 3, 3, 3 $	$5$	$3$	$( 1, 6,11)( 2,12, 7)( 3,13, 8)( 4,14, 9)( 5,15,10)$

Group invariants

Order:		$405=3^{4} \cdot 5$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		[405, 15]

Character table: Data not available.