Properties

Label 15T104
Degree $15$
Order $1.308\times 10^{12}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no

Related objects

Learn more about

Group action invariants

Degree $n$:  $15$
Transitive number $t$:  $104$
CHM label:  $S15$
Parity:  $-1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,2), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 5: None

Low degree siblings

30T5467

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 176 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1307674368000=2^{11} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.