Properties

Label 15T104
Order \(1307674368000\)
n \(15\)
Cyclic No
Abelian No
Solvable No
Primitive Yes
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $15$
Transitive number $t$ :  $104$
CHM label :  $S15$
Parity:  $-1$
Primitive:  Yes
Generators:  (1,2), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
$|\Aut(F/K)|$:  $1$

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:  Data not available
Character table: Data not available.