Properties

Label 18T913
Order \(725760\)
n \(18\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $18$
Transitive number $t$ :  $913$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,3,12,8,15,18)(2,4,11,7,16,17)(5,14,10,6,13,9), (1,5,10,12,7,4,15,17)(2,6,9,11,8,3,16,18)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
362880:  $S_9$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: None

Degree 6: None

Degree 9: $S_9$

Low degree siblings

18T913

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 60 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $725760=2^{8} \cdot 3^{4} \cdot 5 \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.