Properties

Label 18T962
Order \(33592320\)
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 $t$ :  $962$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,16,4)(2,18,5)(3,17,6)(7,15)(8,13,9,14), (1,3)(4,13,12,8)(5,15,11,9,6,14,10,7)(16,18,17)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
720:  $S_6$
1440:  $S_6\times C_2$
23040:  30T937
46080:  12T293

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: None

Degree 6: $S_6$

Degree 9: None

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 221 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $33592320=2^{10} \cdot 3^{8} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.