Properties

Label 21T148
Order \(352719360\)
n \(21\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $148$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,19,5,14,12,8,16,3,21,4,13,10,7,17,2,20,6,15,11,9,18), (1,14,17,12,20,9,4,3,13,16,11,19,8,5,2,15,18,10,21,7,6)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2520:  $A_7$
161280:  14T53

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $A_7$

Low degree siblings

42T4491

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 150 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $352719360=2^{9} \cdot 3^{9} \cdot 5 \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.