Properties

Label 21T132
Order \(5511240\)
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 $t$ :  $132$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,11,18,8,21)(2,12,16,7,20)(3,10,17,9,19)(13,14,15), (1,14,19,8,16,4,11,2,13,21,7,17,6,12,3,15,20,9,18,5,10)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
2520:  $A_7$
7560:  21T44
1837080:  21T121

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $A_7$

Low degree siblings

21T132

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 246 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $5511240=2^{3} \cdot 3^{9} \cdot 5 \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.