Properties

Label 21T140
Order \(11022480\)
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 $t$ :  $140$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (4,17,10,9,20,5,16,12,8,19,6,18,11,7,21), (1,16,4,2,18,6)(3,17,5)(7,12,14,9,10,13)(8,11,15)(19,21)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$
2520:  $A_7$
5040:  $A_7\times C_2$
15120:  21T57
3674160:  21T128

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $A_7$

Low degree siblings

21T140, 42T2643 x 2

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:  $11022480=2^{4} \cdot 3^{9} \cdot 5 \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.