Properties

Label 21T146
Order \(28449792\)
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 $t$ :  $146$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,18)(2,17,3,19)(4,20,7,21)(5,16)(6,15)(8,12,11,10)(13,14), (1,6,2)(4,5,7)(8,15,14,16,11,17)(9,21,10,18,12,19)(13,20)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

21T146, 24T24314, 42T3078 x 2, 42T3079 x 2, 42T3080 x 2

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

Conjugacy Classes

There are 98 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $28449792=2^{10} \cdot 3^{4} \cdot 7^{3}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.