Properties

Label 21T46
Order \(8232\)
n \(21\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $46$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,8,20,7,11,18,6,14,16,5,10,21,4,13,19,3,9,17,2,12,15), (1,5)(2,4)(6,7)(8,16,9,19)(10,15,14,20)(11,18,13,17)(12,21)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$
24:  $S_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

28T347, 42T538, 42T539, 42T540, 42T548

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 70 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $8232=2^{3} \cdot 3 \cdot 7^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.