Properties

Label 21T45
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 $t$ :  $45$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,17,9,6,20,11)(2,19,8,5,18,12)(3,21,14,4,16,13)(7,15,10), (1,5,2,6,3,7,4)(8,13,11,9,14,12,10)(15,19)(16,18)(20,21)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
6:  $C_6$
12:  $A_4$
24:  $A_4\times C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 7: None

Low degree siblings

28T349, 28T350 x 2, 42T533, 42T534, 42T535 x 2, 42T536 x 2, 42T537, 42T545 x 2, 42T546

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 55 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.