# Properties

 Label 21T45 Order $$8232$$ n $$21$$ Cyclic No Abelian No Solvable Yes Primitive No $p$-group No

# Related objects

## 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.
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