Properties

Label 21T62
Degree $21$
Order $16464$
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 $t$:  $62$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,16,6,21,4,19,2,17,7,15,5,20,3,18)(8,10,12,14,9,11,13), (1,9,5,10)(2,11,4,8)(3,13)(6,12,7,14)(15,20,18,16,21,19,17)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$24$:  $S_4$
$48$:  $S_4\times C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

28T414, 42T707, 42T708, 42T709, 42T710, 42T711, 42T712, 42T713, 42T714

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 65 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $16464=2^{4} \cdot 3 \cdot 7^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.