Properties

Label 21T37
Degree $21$
Order $4116$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $21$
Transitive number $t$:  $37$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,3,5,7,2,4,6)(8,21,9,18,10,15,11,19,12,16,13,20,14,17), (1,10,15,6,8,16)(2,11,18,5,14,20)(3,12,21,4,13,17)(7,9,19)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$14$:  $D_{7}$
$28$:  $D_{14}$
$84$:  21T8
$588$:  14T25

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

21T37 x 5, 42T392 x 6, 42T393 x 6, 42T394 x 6, 42T400 x 3, 42T401 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 79 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4116=2^{2} \cdot 3 \cdot 7^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.