Properties

Label 21T36
Degree $21$
Order $4116$
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 $t$:  $36$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,4)(2,3)(5,7)(8,11,14,10,13,9,12)(15,20)(16,19)(17,18), (1,13,17,3,9,16,5,12,15,7,8,21,2,11,20,4,14,19,6,10,18)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$3$:  $C_3$
$12$:  $A_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 7: None

Low degree siblings

28T275, 28T276 x 2, 42T390 x 2, 42T391, 42T406 x 2, 42T407

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 53 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.