Properties

Label 21T31
Degree $21$
Order $2058$
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 $t$:  $31$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,16,11,4,19,9)(2,17,8,3,18,12)(5,20,13,7,15,14)(6,21,10), (1,12,19,6,11,21,4,10,16,2,9,18,7,8,20,5,14,15,3,13,17)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$14$:  $D_{7}$
$42$:  $F_7$ x 2, 21T3
$294$:  21T16 x 2, 21T19

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 7: None

Low degree siblings

21T31 x 11, 42T268 x 12

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 71 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2058=2 \cdot 3 \cdot 7^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.