Properties

Label 21T31
Order \(2058\)
n \(21\)
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)
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)
$|\Aut(F/K)|$:  $1$

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:  Data not available
Character table: Data not available.