Properties

Label 21T139
Degree $21$
Order $11022480$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $21$
Transitive number $t$:  $139$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $3$
Generators:  (1,10,2,12,3,11)(4,17)(5,16)(6,18)(7,21,13)(8,20,14)(9,19,15), (1,4)(2,5)(3,6)(7,18,10,8,16,11,9,17,12)(19,20,21)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$5040$:  $S_7$
$15120$:  21T56
$3674160$:  21T130

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $S_7$

Low degree siblings

21T139, 42T2642 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 429 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $11022480=2^{4} \cdot 3^{9} \cdot 5 \cdot 7$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.