Properties

Label 22T46
Degree $22$
Order $39916800$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $46$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,5,13,21,19,18,7,16,9,11,4)(2,6,14,22,20,17,8,15,10,12,3), (1,2)(3,4)(5,15,19,14,11,22,7,17,9,6,16,20,13,12,21,8,18,10)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$19958400$:  $A_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: $A_{11}$

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 62 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $39916800=2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.