Properties

Label 22T45
Degree $22$
Order $39916800$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $45$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,22,20,18,4,7,9,11,5,14)(2,21,19,17,3,8,10,12,6,13)(15,16), (1,4,20,12,9,17,5)(2,3,19,11,10,18,6)(7,15,14)(8,16,13)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: $S_{11}$

Low degree siblings

11T8

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 56 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.