Properties

Label 22T45
Order \(39916800\)
n \(22\)
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)
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)
$|\Aut(F/K)|$:  $2$

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:  Data not available
Character table: Data not available.