Properties

Label 22T51
Degree $22$
Order $40874803200$
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 $t$:  $51$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,14,5,21,11,7,10)(2,13,6,22,12,8,9)(3,19)(4,20)(15,16)(17,18), (1,17,11,3,13,5,16)(2,18,12,4,14,6,15)(7,19,22,10)(8,20,21,9)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$39916800$:  $S_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $S_{11}$

Low degree siblings

22T50, 44T1749

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 376 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $40874803200=2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.