Properties

Label 22T53
Degree $22$
Order $81749606400$
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 $t$:  $53$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,12,4,13,2,11,3,14)(5,7,21,19,6,8,22,20)(9,17)(10,18)(15,16), (1,11,5,4,22,17,20,9)(2,12,6,3,21,18,19,10)(7,16,8,15)(13,14), (1,12,4,20,17,14)(2,11,3,19,18,13)(5,15,8,21,6,16,7,22)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$39916800$:  $S_{11}$
$79833600$:  22T47
$40874803200$:  22T50

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $S_{11}$

Low degree siblings

22T53, 44T1774, 44T1777 x 2, 44T1778 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 752 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $81749606400=2^{19} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.