Properties

Label 22T53
Order \(81749606400\)
n \(22\)
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 $t$ :  $53$
CHM label :  $t22n53$
Parity:  $-1$
Primitive:  No
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)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $V_4$
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:  Data not available
Character table: Data not available.