Properties

Label 22T41
Order \(887040\)
n \(22\)
Cyclic No
Abelian No
Solvable No
Primitive Yes
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $41$
Parity:  $-1$
Primitive:  Yes
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,15,18,2,9,20,13,21,17,3,4,16)(5,12,22,11,8,14)(6,10,19,7), (1,22,17,12,15)(2,5,8,20,21)(3,16,11,9,7)(4,10,6,13,18)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: None

Low degree siblings

44T405

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

Cycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $1155$ $2$ $( 1,20)( 2, 4)( 3,11)( 5,13)( 6,15)( 7,14)( 8,19)(10,18)$
$ 4, 4, 4, 4, 2, 2, 1, 1 $ $13860$ $4$ $( 1,14,20, 7)( 2,19, 4, 8)( 3,10,11,18)( 5, 6,13,15)(12,21)(17,22)$
$ 8, 8, 4, 1, 1 $ $55440$ $8$ $( 1,19,14, 4,20, 8, 7, 2)( 3,15,10, 5,11, 6,18,13)(12,22,21,17)$
$ 4, 4, 4, 4, 2, 2, 2 $ $9240$ $4$ $( 1, 5,20,13)( 2, 7, 4,14)( 3,15,11, 6)( 8,18,19,10)( 9,16)(12,21)(17,22)$
$ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1 $ $12320$ $3$ $( 1,14,18)( 2,19, 5)( 4, 8,13)( 7,10,20)( 9,21,17)(12,22,16)$
$ 6, 6, 3, 3, 2, 2 $ $36960$ $6$ $( 1,10,14,20,18, 7)( 2,13,19, 4, 5, 8)( 3,11)( 6,15)( 9,17,21)(12,16,22)$
$ 12, 6, 4 $ $73920$ $12$ $( 1, 4,10, 5,14, 8,20, 2,18,13, 7,19)( 3, 6,11,15)( 9,12,17,16,21,22)$
$ 11, 11 $ $80640$ $11$ $( 1,12,21,22, 7,17, 6,14, 9, 4,10)( 2,20,16,11,18,19, 3, 5,13, 8,15)$
$ 5, 5, 5, 5, 1, 1 $ $88704$ $5$ $( 1,15,14,18,11)( 2,22,17, 4,19)( 3,10, 5,12,13)( 7, 9,16,20,21)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $1386$ $2$ $( 1, 4)( 2,14)( 3, 9)( 5,20)( 6, 8)( 7,13)(10,16)(11,17)(12,21)(15,19)(18,22)$
$ 10, 10, 2 $ $88704$ $10$ $( 1,19,14,22,11, 4,15, 2,18,17)( 3,16, 5,21,13, 9,10,20,12, 7)( 6, 8)$
$ 4, 4, 4, 4, 2, 1, 1, 1, 1 $ $13860$ $4$ $( 2,21, 9,11)( 3,17,14,12)( 5,20)( 7,15,22,16)(10,13,19,18)$
$ 8, 8, 4, 2 $ $55440$ $8$ $( 1,15, 7,13,20, 6,14, 5)( 2, 3, 8,18, 4,11,19,10)( 9,16)(12,22,21,17)$
$ 7, 7, 7, 1 $ $63360$ $7$ $( 1,16,15,13, 7,10,21)( 2,17, 3, 8,14,18,11)( 4, 6,22,12, 9, 5,19)$
$ 7, 7, 7, 1 $ $63360$ $7$ $( 1,21,10, 7,13,15,16)( 2,11,18,14, 8, 3,17)( 4,19, 5, 9,12,22, 6)$
$ 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $330$ $2$ $( 2,19)( 3, 6)( 4,17)( 5,11)( 8,22)( 9,18)(12,14)$
$ 6, 6, 3, 3, 2, 1, 1 $ $73920$ $6$ $( 1, 3,10,20,11,18)( 2, 8, 6)( 4,19,15)( 7,14)( 9,22,12,16,17,21)$
$ 14, 7, 1 $ $63360$ $14$ $( 1,10,16,15, 7,20,13)( 2,11,18,14,22, 6,17,19, 5, 9,12, 8, 3, 4)$
$ 14, 7, 1 $ $63360$ $14$ $( 1,15,13,16,20,10, 7)( 2,14,17, 9, 3,11,22,19,12, 4,18, 6, 5, 8)$
$ 4, 4, 4, 4, 2, 2, 1, 1 $ $27720$ $4$ $( 1,22)( 2,16,20, 4)( 3,13,10,15)( 5,19)( 6, 8,17,14)( 7,11, 9,12)$

Group invariants

Order:  $887040=2^{8} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.