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

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.