Properties

Label 22T10
Order \(968\)
n \(22\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
8:  $D_{4}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

22T10, 44T39 x 2, 44T40 x 2, 44T41 x 2, 44T44 x 2

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 $ $1$ $1$ $()$
$ 11, 11 $ $4$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 11 $ $4$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 11 $ $4$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,22,16,21,15,20,14,19,13,18)$
$ 11, 11 $ $4$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 11 $ $8$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,18,13,19,14,20,15,21,16,22,17)$
$ 11, 11 $ $8$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11 $ $8$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,13,14,15,16,17,18,19,20,21,22)$
$ 11, 11 $ $8$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11 $ $8$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 11 $ $8$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,13,14,15,16,17,18,19,20,21,22)$
$ 11, 11 $ $8$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,17,22,16,21,15,20,14,19,13,18)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,17,22,16,21,15,20,14,19,13,18)$
$ 11, 11 $ $8$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,19,15,22,18,14,21,17,13,20,16)$
$ 11, 11 $ $8$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 11 $ $8$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,21,19,17,15,13,22,20,18,16,14)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $22$ $2$ $( 1,15)( 2,21)( 3,16)( 4,22)( 5,17)( 6,12)( 7,18)( 8,13)( 9,19)(10,14)(11,20)$
$ 22 $ $44$ $22$ $( 1,19, 9,12, 6,16, 3,20,11,13, 8,17, 5,21, 2,14,10,18, 7,22, 4,15)$
$ 22 $ $44$ $22$ $( 1,12, 6,20,11,17, 5,14,10,22, 4,19, 9,16, 3,13, 8,21, 2,18, 7,15)$
$ 22 $ $44$ $22$ $( 1,20,11,14,10,19, 9,13, 8,18, 7,12, 6,17, 5,22, 4,16, 3,21, 2,15)$
$ 22 $ $44$ $22$ $( 1,14,10,13, 8,12, 6,22, 4,21, 2,20,11,19, 9,18, 7,17, 5,16, 3,15)$
$ 22 $ $44$ $22$ $( 1,13, 8,22, 4,20,11,18, 7,16, 3,14,10,12, 6,21, 2,19, 9,17, 5,15)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $121$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)$
$ 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $22$ $2$ $(13,22)(14,21)(15,20)(16,19)(17,18)$
$ 11, 2, 2, 2, 2, 2, 1 $ $44$ $22$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,14)(15,22)(16,21)(17,20)(18,19)$
$ 11, 2, 2, 2, 2, 2, 1 $ $44$ $22$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,16)(13,15)(17,22)(18,21)(19,20)$
$ 11, 2, 2, 2, 2, 2, 1 $ $44$ $22$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,20)(13,19)(14,18)(15,17)(21,22)$
$ 11, 2, 2, 2, 2, 2, 1 $ $44$ $22$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17)(13,16)(14,15)(18,22)(19,21)$
$ 11, 2, 2, 2, 2, 2, 1 $ $44$ $22$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22)(13,21)(14,20)(15,19)(16,18)$
$ 4, 4, 4, 4, 4, 2 $ $242$ $4$ $( 1,15,11,20)( 2,21,10,14)( 3,16, 9,19)( 4,22, 8,13)( 5,17, 7,18)( 6,12)$

Group invariants

Order:  $968=2^{3} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [968, 36]
Character table: Data not available.