Properties

Label 22T8
Order \(484\)
n \(22\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{11}:D_{11}.C_2$

Related objects

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Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $8$
Group :  $C_{11}:D_{11}.C_2$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,8)(2,7)(3,6)(4,5)(9,11)(12,19)(13,18)(14,17)(15,16)(20,22), (1,21,11,15)(2,16,10,20)(3,22,9,14)(4,17,8,19)(5,12,7,13)(6,18)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
4:  $C_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

22T8 x 5, 44T28 x 6

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

Group invariants

Order:  $484=2^{2} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [484, 8]
Character table: Data not available.