Properties

Label 22T19
Order \(4840\)
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 $t$ :  $19$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,2,6,11,9)(3,10,5,7,4)(13,15,21,17,16)(14,18,19,22,20), (1,14,5,20)(2,21,4,13)(3,17)(6,16,11,18)(7,12,10,22)(8,19,9,15), (1,5)(2,4)(6,11)(7,10)(8,9)(12,15,18,21,13,16,19,22,14,17,20)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
8:  $D_{4}$
10:  $D_{5}$
20:  $D_{10}$
40:  20T7

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

44T81, 44T82, 44T83

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 $ $20$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 11 $ $20$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 11 $ $20$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11 $ $20$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,17,22,16,21,15,20,14,19,13,18)$
$ 11, 11 $ $20$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $20$ $11$ $(12,16,20,13,17,21,14,18,22,15,19)$
$ 5, 5, 5, 5, 1, 1 $ $242$ $5$ $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(13,15,21,17,16)(14,18,19,22,20)$
$ 5, 5, 5, 5, 1, 1 $ $242$ $5$ $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(13,21,16,15,17)(14,19,20,18,22)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $121$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)$
$ 10, 10, 1, 1 $ $242$ $10$ $( 2, 8, 6, 3, 4,11, 5, 7,10, 9)(13,20,21,18,16,22,15,14,17,19)$
$ 10, 10, 1, 1 $ $242$ $10$ $( 2, 7, 4, 8,10,11, 6, 9, 5, 3)(13,14,16,20,17,22,21,19,15,18)$
$ 4, 4, 4, 4, 4, 2 $ $1210$ $4$ $( 1,14, 5,20)( 2,21, 4,13)( 3,17)( 6,16,11,18)( 7,12,10,22)( 8,19, 9,15)$
$ 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 $ $220$ $22$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14)(15,22)(16,21)(17,20)(18,19)$
$ 10, 5, 5, 1, 1 $ $242$ $10$ $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(13,20,21,18,16,22,15,14,17,19)$
$ 10, 5, 5, 1, 1 $ $242$ $10$ $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(13,14,16,20,17,22,21,19,15,18)$
$ 10, 5, 5, 1, 1 $ $242$ $10$ $( 2, 4,10, 6, 5)( 3, 7, 8,11, 9)(13,19,17,14,15,22,16,18,21,20)$
$ 10, 5, 5, 1, 1 $ $242$ $10$ $( 2,10, 5, 4, 6)( 3, 8, 9, 7,11)(13,18,15,19,21,22,17,20,16,14)$
$ 22 $ $220$ $22$ $( 1,14, 4,13, 7,12,10,22, 2,21, 5,20, 8,19,11,18, 3,17, 6,16, 9,15)$
$ 22 $ $220$ $22$ $( 1,16, 8,21, 4,15,11,20, 7,14, 3,19,10,13, 6,18, 2,12, 9,17, 5,22)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $110$ $2$ $( 1,18)( 2,14)( 3,21)( 4,17)( 5,13)( 6,20)( 7,16)( 8,12)( 9,19)(10,15)(11,22)$
$ 22 $ $220$ $22$ $( 1,19, 3,22, 5,14, 7,17, 9,20,11,12, 2,15, 4,18, 6,21, 8,13,10,16)$
$ 22 $ $220$ $22$ $( 1,13, 2,20, 3,16, 4,12, 5,19, 6,15, 7,22, 8,18, 9,14,10,21,11,17)$
$ 22 $ $220$ $22$ $( 1,21, 7,19, 2,17, 8,15, 3,13, 9,22, 4,20,10,18, 5,16,11,14, 6,12)$

Group invariants

Order:  $4840=2^{3} \cdot 5 \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.