Properties

Label 22T20
Order \(4840\)
n \(22\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
5:  $C_5$
8:  $D_{4}$
10:  $C_{10}$ x 3
20:  20T3
40:  20T12

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

22T20, 44T84 x 2, 44T85 x 2, 44T86 x 2, 44T89 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 $ $40$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $20$ $11$ $(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 11 $ $40$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,15,18,21,13,16,19,22,14,17,20)$
$ 11, 11 $ $20$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,20,17,14,22,19,16,13,21,18,15)$
$ 5, 5, 5, 5, 1, 1 $ $121$ $5$ $( 2, 4,10, 6, 5)( 3, 7, 8,11, 9)(13,15,21,17,16)(14,18,19,22,20)$
$ 5, 5, 5, 5, 1, 1 $ $121$ $5$ $( 2,10, 5, 4, 6)( 3, 8, 9, 7,11)(13,21,16,15,17)(14,19,20,18,22)$
$ 5, 5, 5, 5, 1, 1 $ $121$ $5$ $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(13,16,17,21,15)(14,20,22,19,18)$
$ 5, 5, 5, 5, 1, 1 $ $121$ $5$ $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(13,17,15,16,21)(14,22,18,20,19)$
$ 10, 5, 5, 1, 1 $ $242$ $10$ $( 2, 7, 4, 8,10,11, 6, 9, 5, 3)(13,17,15,16,21)(14,22,18,20,19)$
$ 10, 5, 5, 1, 1 $ $242$ $10$ $( 2, 8, 6, 3, 4,11, 5, 7,10, 9)(13,16,17,21,15)(14,20,22,19,18)$
$ 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $22$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)$
$ 11, 2, 2, 2, 2, 2, 1 $ $220$ $22$ $( 1, 7)( 2, 6)( 3, 5)( 8,11)( 9,10)(12,16,20,13,17,21,14,18,22,15,19)$
$ 10, 5, 5, 1, 1 $ $242$ $10$ $( 2, 3, 5, 9, 6,11,10, 8, 4, 7)(13,21,16,15,17)(14,19,20,18,22)$
$ 10, 5, 5, 1, 1 $ $242$ $10$ $( 2, 9,10, 7, 5,11, 4, 3, 6, 8)(13,15,21,17,16)(14,18,19,22,20)$
$ 10, 10, 1, 1 $ $121$ $10$ $( 2, 7, 4, 8,10,11, 6, 9, 5, 3)(13,18,15,19,21,22,17,20,16,14)$
$ 10, 10, 1, 1 $ $121$ $10$ $( 2, 8, 6, 3, 4,11, 5, 7,10, 9)(13,19,17,14,15,22,16,18,21,20)$
$ 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 $ $121$ $10$ $( 2, 3, 5, 9, 6,11,10, 8, 4, 7)(13,14,16,20,17,22,21,19,15,18)$
$ 10, 10, 1, 1 $ $121$ $10$ $( 2, 9,10, 7, 5,11, 4, 3, 6, 8)(13,20,21,18,16,22,15,14,17,19)$
$ 20, 2 $ $242$ $20$ $( 1,20, 6,19, 8,12,11,18,10,16, 3,13, 9,14, 7,21, 4,15, 5,17)( 2,22)$
$ 20, 2 $ $242$ $20$ $( 1,14, 8,12, 9,18, 6,22, 4,21,10,13, 3,15, 2,20, 5,16, 7,17)(11,19)$
$ 20, 2 $ $242$ $20$ $( 1,18, 5,13, 7,16, 8,12, 3,21, 6,20, 2,14,11,22,10,15, 4,17)( 9,19)$
$ 20, 2 $ $242$ $20$ $( 1,22, 5,21, 2,19, 7,15, 6,18, 4,13,11,14, 3,16, 9,20,10,17)( 8,12)$
$ 4, 4, 4, 4, 4, 2 $ $242$ $4$ $( 1,19, 3,17)( 2,18)( 4,16,11,20)( 5,15,10,21)( 6,14, 9,22)( 7,13, 8,12)$
$ 22 $ $220$ $22$ $( 1,19,10,21, 8,12, 6,14, 4,16, 2,18,11,20, 9,22, 7,13, 5,15, 3,17)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $22$ $2$ $( 1,12)( 2,22)( 3,21)( 4,20)( 5,19)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)$
$ 10, 10, 2 $ $242$ $10$ $( 1,22, 8,12, 5,21,11,14,10,17)( 2,19, 6,18, 9,20, 3,16, 4,13)( 7,15)$
$ 10, 10, 2 $ $242$ $10$ $( 1,20, 7,21, 9,14, 6,19, 5,17)( 2,22,11,18, 3,13, 4,15, 8,12)(10,16)$
$ 10, 10, 2 $ $242$ $10$ $( 1,18, 8,12,10,15, 9,19, 4,17)( 2,14)( 3,21, 7,16, 5,13, 6,20,11,22)$
$ 10, 10, 2 $ $242$ $10$ $( 1,14, 5,16, 6,22, 9,18, 7,17)( 2,20, 8,12, 4,21, 3,15,11,19)(10,13)$

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.