Properties

Label 22T1
Order \(22\)
n \(22\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive No
$p$-group No
Group: $C_{22}$

Related objects

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Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $1$
Group :  $C_{22}$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $1$
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)
$|\Aut(F/K)|$:  $22$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
11:  $C_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: $C_{11}$

Low degree siblings

There are no siblings 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 $ $1$ $1$ $()$
$ 22 $ $1$ $22$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22)$
$ 11, 11 $ $1$ $11$ $( 1, 3, 5, 7, 9,11,13,15,17,19,21)( 2, 4, 6, 8,10,12,14,16,18,20,22)$
$ 22 $ $1$ $22$ $( 1, 4, 7,10,13,16,19,22, 3, 6, 9,12,15,18,21, 2, 5, 8,11,14,17,20)$
$ 11, 11 $ $1$ $11$ $( 1, 5, 9,13,17,21, 3, 7,11,15,19)( 2, 6,10,14,18,22, 4, 8,12,16,20)$
$ 22 $ $1$ $22$ $( 1, 6,11,16,21, 4, 9,14,19, 2, 7,12,17,22, 5,10,15,20, 3, 8,13,18)$
$ 11, 11 $ $1$ $11$ $( 1, 7,13,19, 3, 9,15,21, 5,11,17)( 2, 8,14,20, 4,10,16,22, 6,12,18)$
$ 22 $ $1$ $22$ $( 1, 8,15,22, 7,14,21, 6,13,20, 5,12,19, 4,11,18, 3,10,17, 2, 9,16)$
$ 11, 11 $ $1$ $11$ $( 1, 9,17, 3,11,19, 5,13,21, 7,15)( 2,10,18, 4,12,20, 6,14,22, 8,16)$
$ 22 $ $1$ $22$ $( 1,10,19, 6,15, 2,11,20, 7,16, 3,12,21, 8,17, 4,13,22, 9,18, 5,14)$
$ 11, 11 $ $1$ $11$ $( 1,11,21, 9,19, 7,17, 5,15, 3,13)( 2,12,22,10,20, 8,18, 6,16, 4,14)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $1$ $2$ $( 1,12)( 2,13)( 3,14)( 4,15)( 5,16)( 6,17)( 7,18)( 8,19)( 9,20)(10,21)(11,22)$
$ 11, 11 $ $1$ $11$ $( 1,13, 3,15, 5,17, 7,19, 9,21,11)( 2,14, 4,16, 6,18, 8,20,10,22,12)$
$ 22 $ $1$ $22$ $( 1,14, 5,18, 9,22,13, 4,17, 8,21,12, 3,16, 7,20,11, 2,15, 6,19,10)$
$ 11, 11 $ $1$ $11$ $( 1,15, 7,21,13, 5,19,11, 3,17, 9)( 2,16, 8,22,14, 6,20,12, 4,18,10)$
$ 22 $ $1$ $22$ $( 1,16, 9, 2,17,10, 3,18,11, 4,19,12, 5,20,13, 6,21,14, 7,22,15, 8)$
$ 11, 11 $ $1$ $11$ $( 1,17,11, 5,21,15, 9, 3,19,13, 7)( 2,18,12, 6,22,16,10, 4,20,14, 8)$
$ 22 $ $1$ $22$ $( 1,18,13, 8, 3,20,15,10, 5,22,17,12, 7, 2,19,14, 9, 4,21,16,11, 6)$
$ 11, 11 $ $1$ $11$ $( 1,19,15,11, 7, 3,21,17,13, 9, 5)( 2,20,16,12, 8, 4,22,18,14,10, 6)$
$ 22 $ $1$ $22$ $( 1,20,17,14,11, 8, 5, 2,21,18,15,12, 9, 6, 3,22,19,16,13,10, 7, 4)$
$ 11, 11 $ $1$ $11$ $( 1,21,19,17,15,13,11, 9, 7, 5, 3)( 2,22,20,18,16,14,12,10, 8, 6, 4)$
$ 22 $ $1$ $22$ $( 1,22,21,20,19,18,17,16,15,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$

Group invariants

Order:  $22=2 \cdot 11$
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [22, 2]
Character table: Data not available.