# Properties

 Label 22T18 Degree $22$ Order $2420$ Cyclic no Abelian no Solvable yes Primitive no $p$-group no

# Related objects

## Group action invariants

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

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$
$5$:  $C_5$
$10$:  $C_{10}$
$20$:  20T1

Resolvents shown for degrees $\leq 47$

## Subfields

Degree 2: $C_2$

Degree 11: None

## Low degree siblings

22T18 x 5, 44T62 x 6

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

## Conjugacy classes

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

## Group invariants

 Order: $2420=2^{2} \cdot 5 \cdot 11^{2}$ Cyclic: no Abelian: no Solvable: yes GAP id: not available
 Character table: not available.