Properties

Label 22T31
Degree $22$
Order $24200$
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 $t$:  $31$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,17,2,16,3,15,4,14,5,13,6,12,7,22,8,21,9,20,10,19,11,18), (1,6,4,7,8)(2,10,9,5,11)(12,21,17,20,15,16,18,22,19,13)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$5$:  $C_5$
$8$:  $D_{4}$
$10$:  $D_{5}$, $C_{10}$ x 3
$20$:  $D_{10}$, 20T3
$40$:  20T7, 20T12
$50$:  $D_5\times C_5$
$100$:  20T24
$200$:  20T53

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

44T218, 44T219, 44T220

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 77 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $24200=2^{3} \cdot 5^{2} \cdot 11^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.