# Properties

 Label 22T28 Degree $22$ Order $22528$ Cyclic no Abelian no Solvable yes Primitive no $p$-group no

# Related objects

## Group action invariants

 Degree $n$: $22$ Transitive number $t$: $28$ Parity: $-1$ Primitive: no Nilpotency class: $-1$ (not nilpotent) $|\Aut(F/K)|$: $2$ Generators: (1,9,17,4,11,20,6,13,21,7,16,2,10,18,3,12,19,5,14,22,8,15), (1,14,4,15,6,18,7,20,10,21,11)(2,13,3,16,5,17,8,19,9,22,12)

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$11$:  $C_{11}$
$22$:  22T1
$11264$:  22T23

Resolvents shown for degrees $\leq 47$

## Subfields

Degree 2: None

Degree 11: $C_{11}$

## Low degree siblings

22T28 x 92, 44T146 x 93, 44T149 x 93, 44T150 x 465, 44T151 x 465, 44T152 x 465, 44T153 x 465, 44T154 x 465, 44T155 x 465, 44T156 x 930, 44T157 x 930, 44T158 x 930, 44T159 x 930, 44T160 x 930, 44T161 x 930, 44T162 x 930, 44T163 x 930, 44T164 x 930, 44T165 x 930, 44T166 x 930, 44T167 x 930, 44T168 x 930, 44T169 x 930, 44T170 x 930, 44T171 x 930, 44T172 x 930, 44T173 x 930, 44T174 x 930, 44T175 x 930, 44T176 x 930, 44T177 x 930, 44T178 x 930, 44T179 x 930, 44T180 x 930, 44T181 x 930, 44T182 x 930, 44T183 x 930, 44T184 x 930, 44T185 x 930, 44T186 x 930, 44T187 x 930, 44T188 x 930, 44T189 x 930, 44T190 x 930, 44T191 x 930, 44T192 x 930, 44T193 x 930, 44T194 x 930, 44T195 x 930, 44T196 x 930, 44T197 x 930, 44T198 x 930, 44T199 x 930, 44T200 x 930, 44T201 x 930, 44T202 x 930, 44T203 x 930

Siblings are shown with degree $\leq 47$

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

## Conjugacy classes

There are 208 conjugacy classes of elements. Data not shown.

## Group invariants

 Order: $22528=2^{11} \cdot 11$ Cyclic: no Abelian: no Solvable: yes GAP id: not available
 Character table: not available.