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Properties

Label 22T28
Degree $22$
Order $22528$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{15}\times C_{420}$

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Show commands: Magma

magma: G := TransitiveGroup(22, 28);
 

Group action invariants

Degree $n$:  $22$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $28$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{15}\times C_{420}$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $2$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
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)
magma: Generators(G);
 

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

The 208 conjugacy class representatives for $C_{15}\times C_{420}$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $22528=2^{11} \cdot 11$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  22528.c
magma: IdentifyGroup(G);
 
Character table:    208 x 208 character table

magma: CharacterTable(G);