↑

Properties

Label 22T28
22T28 1 9 1->9 14 1->14 2 10 2->10 13 2->13 3 12 3->12 16 3->16 4 11 4->11 15 4->15 5 5->14 17 5->17 6 6->13 18 6->18 7 7->16 20 7->20 8 8->15 19 8->19 9->17 22 9->22 10->18 21 10->21 11->1 11->20 12->2 12->19 13->3 13->21 14->4 14->22 15->1 15->6 16->2 16->5 17->4 17->8 18->3 18->7 19->5 19->9 20->6 20->10 21->7 21->11 22->8 22->12
Degree $22$
Order $22528$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^{10}.C_{22}$

Related objects

Downloads

Learn more

Show commands: Magma

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

Group invariants

Abstract group:  $C_2^{10}.C_{22}$
Copy content magma:IdentifyGroup(G);
 
Order:  $22528=2^{11} \cdot 11$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $22$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $28$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,9,17,4,11,20,6,13,21,7,16,2,10,18,3,12,19,5,14,22,8,15)$, $(1,14,4,15,6,18,7,20,10,21,11)(2,13,3,16,5,17,8,19,9,22,12)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$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

Conjugacy classes not computed

Copy content magma:ConjugacyClasses(G);
 

Character table

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed