↑

Properties

Label 21T152
21T152 1 18 1->18 20 1->20 2 16 2->16 19 2->19 3 17 3->17 21 3->21 4 4->1 7 4->7 5 5->3 8 5->8 6 6->2 9 6->9 14 7->14 7->20 15 8->15 8->21 13 9->13 9->19 10 11 10->11 10->17 11->16 12 12->18 13->3 14->1 15->2 16->5 16->10 17->4 17->12 18->6 18->11 19->4 19->8 20->6 20->9 21->5 21->7
Degree $21$
Order $1410877440$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_3^7.(C_2^7.S_7)$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(21, 152);
 

Group invariants

Abstract group:  $C_3^7.(C_2^7.S_7)$
Copy content magma:IdentifyGroup(G);
 
Order:  $1410877440=2^{11} \cdot 3^{9} \cdot 5 \cdot 7$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  no
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $21$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $152$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,18,6,2,16,5,3,17,4)(7,20,9,19,8,21)(10,11)$, $(1,20,6,9,13,3,21,5,8,15,2,19,4,7,14)(10,17,12,18,11,16)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$5040$:  $S_7$
$10080$:  $S_7\times C_2$
$322560$:  14T54
$645120$:  14T57

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $S_7$

Low degree siblings

42T5388, 42T5389, 42T5390, 42T5391, 42T5392, 42T5393, 42T5394

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