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Properties

Label 28T1371
28T1371 1 18 1->18 2 7 2->7 17 2->17 3 6 3->6 16 3->16 4 5 4->5 15 4->15 21 5->21 20 6->20 19 7->19 8 8->6 27 8->27 9 9->1 23 9->23 10 10->3 26 10->26 11 11->5 22 11->22 12 12->7 25 12->25 13 13->2 28 13->28 14 14->4 24 14->24 15->17 15->24 16->23 17->22 18->21 18->28 19->20 19->27 20->26 21->25 22->9 22->14 23->11 23->14 24->8 24->12 25->10 25->12 26->8 26->9 27->13 27->13 28->10 28->11
Degree $28$
Order $3111696$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_7^4:(C_2\times C_3^3:S_4)$

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Copy content magma:G := TransitiveGroup(28, 1371);
 

Group invariants

Abstract group:  $C_7^4:(C_2\times C_3^3:S_4)$
Copy content magma:IdentifyGroup(G);
 
Order:  $3111696=2^{4} \cdot 3^{4} \cdot 7^{4}$
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 $n$:  $28$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $1371$
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:  $(2,7)(3,6)(4,5)(8,27,13,28,11,22,9,23,14,24,12,25,10,26)(15,17)(18,21)(19,20)$, $(1,18,28,10,3,16,23,11,5,21,25,12,7,19,27,13,2,17,22,14,4,15,24,8,6,20,26,9)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$24$:  $S_4$
$48$:  $S_4\times C_2$
$648$:  $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$
$1296$:  18T305

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: $S_4$

Degree 7: None

Degree 14: None

Low degree siblings

There are no siblings 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

100 x 100 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed