Properties

Label 35T46
Degree $35$
Order $48020$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_7^4:F_5$

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Show commands: Magma

magma: G := TransitiveGroup(35, 46);
 

Group action invariants

Degree $n$:  $35$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $46$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_7^4:F_5$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $7$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,34,12,16)(2,30,11,18)(3,33,14,17)(4,29,9,15)(5,32,8,21)(6,35,13,19)(7,31,10,20), (1,21,26,13,4,20,23,11,6,17,27,8,2,16,25,10,5,15,22,14,7,19,24,12,3,18,28,9)(29,34,33,31,32,30,35)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$
$20$:  $F_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $F_5$

Degree 7: None

Low degree siblings

35T47

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 179 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $48020=2^{2} \cdot 5 \cdot 7^{4}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  48020.g
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);