Label 1T1
Degree $1$
Order $1$
Cyclic yes
Abelian yes
Solvable yes
Primitive yes
$p$-group yes
Group: Trivial

Related objects


Learn more

Show commands: Magma

magma: G := TransitiveGroup(1, 1);

Group action invariants

Degree $n$:  $1$
magma: t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:  $1$
magma: t, n := TransitiveGroupIdentification(G); t;
Group:  Trivial
CHM label:   Trivial group
Parity:  $1$
magma: IsEven(G);
Primitive:  yes
magma: IsPrimitive(G);
magma: NilpotencyClass(G);
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
Generators:  None needed
magma: Generators(G);

Low degree resolvents


Resolvents shown for degrees $\leq 47$


Degree 1 - 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

LabelCycle TypeSizeOrderRepresentative
1A $1$ $1$ $1$ $()$

magma: ConjugacyClasses(G);

Group invariants

Order:  $1$
magma: Order(G);
Cyclic:  yes
magma: IsCyclic(G);
Abelian:  yes
magma: IsAbelian(G);
Solvable:  yes
magma: IsSolvable(G);
Nilpotency class:  $0$
Label:  1.1
magma: IdentifyGroup(G);
Character table:

Size 1
1.1.1a R 1

magma: CharacterTable(G);