Label 40T15
Degree $40$
Order $80$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_5\times \OD_{16}$


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Show commands: Magma

magma: G := TransitiveGroup(40, 15);

Group action invariants

Degree $n$:  $40$
magma: t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:  $15$
magma: t, n := TransitiveGroupIdentification(G); t;
Group:  $C_5\times \OD_{16}$
Parity:  $-1$
magma: IsEven(G);
Primitive:  no
magma: IsPrimitive(G);
Nilpotency class:  $2$
magma: NilpotencyClass(G);
$\card{\Aut(F/K)}$:  $20$
magma: Order(Centralizer(SymmetricGroup(n), G));
Generators:  (1,21,3,23,2,22,4,24)(5,26,7,28,6,25,8,27)(9,32,11,30,10,31,12,29)(13,35,16,34,14,36,15,33)(17,37,19,40,18,38,20,39), (1,14,25,37,10,24,33,6,18,30,3,15,27,40,12,21,35,8,20,31,2,13,26,38,9,23,34,5,17,29,4,16,28,39,11,22,36,7,19,32)
magma: Generators(G);

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_4$ x 2, $C_2^2$
$5$:  $C_5$
$8$:  $C_4\times C_2$
$10$:  $C_{10}$ x 3
$16$:  $C_8:C_2$
$20$:  20T1 x 2, 20T3
$40$:  40T2

Resolvents shown for degrees $\leq 47$


Degree 2: $C_2$

Degree 4: $C_4$

Degree 5: $C_5$

Degree 8: $C_8:C_2$

Degree 10: $C_{10}$

Degree 20: 20T1

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

There are 50 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);

Group invariants

Order:  $80=2^{4} \cdot 5$
magma: Order(G);
Cyclic:  no
magma: IsCyclic(G);
Abelian:  no
magma: IsAbelian(G);
Solvable:  yes
magma: IsSolvable(G);
Label:  80.24
magma: IdentifyGroup(G);
Character table: not available.

magma: CharacterTable(G);