Show commands:
Magma
magma: G := TransitiveGroup(38, 15);
Group action invariants
Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
Transitive number $t$: | $15$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
Group: | $D_{19}\wr C_2$ | ||
Parity: | $-1$ | magma: IsEven(G);
| |
Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
$\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
Generators: | (1,4,7,10,13,16,19,3,6,9,12,15,18,2,5,8,11,14,17)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(34,38)(35,37), (1,20,19,24)(2,35,18,28)(3,31,17,32)(4,27,16,36)(5,23,15,21)(6,38,14,25)(7,34,13,29)(8,30,12,33)(9,26,11,37)(10,22) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T15Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 77 conjugacy class representatives for $D_{19}\wr C_2$
magma: ConjugacyClasses(G);
Group invariants
Order: | $2888=2^{3} \cdot 19^{2}$ | magma: Order(G);
| |
Cyclic: | no | magma: IsCyclic(G);
| |
Abelian: | no | magma: IsAbelian(G);
| |
Solvable: | yes | magma: IsSolvable(G);
| |
Nilpotency class: | not nilpotent | ||
Label: | 2888.m | magma: IdentifyGroup(G);
| |
Character table: | 77 x 77 character table |
magma: CharacterTable(G);