Show commands:
Magma
magma: G := TransitiveGroup(38, 19);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $19$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $D_{19}^2:C_3$ | ||
| 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: | (1,26,16,34,10,27)(2,24,8,31,17,32)(3,22,19,28,5,37)(4,20,11,25,12,23)(6,35,14,38,7,33)(9,29)(13,21,15,36,18,30), (1,31,13,36,12,34)(2,33,5,20,19,29)(3,35,16,23,7,24)(4,37,8,26,14,38)(6,22,11,32,9,28)(10,30,17,25,18,27)(15,21) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $3$: $C_3$ $4$: $C_2^2$ $6$: $C_6$ x 3 $12$: $C_6\times C_2$ $114$: $C_{19}:C_{6}$ x 2 $228$: 38T6 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T19 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 51 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $4332=2^{2} \cdot 3 \cdot 19^{2}$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 4332.p | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);