Show commands:
Magma
magma: G := TransitiveGroup(34, 16);
Group action invariants
| Degree $n$: | $34$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $16$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $D_{17}^2.C_2$ | ||
| 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: | (1,31,9,24)(2,28,8,27)(3,25,7,30)(4,22,6,33)(5,19)(10,21,17,34)(11,18,16,20)(12,32,15,23)(13,29,14,26), (1,32,12,28,6,24,17,20,11,33,5,29,16,25,10,21,4,34,15,30,9,26,3,22,14,18,8,31,2,27,13,23,7,19) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_4$ x 2, $C_2^2$ $8$: $C_4\times C_2$ $68$: $C_{17}:C_{4}$ x 2 $136$: 34T5 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T16 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 56 conjugacy class representatives for $D_{17}^2.C_2$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $2312=2^{3} \cdot 17^{2}$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 2312.o | magma: IdentifyGroup(G);
| |
| Character table: | 56 x 56 character table |
magma: CharacterTable(G);