Show commands:
Magma
magma: G := TransitiveGroup(28, 33);
Group action invariants
| Degree $n$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_7:C_{28}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
| |
| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
| $\card{\Aut(F/K)}$: | $14$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,2)(3,23,15,8,28,19,12,4,24,16,7,27,20,11)(5,6)(9,10)(13,14)(17,18)(21,22)(25,26), (1,27,5,3,9,8,14,12,17,16,21,20,25,23,2,28,6,4,10,7,13,11,18,15,22,19,26,24) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $7$: $C_7$ $14$: $D_{7}$, $C_{14}$ $28$: $C_{28}$, 28T3 $98$: $C_7 \wr C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 7: None
Degree 14: $C_7 \wr C_2$
Low degree siblings
28T33 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 70 conjugacy class representatives for $C_7:C_{28}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $196=2^{2} \cdot 7^{2}$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 196.5 | magma: IdentifyGroup(G);
| |
| Character table: | 70 x 70 character table |
magma: CharacterTable(G);