Show commands:
Magma
magma: G := TransitiveGroup(35, 45);
Group action invariants
| Degree $n$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $45$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_7^4:D_{10}$ | ||
| 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: | (1,23)(2,22)(3,26)(4,27)(5,24)(6,25)(7,28)(8,21,10,20,14,17,12,16,9,15,13,19,11,18)(29,34,33,31,32,30,35), (1,12)(2,8)(3,9)(4,14)(5,11)(6,10)(7,13)(15,31,16,33,17,34,20,29,21,35,18,30,19,32)(22,23)(24,26)(25,27) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $10$: $D_{5}$ $20$: $D_{10}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $D_{5}$
Degree 7: None
Low degree siblings
35T45 x 15Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 200 conjugacy class representatives for $C_7^4:D_{10}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $48020=2^{2} \cdot 5 \cdot 7^{4}$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 48020.f | magma: IdentifyGroup(G);
| |
| Character table: | 200 x 200 character table |
magma: CharacterTable(G);