Show commands:
Magma
magma: G := TransitiveGroup(23, 7);
Group action invariants
| Degree $n$: | $23$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $7$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $S_{23}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
| |
| Primitive: | yes | magma: IsPrimitive(G);
| |
| Nilpotency class: | $-1$ (not nilpotent) | magma: NilpotencyClass(G);
| |
| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,2), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Prime degree - none
Low degree siblings
46T44Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 1,255 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $25852016738884976640000=2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | no | magma: IsSolvable(G);
| |
| Label: | 25852016738884976640000.a | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);