Finite Group DatabasebetaFinite Group Databasebeta| order | 19629 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C727⋊C27 |
| derived, Sylow | C727 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C727⋊C3 |
| commutator, hypocenter | C727 | C27 |
| Fitting, cosocle | C9×C727 | C3 |
| socle, prime radical | C3×C727 | C9 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19629 |
Polycyclic presentation:
3^3,727|a^3=b,b^3=c,d^a=d^4452205 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19629, 6);