Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C27 · Schur multiplier (H2) = C9 |
| direct product | C9×#14520291 |
| derived, Sylow | C73 ⋊ C9×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C92 | C73⋊C3 |
| commutator, hypocenter | C73 | C9×C27 |
| Frattini | C3×C9 | C3×C73⋊C3 |
| Fitting | C92×C73 | C3 |
| socle, prime radical | C32×C73 | C3×C9 |
| cosocle | C3×C9×C73 | C32 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C92 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17739 |
2187 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 89);