Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C27 · Schur multiplier (H2) = C9 |
| direct product | C27×#10620323 |
| Fitting | C27×C73 ⋊ C9 |
| derived, Sylow | C73 ⋊ C9×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | #10620323 |
| commutator, hypocenter | C73 | C9×C27 |
| Frattini | C9 | C3×#10620323 |
| Fitting | C27×C73 | C9 |
| socle | C3×C73 | C92 |
| prime radical | C3×C73⋊C3 | C3×C9 |
| cosocle | C9×C73⋊C3 | C32 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C27 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1971 |
459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 312);