Finite Group DatabasebetaFinite Group Databasebeta| order | 18549 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C3×C229⋊C27 |
| unambiguous semidirect product | (C3×C229)⋊C27 |
| derived, Sylow | C229 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | C229⋊C3 |
| commutator, hypocenter | C229 | C3×C27 |
| Frattini | C9 | C3×C229⋊C3 |
| Fitting | C3×C9×C229 | C3 |
| socle, prime radical | C32×C229 | C9 |
| cosocle | C9×C229 | C32 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C3×C9 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18549 |
2133 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18549, 24);