Finite Group DatabasebetaFinite Group Databasebeta| order | 18549 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
| direct product | C33×C229⋊C3 |
| unambiguous semidirect product | C229⋊C34 |
| unambiguous semidirect product | (C3×C229)⋊C33 |
| Fitting, socle | C33×C229 ⋊ C3 |
| derived, Sylow | C229 ⋊ C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C229⋊C3 |
| commutator, cosocle, hypocenter | C229 | C34 |
| Frattini | C1 | G |
| Fitting, socle | C33×C229 | C3 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C33 | |
424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6183 |
2133 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18549, 49);