Finite Group DatabasebetaFinite Group Databasebeta| order | 18324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D509 |
| unambiguous semidirect product | C509⋊(C22×C9) |
| unambiguous semidirect product | (C2×C509)⋊(C2×C9) |
| Fitting | C2×C9×C509 ⋊ C2 |
| derived, Sylow | C509 ⋊ C22×C9 |
| Hall | C9×C509 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D509 |
| commutator, hypocenter | C509 | C22×C9 |
| Frattini | C3 | C2×C3×D509 |
| Fitting | C2×C9×C509 | C2 |
| socle | C2×C3×C509 | C2×C3 |
| prime radical | C2×C3×D509 | C3 |
| cosocle | C3×C509 | C22×C3 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C2×C9 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9162 |
4608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18324, 12);