Finite Group DatabasebetaFinite Group Databasebeta| order | 18324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#14523266 |
| Fitting, Hall | C9×C509 ⋊ C4 |
| derived, Sylow | C509 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #14523266 |
| commutator, hypocenter | C509 | C4×C9 |
| Frattini | C3 | C3×#14523266 |
| Fitting | C9×C509 | C4 |
| socle | C3×C509 | C3×C4 |
| prime radical, cosocle | C3×D509 | C2×C3 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C9 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4581 |
1179 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18324, 6);