Finite Group DatabasebetaFinite Group Databasebeta| order | 18324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C509 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3×C509 |
| unambiguous semidirect product | C3⋊(C3×C4×C509) |
| derived | C3 ⋊ C3×C4×C509 |
| Hall | C32×C509 ⋊ C4 |
| Sylow | C32 ⋊ C4×C509 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C509 | D3 |
| commutator, hypocenter | C3 | C3×C4×C509 |
| Frattini | C2 | C3×D3×C509 |
| Fitting, socle, prime radical | C2×C32×C509 | C2 |
| cosocle | C2×C3 | C2×C3×C509 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C3×C509 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6108 |
9162 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18324, 15);