Finite Group DatabasebetaFinite Group Databasebeta| order | 18324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D1527 |
| unambiguous semidirect product | (C2×C3)⋊D1527 |
| unambiguous semidirect product | (C2×C509)⋊(C3⋊D3) |
| Fitting, socle | C2×C32×C509 ⋊ C2 |
| derived, Hall | C32×C509 ⋊ C22 |
| Sylow | C509 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D509 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D1527 |
| commutator, cosocle, hypocenter | C32×C509 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C509 | C2 |
| LCS | G ▷ C32×C509 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9162 |
4584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18324, 32);