Finite Group DatabasebetaFinite Group Databasebeta| order | 36324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#22583792⋊C2 |
| unambiguous semidirect product | #22583792⋊C22 |
| unambiguous semidirect product | (C2×#22583792)⋊C2 |
| derived, Sylow | C1009 ⋊ C22×C9 |
| Hall | #22583792 ⋊ C22 |
| Hall | C2×D1009 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1009⋊C3 |
| commutator, hypocenter | C1009 | C22×C9 |
| Frattini | C3 | C2×D1009⋊C3 |
| Fitting, socle | C2×C3×C1009 | C2×C3 |
| prime radical | C2×C3×D1009 | C3 |
| cosocle | C3×C1009 | C22×C3 |
| LCS | G ▷ C1009 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18162 |
1044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36324, 9);