Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#30659079 |
| derived, Sylow | C432 ⋊ C2×C9 |
| Hall | C2×C432 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #19149815 |
| commutator, hypocenter | C432 | C2×C9 |
| Frattini | C3 | C2×#19149815 |
| Fitting, socle, prime radical | C2×C3×C432 | C3 |
| cosocle | C3×C432 | C2×C3 |
| LCS | G ▷ C432 | |
| UCS | C1 ◁ C2×C3 | |
276 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33282 |
3714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 27);