Finite Group DatabasebetaFinite Group Databasebeta| order | 33330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×D11×C101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×C101⋊C5 |
| commutator, cosocle, hypocenter | C11×C101 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C101 | C2×C5 |
| LCS | G ▷ C11×C101 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3333 |
525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33330, 29);