Finite Group DatabasebetaFinite Group Databasebeta| order | 33330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C101 · Schur multiplier (H2) = C1 |
| direct product | C5×D33×C101 |
| unambiguous semidirect product | C3⋊(C5×D11×C101) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C101 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C5×C101 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11×C101 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C5×C101 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16665 |
9090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33330, 17);