Finite Group DatabasebetaFinite Group Databasebeta| order | 33330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×D303 |
| unambiguous semidirect product | C3⋊(C11⋊C5×D101) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C101 | C2×C5 |
| LCS | G ▷ C3×C11×C101 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3333 |
1071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33330, 48);