Finite Group DatabasebetaFinite Group Databasebeta| order | 33366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D83×C67⋊C3 |
| unambiguous semidirect product | C83⋊(C2×C67⋊C3) |
| unambiguous semidirect product | (C67×D83)⋊C3 |
| Fitting, socle, derived, Hall | C67×C83 ⋊ C2×C3 |
| Hall | C83×C67⋊C3 ⋊ C2 |
| Hall | C67×D83 ⋊ C3 |
| Sylow | C83 ⋊ C2×C67⋊C3 |
| Sylow | C67 ⋊ C3×D83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C67×C83 | C2×C3 |
| LCS | G ▷ C67×C83 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5561 |
1075 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33366, 10);