Finite Group DatabasebetaFinite Group Databasebeta| order | 33681 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C109 · Schur multiplier (H2) = C1 |
| direct product | C109×C103⋊C3 |
| unambiguous semidirect product | C103⋊(C3×C109) |
| Fitting, socle, Hall | C103×C109 ⋊ C3 |
| derived, Sylow | C103 ⋊ C3×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | C103⋊C3 |
| commutator, cosocle, hypocenter | C103 | C3×C109 |
| Frattini | C1 | G |
| Fitting, socle | C103×C109 | C3 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C109 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11227 |
4033 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33681, 1);