Finite Group DatabasebetaFinite Group Databasebeta| order | 33573 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C361 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×C361 |
| unambiguous semidirect product | C31⋊(C3×C361) |
| Fitting, Hall | C31×C361 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C361 | C31⋊C3 |
| commutator, hypocenter | C31 | C3×C361 |
| Frattini | C19 | C19×C31⋊C3 |
| Fitting | C31×C361 | C3 |
| socle, cosocle | C19×C31 | C3×C19 |
| prime radical | C19×C31⋊C3 | C19 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C361 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11191 |
4693 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33573, 3);