Finite Group DatabasebetaFinite Group Databasebeta| order | 33573 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C361⋊C3 |
| unambiguous semidirect product | C361⋊(C3×C31) |
| Fitting, Hall | C31×C361 ⋊ C3 |
| derived, Sylow | C361 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C361⋊C3 |
| commutator, cosocle, hypocenter | C361 | C3×C31 |
| Frattini | C19 | C31×C19⋊C3 |
| Fitting | C31×C361 | C3 |
| socle | C19×C31 | C19⋊C3 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C31 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11191 |
3813 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33573, 2);