Finite Group DatabasebetaFinite Group Databasebeta| order | 33945 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20291755⋊C5 |
| Fitting, socle, derived, Hall | C31×C73 ⋊ C3×C5 |
| Hall | C73×ΓL(1,𝔽32) ⋊ C3 |
| Hall | #20291755 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C73⋊C3 |
| Sylow | C73 ⋊ (C31⋊C3)⋊C5 |
| Sylow | C31 ⋊ C5×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C73 | C3×C5 |
| LCS | G ▷ C31×C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2263 |
Polycyclic presentation:
3,5,31,73|c^a=c^25,d^a=d^64,c^b=c^16281 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33945, 10);