Finite Group DatabasebetaFinite Group Databasebeta| order | 33975 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C25 · Schur multiplier (H2) = C3 |
| direct product | C3×#16836851⋊C3 |
| unambiguous semidirect product | #16836851⋊C32 |
| unambiguous semidirect product | (C3×#16836851)⋊C3 |
| Fitting, socle | C3×C151 ⋊ C3×C25 |
| derived, Sylow | C151 ⋊ C32×C25 |
| Hall | #16836851 ⋊ C32 |
| Hall | C3×C151⋊C3 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16836851⋊C3 |
| commutator, hypocenter | C151 | C32×C25 |
| Frattini | C1 | G |
| Fitting, socle | C3×C151 | C3×C25 |
| prime radical | C3×(C151⋊C3)⋊C5 | C5 |
| cosocle | C151⋊C5 | C32×C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 453 |
231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33975, 18);