Finite Group DatabasebetaFinite Group Databasebeta| order | 33450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D223⋊C3 |
| unambiguous semidirect product | D223⋊(C3×C25) |
| unambiguous semidirect product | (C223⋊C3)⋊(C2×C25) |
| unambiguous semidirect product | (C25×D223)⋊C3 |
| Fitting, Hall | C25×C223 ⋊ C2×C3 |
| derived, Sylow | C223 ⋊ C2×C3×C25 |
| Hall | C25×C223⋊C3 ⋊ C2 |
| Hall | C25×D223 ⋊ C3 |
| Hall | C223⋊C3 ⋊ C2×C25 |
| Hall | D223 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D223⋊C3 |
| commutator, hypocenter | C223 | C2×C3×C25 |
| Frattini | C5 | C5×D223⋊C3 |
| Fitting | C25×C223 | C2×C3 |
| socle, cosocle | C5×C223 | C2×C3×C5 |
| prime radical | C5×D223⋊C3 | C5 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5575 |
1075 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33450, 10);