Finite Group DatabasebetaFinite Group Databasebeta| order | 33450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D25×C223⋊C3 |
| unambiguous semidirect product | C25⋊(C2×C223⋊C3) |
| unambiguous semidirect product | (D25×C223)⋊C3 |
| Fitting, derived, Hall | C25×C223 ⋊ C2×C3 |
| Hall | C25×C223⋊C3 ⋊ C2 |
| Hall | D25×C223 ⋊ C3 |
| Sylow | C223 ⋊ C3×D25 |
| Sylow | C25 ⋊ C2×C223⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C223 | C2×C3 |
| Frattini | C5 | D5×C223⋊C3 |
| socle | C5×C223 | C3×D5 |
| LCS | G ▷ C25×C223 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5575 |
1078 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33450, 11);