Finite Group DatabasebetaFinite Group Databasebeta| order | 32450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C59 · Schur multiplier (H2) = C1 |
| direct product | C11×D25×C59 |
| unambiguous semidirect product | C25⋊(C2×C11×C59) |
| Fitting, Hall | C11×C25×C59 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C11×C59 |
| Hall | C25×C59 ⋊ C2×C11 |
| Hall | C11×C25 ⋊ C2×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C59 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C11×C59 |
| Frattini | C5 | D5×C11×C59 |
| Fitting | C11×C25×C59 | C2 |
| socle | C5×C11×C59 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C11×C59 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16225 |
9086 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32450, 6);