Finite Group DatabasebetaFinite Group Databasebeta| order | 32450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×D275 |
| unambiguous semidirect product | C11⋊(D25×C59) |
| unambiguous semidirect product | C25⋊(D11×C59) |
| Fitting, Hall | C11×C25×C59 ⋊ C2 |
| derived, Hall | C11×C25 ⋊ C2×C59 |
| Hall | C25×C59 ⋊ D11 |
| Hall | C11×C59 ⋊ D25 |
| Sylow | C25 ⋊ D11×C59 |
| Sylow | C11 ⋊ D25×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | D275 |
| commutator, cosocle, hypocenter | C11×C25 | C2×C59 |
| Frattini | C5 | C59×D55 |
| Fitting | C11×C25×C59 | C2 |
| socle | C5×C11×C59 | D5 |
| LCS | G ▷ C11×C25 | |
| UCS | C1 ◁ C59 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16225 |
8201 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32450, 8);