Finite Group DatabasebetaFinite Group Databasebeta| order | 24650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D493 |
| unambiguous semidirect product | C17⋊(C25×D29) |
| unambiguous semidirect product | C29⋊(C25×D17) |
| Fitting, Hall | C17×C25×C29 ⋊ C2 |
| derived, Hall | C17×C29 ⋊ C2×C25 |
| Hall | C25×C29 ⋊ D17 |
| Hall | C17×C25 ⋊ D29 |
| Sylow | C29 ⋊ C25×D17 |
| Sylow | C17 ⋊ C25×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D493 |
| commutator, hypocenter | C17×C29 | C2×C25 |
| Frattini | C5 | C5×D493 |
| Fitting | C17×C25×C29 | C2 |
| socle, cosocle | C5×C17×C29 | C2×C5 |
| prime radical | C5×D493 | C5 |
| LCS | G ▷ C17×C29 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12325 |
6200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24650, 4);