Finite Group DatabasebetaFinite Group Databasebeta| order | 24650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D725 |
| unambiguous semidirect product | C25⋊(C17×D29) |
| unambiguous semidirect product | C29⋊(C17×D25) |
| Fitting, Hall | C17×C25×C29 ⋊ C2 |
| derived, Hall | C25×C29 ⋊ C2×C17 |
| Hall | C17×C29 ⋊ D25 |
| Hall | C17×C25 ⋊ D29 |
| Sylow | C29 ⋊ C17×D25 |
| Sylow | C25 ⋊ C17×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D725 |
| commutator, cosocle, hypocenter | C25×C29 | C2×C17 |
| Frattini | C5 | C17×D145 |
| Fitting | C17×C25×C29 | C2 |
| socle | C5×C17×C29 | D5 |
| LCS | G ▷ C25×C29 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12325 |
6188 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24650, 6);