Finite Group DatabasebetaFinite Group Databasebeta| order | 24475 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C89⋊C11 |
| unambiguous semidirect product | C89⋊(C11×C25) |
| unambiguous semidirect product | (C25×C89)⋊C11 |
| Fitting, Hall | C25×C89 ⋊ C11 |
| derived, Sylow | C89 ⋊ C11×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C89⋊C11 |
| commutator, hypocenter | C89 | C11×C25 |
| Frattini | C5 | C5×C89⋊C11 |
| Fitting | C25×C89 | C11 |
| socle, cosocle | C5×C89 | C5×C11 |
| prime radical | C5×C89⋊C11 | C5 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2225 |
475 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24475, 2);