Finite Group DatabasebetaFinite Group Databasebeta| order | 24805 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×C41⋊C5 |
| unambiguous semidirect product | C41⋊(C5×C121) |
| Fitting, Hall | C41×C121 ⋊ C5 |
| derived, Sylow | C41 ⋊ C5×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | C41⋊C5 |
| commutator, hypocenter | C41 | C5×C121 |
| Frattini | C11 | C11×C41⋊C5 |
| Fitting | C41×C121 | C5 |
| socle, cosocle | C11×C41 | C5×C11 |
| prime radical | C11×C41⋊C5 | C11 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C121 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4961 |
1573 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24805, 3);