Finite Group DatabasebetaFinite Group Databasebeta| order | 24345 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C541⋊C5 |
| unambiguous semidirect product | (C9×C541)⋊C5 |
| Fitting, Hall | C9×C541 ⋊ C5 |
| derived, Sylow | C541 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C541⋊C5 |
| commutator, hypocenter | C541 | C5×C9 |
| Frattini | C3 | C3×C541⋊C5 |
| Fitting | C9×C541 | C5 |
| socle, cosocle | C3×C541 | C3×C5 |
| prime radical | C3×C541⋊C5 | C3 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4869 |
1017 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24345, 3);