Finite Group DatabasebetaFinite Group Databasebeta| order | 24345 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19096457⋊C5 |
| derived, Sylow | C541 ⋊ C5×C9 |
| Hall | #19096457 ⋊ C5 |
| Hall | C541⋊C5 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C541⋊C3)⋊C5 |
| commutator, hypocenter | C541 | C5×C9 |
| Fitting, socle, cosocle | C3×C541 | C3×C5 |
| prime radical | C3×C541⋊C5 | C3 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4869 |
Polycyclic presentation:
3,5,541,3|a^3=d,c^a=c^129,c^b=c^48153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24345, 2);