Finite Group DatabasebetaFinite Group Databasebeta| order | 24345 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19096459⋊C5 |
| Fitting, socle, derived, Sylow | C541 ⋊ C5×C9 |
| Hall | #19096459 ⋊ C5 |
| Hall | C541⋊C5 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C541 | C5×C9 |
| prime radical | (C541⋊C3)⋊C5 | C3 |
| cosocle | C541⋊C3 | C3×C5 |
| LCS | G ▷ C541 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 541 |
Polycyclic presentation:
3,5,3,541|a^3=c,d^a=d^225,d^b=d^48,d^c=d^41157 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24345, 6);