Finite Group DatabasebetaFinite Group Databasebeta| order | 9375 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #15691114⋊C3 |
| Fitting, Sylow | #15691114 ⋊ C3 |
| derived | C252 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C252 | C3×C5 |
| Frattini, socle | C52 | C5×C52⋊C3 |
| Fitting | #15691114 | C3 |
| LCS | G ▷ C252 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
3,5^5|c^5=e,d^5=f,c^a=c^2def^2,d^a=c^3d^2e^2f^3,e^a=e^2f,f^a=e^3f^2,c^b=ce,d^b=df95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9375, 90);