Finite Group DatabasebetaFinite Group Databasebeta| order | 7935 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×C232⋊C3 |
| unambiguous semidirect product | C232⋊(C3×C5) |
| unambiguous semidirect product | (C5×C232)⋊C3 |
| Fitting, socle, Hall | C5×C232 ⋊ C3 |
| derived, Sylow | C232 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C232⋊C3 |
| commutator, hypocenter | C232 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C232 | C3 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
895 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7935, 3);