Finite Group DatabasebetaFinite Group Databasebeta| order | 5415 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C19 |
| direct product | C3×C192⋊C5 |
| unambiguous semidirect product | (C3×C192)⋊C5 |
| Fitting, socle, Hall | C3×C192 ⋊ C5 |
| derived, Sylow | C192 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C192⋊C5 |
| commutator, hypocenter | C192 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C192 | C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5415, 5);