Finite Group DatabasebetaFinite Group Databasebeta| order | 5415 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×C19⋊C3 |
| unambiguous semidirect product | C19⋊(C3×C5×C19) |
| unambiguous semidirect product | (C5×C19)⋊(C3×C19) |
| Fitting, socle, Hall | C5×C192 ⋊ C3 |
| derived | C19 ⋊ C3×C5×C19 |
| Sylow | C192 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | C19⋊C3 |
| commutator, hypocenter | C19 | C3×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C5×C19 | |
28 conjugacy classes of subgroups.
855 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5415, 6);