Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#13133343 |
| Fitting, socle, Hall | C3×C52×C17 ⋊ C4 |
| derived, Hall | C52×C17 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ #595 |
| Hall | C3×C17 ⋊ #1043 |
| Sylow | C52 ⋊ C3×#595 |
| Sylow | C17 ⋊ C3×#1043 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13133343 |
| commutator, hypocenter | C52×C17 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C4 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 84);