Finite Group DatabasebetaFinite Group Databasebeta| order | 5310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D885 |
| unambiguous semidirect product | C3⋊(C3×D295) |
| unambiguous semidirect product | C5⋊(C3×D177) |
| unambiguous semidirect product | C59⋊(C3×D15) |
| Fitting, socle, Hall | C32×C5×C59 ⋊ C2 |
| derived | C3×C5×C59 ⋊ C2×C3 |
| Hall | C32×C59 ⋊ D5 |
| Hall | C5×C59 ⋊ C3×D3 |
| Sylow | C59 ⋊ C3×D15 |
| Hall | C32×C5 ⋊ D59 |
| Sylow | C32 ⋊ D295 |
| Sylow | C5 ⋊ C3×D177 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D885 |
| commutator, hypocenter | C3×C5×C59 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C59 | C2 |
| LCS | G ▷ C3×C5×C59 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
1332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D4425, C3×C5×D885, C3×C3⋊(C5⋊D295), … |
| maximal normal subgroup of | C3×C5×D885, C3×C7×D885 |
| maximal quotient of | C3×D4425, C3×C5×D885, C3×C3⋊(C5⋊D295), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5310, 16);