Finite Group DatabasebetaFinite Group Databasebeta| order | 16410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1641 |
| unambiguous semidirect product | C3⋊(C5×D547) |
| unambiguous semidirect product | C547⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C547 ⋊ C2 |
| derived, Hall | C3×C547 ⋊ C2×C5 |
| Hall | C5×C547 ⋊ D3 |
| Sylow | C547 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D547 |
| Sylow | C3 ⋊ C5×D547 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1641 |
| commutator, cosocle, hypocenter | C3×C547 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C547 | C2 |
| LCS | G ▷ C3×C547 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8205 |
4110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D547, D5×D1641, D15⋊D547, … |
| maximal normal subgroup of | C5×D3×D547, D5×D1641, D15⋊D547, … |
| maximal quotient of | C5×Dic1641, C2×C5×D1641 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16410, 7);