Finite Group DatabasebetaFinite Group Databasebeta| order | 8650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D865 |
| unambiguous semidirect product | C5⋊(C5×D173) |
| unambiguous semidirect product | C173⋊(C5×D5) |
| Fitting, socle, Hall | C52×C173 ⋊ C2 |
| derived | C5×C173 ⋊ C2×C5 |
| Sylow | C173 ⋊ C5×D5 |
| Sylow | C52 ⋊ D173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D865 |
| commutator, hypocenter | C5×C173 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C173 | C2 |
| LCS | G ▷ C5×C173 | |
| UCS | C1 ◁ C5 | |
20 conjugacy classes of subgroups.
2170 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#16812337, C5×#16812338, C5×D5×D173, … |
| maximal normal subgroup of | C5×#16812337, C5×#16812338, C5×D5×D173, … |
| maximal quotient of | C5×Dic865, C2×C5×D865, C3×C5×D865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8650, 8);