Finite Group DatabasebetaFinite Group Databasebeta| order | 8510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D851 |
| unambiguous semidirect product | C23⋊(C5×D37) |
| unambiguous semidirect product | C37⋊(C5×D23) |
| Fitting, socle, Hall | C5×C23×C37 ⋊ C2 |
| derived, Hall | C23×C37 ⋊ C2×C5 |
| Hall | C5×C37 ⋊ D23 |
| Hall | C5×C23 ⋊ D37 |
| Sylow | C37 ⋊ C5×D23 |
| Sylow | C23 ⋊ C5×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D851 |
| commutator, hypocenter | C23×C37 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C37 | C2 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
2135 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D23×D37, D5×D851, D115⋊D37, … |
| maximal normal subgroup of | C5×D23×D37, D5×D851, D115⋊D37, … |
| maximal quotient of | C5×Dic851, C2×C5×D851, C3×C5×D851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8510, 4);