Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C19 |
| direct product | C3×C5⋊(C19⋊D19) |
| unambiguous semidirect product | C5⋊(C3×C19⋊D19) |
| Fitting, socle, Hall | C3×C5×C192 ⋊ C2 |
| derived, Hall | C5×C192 ⋊ C2×C3 |
| Hall | C3×C192 ⋊ D5 |
| Sylow | C192 ⋊ C3×D5 |
| Hall | C3×C5 ⋊ C19⋊D19 |
| Sylow | C5 ⋊ C3×C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊(C19⋊D19) |
| commutator, cosocle, hypocenter | C5×C192 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C192 | C2 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 ◁ C3 | |
176 conjugacy classes of subgroups.
2712 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 51);