Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×(C19⋊C3)⋊D19 |
| unambiguous semidirect product | (C19⋊C3)⋊(C5×D19) |
| Fitting, socle, Hall | C5×C192 ⋊ C2×C3 |
| derived, Sylow | C192 ⋊ C2×C3×C5 |
| Hall | C5×C19×C19⋊C3 ⋊ C2 |
| Hall | C5×C19⋊D19 ⋊ C3 |
| Hall | C19×C19⋊C3 ⋊ C2×C5 |
| Hall | C19⋊D19 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C19⋊C3)⋊D19 |
| commutator, cosocle, hypocenter | C192 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C2×C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
56 conjugacy classes of subgroups.
450 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 27);