Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C361⋊C3 |
| unambiguous semidirect product | (C2×C361)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×C361)⋊C3 |
| Fitting, Hall | C2×C5×C361 ⋊ C3 |
| derived, Sylow | C361 ⋊ C2×C3×C5 |
| Hall | C5×C361 ⋊ C2×C3 |
| Hall | C2×C361 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C361⋊C3 |
| commutator, cosocle, hypocenter | C361 | C2×C3×C5 |
| Frattini | C19 | C2×C5×C19⋊C3 |
| Fitting | C2×C5×C361 | C3 |
| socle | C2×C5×C19 | C19⋊C3 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
1230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 5);