Finite Group DatabasebetaFinite Group Databasebeta| order | 10758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D163⋊C3 |
| unambiguous semidirect product | D163⋊(C3×C11) |
| unambiguous semidirect product | (C163⋊C3)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D163)⋊C3 |
| Fitting, socle, Hall | C11×C163 ⋊ C2×C3 |
| derived, Sylow | C163 ⋊ C2×C3×C11 |
| Hall | C11×C163⋊C3 ⋊ C2 |
| Hall | C11×D163 ⋊ C3 |
| Hall | C163⋊C3 ⋊ C2×C11 |
| Hall | D163 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D163⋊C3 |
| commutator, cosocle, hypocenter | C163 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C163 | C2×C3 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
363 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10758, 10);