Finite Group DatabasebetaFinite Group Databasebeta| order | 29766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C112 · Schur multiplier (H2) = C11 |
| direct product | C3×C112×D41 |
| unambiguous semidirect product | C41⋊(C2×C3×C112) |
| Fitting, socle, Hall | C3×C112×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C3×C112 |
| Hall | C112×C41 ⋊ C2×C3 |
| Hall | C3×C41 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C112 | D41 |
| commutator, cosocle, hypocenter | C41 | C2×C3×C112 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C41 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C112 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14883 |
7986 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29766, 16);