Finite Group DatabasebetaFinite Group Databasebeta| order | 29766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| direct product | D41×C112⋊C3 |
| unambiguous semidirect product | C41⋊(C2×C112⋊C3) |
| unambiguous semidirect product | (C112×D41)⋊C3 |
| Fitting, socle, derived, Hall | C112×C41 ⋊ C2×C3 |
| Hall | C41×C112⋊C3 ⋊ C2 |
| Hall | C112×D41 ⋊ C3 |
| Sylow | C112 ⋊ C3×D41 |
| Sylow | C41 ⋊ C2×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C41 | C2×C3 |
| LCS | G ▷ C112×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1353 |
946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29766, 10);