Finite Group DatabasebetaFinite Group Databasebeta| order | 29778 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C709 · Schur multiplier (H2) = C1 |
| direct product | D21×C709 |
| unambiguous semidirect product | C3⋊(D7×C709) |
| unambiguous semidirect product | C7⋊(D3×C709) |
| Fitting, socle, Hall | C3×C7×C709 ⋊ C2 |
| derived, Hall | C3×C7 ⋊ C2×C709 |
| Hall | C7×C709 ⋊ D3 |
| Hall | C3×C709 ⋊ D7 |
| Sylow | C7 ⋊ D3×C709 |
| Sylow | C3 ⋊ D7×C709 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C709 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C2×C709 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C709 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C709 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14889 |
8508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29778, 11);