Finite Group DatabasebetaFinite Group Databasebeta| order | 29865 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×(C181⋊C3)⋊C5 |
| unambiguous semidirect product | (C181⋊C3)⋊(C5×C11) |
| unambiguous semidirect product | (C181⋊C5)⋊(C3×C11) |
| unambiguous semidirect product | (C11×C181⋊C5)⋊C3 |
| Fitting, socle, Hall | C11×C181 ⋊ C3×C5 |
| derived, Sylow | C181 ⋊ C3×C5×C11 |
| Hall | C11×C181⋊C5 ⋊ C3 |
| Hall | C11×C181⋊C3 ⋊ C5 |
| Hall | C181⋊C5 ⋊ C3×C11 |
| Hall | C181⋊C3 ⋊ C5×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | (C181⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C181 | C3×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C181 | C3×C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1991 |
297 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29865, 9);