Finite Group DatabasebetaFinite Group Databasebeta| order | 29799 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#14582151 |
| derived, Hall | C7×C43 ⋊ C9×C11 |
| Hall | C7×C11×C43 ⋊ C9 |
| Hall | C11×C43 ⋊ C7⋊C9 |
| Hall | C7×C11 ⋊ C43⋊C9 |
| Sylow | C43 ⋊ C11×C7⋊C9 |
| Sylow | C7 ⋊ C11×C43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #11744749 |
| commutator, hypocenter | C7×C43 | C9×C11 |
| Frattini | C3 | C11×#11744749 |
| Fitting, socle, prime radical | C3×C7×C11×C43 | C3 |
| cosocle | C3×C7×C43 | C3×C11 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C3×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 29799 |
3399 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29799, 5);