Finite Group DatabasebetaFinite Group Databasebeta| order | 11715 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×#16840847 |
| Fitting, socle, Hall | C3×C11×C71 ⋊ C5 |
| derived, Hall | C11×C71 ⋊ C3×C5 |
| Hall | C3×C71 ⋊ C11⋊C5 |
| Sylow | C71 ⋊ C3×C11⋊C5 |
| Hall | C3×C11 ⋊ C71⋊C5 |
| Sylow | C11 ⋊ C3×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16840847 |
| commutator, cosocle, hypocenter | C11×C71 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C71 | C5 |
| LCS | G ▷ C11×C71 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
483 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11715, 7);