Finite Group DatabasebetaFinite Group Databasebeta| order | 8052 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C11⋊#6923 |
| unambiguous semidirect product | C11⋊(C3×#6923) |
| Fitting, socle, Hall | C3×C11×C61 ⋊ C4 |
| derived, Hall | C11×C61 ⋊ C3×C4 |
| Hall | C3×C61 ⋊ Dic11 |
| Sylow | C61 ⋊ C3×Dic11 |
| Hall | C3×C11 ⋊ #6923 |
| Sylow | C11 ⋊ C3×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊#6923 |
| commutator, hypocenter | C11×C61 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C61 | C4 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
537 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8052, 21);