Finite Group DatabasebetaFinite Group Databasebeta| order | 8228 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C11⋊#595 |
| unambiguous semidirect product | C11⋊(C11×#595) |
| Fitting, socle, Hall | C112×C17 ⋊ C4 |
| derived | C11×C17 ⋊ C4×C11 |
| Sylow | C112 ⋊ #595 |
| Sylow | C17 ⋊ C11×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C11⋊#595 |
| commutator, hypocenter | C11×C17 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C17 | C4 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C11 | |
44 conjugacy classes of subgroups.
638 conjugacy classes — view the full character table.
| maximal subgroup of | #37590608, C3×C11×C11⋊#595, C11×C3⋊(C11⋊#595) |
| maximal normal subgroup of | C3×C11×C11⋊#595 |
| maximal quotient of | C3×C11×C11⋊#595, C11×C3⋊(C11⋊#595) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8228, 20);