Finite Group DatabasebetaFinite Group Databasebeta| order | 5766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#15668332 |
| Fitting, socle, Hall | C2×C312 ⋊ C3 |
| derived, Sylow | C312 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #15668332 |
| commutator, hypocenter | C312 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C312 | C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
136 conjugacy classes of subgroups.
646 conjugacy classes — view the full character table.
| maximal subgroup of | #26040335, #26040337, C4×#15668332, … |
| maximal normal subgroup of | #26040335, #26040337, C4×#15668332, … |
| maximal quotient of | C4×#15668332, C22×#15668332, C2×#22575710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5766, 17);