Finite Group DatabasebetaFinite Group Databasebeta| order | 8649 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C31 |
| direct product | C3×#15668333 |
| Fitting, socle | C3×C312 ⋊ C3 |
| derived, Sylow | C312 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15668333 |
| commutator, hypocenter | C312 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C312 | C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C3 | |
44 conjugacy classes of subgroups.
969 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8649, 12);