Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C9 |
| direct product | C9×C79⋊C9 |
| unambiguous semidirect product | C79⋊C92 |
| derived, Sylow | C79 ⋊ C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | C79⋊C3 |
| commutator, hypocenter | C79 | C92 |
| Frattini | C32 | C3×C79⋊C3 |
| Fitting | C3×C9×C79 | C3 |
| socle | C32×C79 | C32 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3×C9 | |
46 conjugacy classes of subgroups.
783 conjugacy classes — view the full character table.
| maximal subgroup of | C27×C79⋊C9, #34063161, #34063162, … |
| maximal normal subgroup of | C27×C79⋊C9, #34063161, #34063162, … |
| maximal quotient of | C79⋊#6855, C27×C79⋊C9, C9×C79⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 17);