Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| isoclinism | isoclinic class of C79⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C27×C79⋊C3 |
| Fitting | C27×C79 ⋊ C3 |
| derived, Sylow | C79 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C79⋊C3 |
| commutator, hypocenter | C79 | C3×C27 |
| Frattini | C9 | C3×C79⋊C3 |
| Fitting | C27×C79 | C3 |
| socle | C3×C79 | C3×C9 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C27 | |
28 conjugacy classes of subgroups.
783 conjugacy classes — view the full character table.
| maximal subgroup of | C81×C79⋊C3, #34063197, #34063198, … |
| maximal normal subgroup of | C81×C79⋊C3, #34063197, #34063198, … |
| maximal quotient of | C27×C79⋊C9, (C3×C79⋊C3)⋊C27, (C79⋊C9)⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 23);