Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C79⋊C81 |
| derived, Sylow | C79 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C27 | C79⋊C3 |
| commutator, hypocenter | C79 | C81 |
| Fitting | C27×C79 | C3 |
| socle | C3×C79 | C27 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C27 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,79|a^3=b,b^3=c,c^3=d,e^a=e^23783 conjugacy classes — view the full character table.
| maximal subgroup of | C81×C79⋊C3, C3×C79⋊C81, #34063197, … |
| maximal normal subgroup of | C81×C79⋊C3, C3×C79⋊C81, #34063197, … |
| maximal quotient of | C79⋊C243, C3×C79⋊C81 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 16);