Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
| direct product | C3×#14523840 |
| Sylow | C79 ⋊ C3×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×C79⋊C3 |
| commutator | C3×C79 | C33 |
| Frattini | C3 | C32×C79⋊C3 |
| Fitting | C33×C79 | C3 |
| socle | C32×C79 | C32 |
| hypercenter | C33 | C79⋊C3 |
| hypocenter | C79 | C3×3−1+2 |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C32 ◁ C33 | |
76 conjugacy classes of subgroups.
735 conjugacy classes — view the full character table.
| maximal subgroup of | #34063143, #34063144, #34063145, … |
| maximal normal subgroup of | #34063143, #34063144, #34063145, … |
| maximal quotient of | C3×C32⋊(C79⋊C9), C3×(C79⋊C9)⋊C9, C9×#14523840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 45);