Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C9×C79 ⋊ C3 |
| Sylow | C79 ⋊ #737 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | C3×C79⋊C3 |
| commutator, socle | C3×C79 | C33 |
| Frattini | C3 | C32×C79⋊C3 |
| Fitting | C3×C9×C79 | C3 |
| hypercenter | C3×C9 | C79⋊C3 |
| hypocenter | C79 | #737 |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C9 ◁ C3×C9 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,79|c^3=d,b^a=bd,e^b=e^23735 conjugacy classes — view the full character table.
| maximal subgroup of | #34063181, #34063183, #34063184, … |
| maximal normal subgroup of | #34063181, #34063183, #34063184, … |
| maximal quotient of | #34063235, #34063237, C9×C32⋊(C79⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 47);