Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C9 | C3×C79⋊C3 |
| commutator, socle | C3×C79 | C3×C9 |
| Fitting | C3×C9×C79 | C3 |
| hypercenter | C3×C9 | C79⋊C3 |
| hypocenter | C79 | C27⋊C3 |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C9 ◁ C3×C9 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,79|a^3=c,c^3=d,b^a=bd,e^a=e^23735 conjugacy classes — view the full character table.
| maximal subgroup of | #34063172, #34063173, #34063181, … |
| maximal normal subgroup of | #34063172, #34063173, #34063181, … |
| maximal quotient of | #34063163, C32⋊(C79⋊C27), #34063188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 27);