Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C27×C79 ⋊ C3 |
| Sylow | C79 ⋊ C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C9 | C3×C79⋊C3 |
| commutator, socle | C3×C79 | C3×C9 |
| Fitting | C27×C79 | C3 |
| hypercenter | C27 | C79⋊C3 |
| hypocenter | C79 | C27⋊C3 |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C9 ◁ C27 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,79|a^3=c,c^3=d,b^a=bd,e^b=e^23735 conjugacy classes — view the full character table.
| maximal subgroup of | C27⋊C3×C79⋊C3, C3×#20264241, #34063311, … |
| maximal normal subgroup of | C27⋊C3×C79⋊C3, C3×#20264241, #34063311, … |
| maximal quotient of | #34063161, (C3×C79⋊C3)⋊C27, (C79⋊C9)⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 25);