Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C33×C79 ⋊ C3 |
| Sylow | C79 ⋊ AΣL(1,𝔽27) |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C32⋊(C79⋊C3) |
| commutator | C32×C79 | C32 |
| Frattini | C32 | C3×C79⋊C3 |
| Fitting | C33×C79 | C3 |
| socle | C3×C79 | H(3,𝔽3) |
| hypercenter | C33 | C79⋊C3 |
| hypocenter | C79 | AΣL(1,𝔽27) |
| LCS | G ▷ C32×C79 ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C3 ◁ C32 ◁ C33 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,79|b^a=bc,c^a=cd,e^a=e^23719 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽27)×C79⋊C3, C3×#20264245, #34063328, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C79⋊C3, C3×#20264245, #34063328, … |
| maximal quotient of | #34063141, #34063143, #34063144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 29);