Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | H(3,𝔽3)×C79 ⋊ C3 |
| Sylow | C79 ⋊ AΣL(1,𝔽27) |
40 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,79|b^a=bc,c^a=cd,e^b=e^23303 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽27)×C79⋊C3, C3×#20264244, #34063329, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C79⋊C3, C3×#20264244, #34063329, … |
| maximal quotient of | #34063141, #34063144, #34063145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 28);