Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C79 ⋊ #733 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C32⋊(C79⋊C3) |
| commutator | C32×C79 | C32 |
| Frattini | C32 | C3×C79⋊C3 |
| Fitting | 3−1+2×C79 | C3 |
| socle | C3×C79 | H(3,𝔽3) |
| hypercenter | 3−1+2 | C79⋊C3 |
| hypocenter | C79 | #733 |
| LCS | G ▷ C32×C79 ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C3 ◁ C32 ◁ 3−1+2 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,79|a^3=d,b^3=d^2,b^a=bc,c^a=cd,e^b=e^23303 conjugacy classes — view the full character table.
| maximal subgroup of | #733×C79⋊C3, C3×#20264252, #34063328, … |
| maximal normal subgroup of | #733×C79⋊C3, C3×#20264252, #34063328, … |
| maximal quotient of | #34063146, #34063147, #34063149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 36);