Finite Group DatabasebetaFinite Group Databasebeta| order | 6399 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | 3−1+2×C79 ⋊ C3 |
| Sylow | C79 ⋊ #737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C79⋊C3 |
| commutator, socle | C3×C79 | C33 |
| Fitting | 3−1+2×C79 | C3 |
| hypercenter | 3−1+2 | C79⋊C3 |
| hypocenter | C79 | #737 |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C3 ◁ 3−1+2 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,79|c^3=d,b^a=bd,e^a=e^55,e^c=e^23319 conjugacy classes — view the full character table.
| maximal subgroup of | #34063328, #34063331, #34063333, … |
| maximal normal subgroup of | #34063328, #34063331, #34063333, … |
| maximal quotient of | #34063234, #34063236, #34063238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6399, 48);