Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×#6157 |
| Fitting | 2−1+4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#6157 |
| commutator, socle | C2×C53 | C24×C4 |
| Fitting | 2−1+4×C53 | C4 |
| hypercenter | 2−1+4 | #6157 |
| hypocenter | C53 | C4×2−1+4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
289 conjugacy classes — view the full character table.
| maximal subgroup of | #454×#6157, #456×#6157, #28320988, … |
| maximal normal subgroup of | #454×#6157, #456×#6157, #28320988, … |
| maximal quotient of | #520×#6157, #519×#6157, #536×#6157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21492);