Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×#16811462 |
| derived, Sylow | C53 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #6157 |
| commutator, hypocenter | C53 | C2×C64 |
| Frattini | C16 | C2×#6157 |
| Fitting | C2×C16×C53 | C4 |
| socle | C22×C53 | C32 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C16 | |
40 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16811462, #28299310, #28299312, … |
| maximal normal subgroup of | C4×#16811462, #28299310, #28299312, … |
| maximal quotient of | C4×#16811462, C22⋊#16811462, C4⋊#16811462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19677);