Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×M16×#6157 |
| Fitting | C2×M16×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6157 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C4 | C23×#6157 |
| Fitting | C2×M16×C53 | C4 |
| socle | C22×C53 | C2×C42 |
| hypercenter | C2×M16 | #6157 |
| hypocenter | C53 | C2×C4×M16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
656 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,ℤ/4)×#6157, #338×#6157, #339×#6157, … |
| maximal normal subgroup of | H(3,ℤ/4)×#6157, #338×#6157, #339×#6157, … |
| maximal quotient of | C2×M16×#88324, M16×D53⋊C8, C2×#20289913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21064);