Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#16811389 |
| Fitting | C22×M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D53 |
| commutator | C2×C53 | C24×C4 |
| Frattini | C4 | C24×D53 |
| Fitting | C22×M16×C53 | C2 |
| socle | C22×C53 | C23×C4 |
| hypercenter | C22×M16 | D53 |
| hypocenter | C53 | C2×#568 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
1460 conjugacy classes of subgroups.
1108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289418, #27289421, #27289428, … |
| maximal normal subgroup of | #27289418, #27289421, #27289428, … |
| maximal quotient of | C2×#20283132, C2×#20283133, C2×#20283140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19219);