Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#16811509 |
| derived, Sylow | C53 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #6157 |
| commutator, hypocenter | C53 | C2×C4×C16 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | C22×C8×C53 | C4 |
| socle | C23×C53 | C2×C8 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C8 | |
216 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | #28298255, #28298268, #28298367, … |
| maximal normal subgroup of | #28298255, #28298268, #28298367, … |
| maximal quotient of | C2×C8×#11719910, C2×#20289630, #28307807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20708);