Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16811510 |
| Fitting | C2×C16×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#346 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×#6157 |
| commutator | C2×C53 | C2×C4×C8 |
| Frattini | C8 | C22×#6157 |
| Fitting | C2×C16×C53 | C4 |
| socle | C22×C53 | C4×C8 |
| hypercenter | C2×C16 | #6157 |
| hypocenter | C53 | C2×#346 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
200 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
496 conjugacy classes — view the full character table.
| maximal subgroup of | #28299161, #28299167, #346×#6157, … |
| maximal normal subgroup of | #28299161, #28299167, #346×#6157, … |
| maximal quotient of | C2×#20289626, #28307748, C2×#88324⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20709);