Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×#11719910 |
| Sylow | C53 ⋊ D4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6157 |
| commutator | C2×C53 | C22×C16 |
| Fitting | C4×D4×C53 | C4 |
| socle | C22×C53 | C22×C8 |
| hypercenter | C4×D4 | #6157 |
| hypocenter | C53 | D4×C16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
174 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
340 conjugacy classes — view the full character table.
| maximal subgroup of | D8×#11719910, #28309955, #28309957, … |
| maximal normal subgroup of | D8×#11719910, #28309955, #28309957, … |
| maximal quotient of | D8×#11719910, SD16×#11719910, Q16×#11719910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20887);