Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | #488×D53 |
| Fitting | C53×#488 ⋊ C2 |
| Sylow | C53 ⋊ C2×#488 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D53 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#488 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #488 | D53 |
| hypocenter | C53 | C2×#488 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #488 | |
412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1414, C2×#488×D53, D53×#3131, … |
| maximal normal subgroup of | D53×#1414, C2×#488×D53, D53×#3131, … |
| maximal quotient of | D53×#1835, D53×#1933, D53×#1934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14823);