Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | #393×D53 |
| Fitting | C53×#393 ⋊ C2 |
| Sylow | C53 ⋊ C2×#393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C53×#393 | C2 |
| hypercenter | #393 | D53 |
| hypocenter | C53 | C2×#393 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #393 | |
1036 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 203 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×#1351, #27294798, D53×#1601, … |
| maximal normal subgroup of | D53×#1351, #27294798, D53×#1601, … |
| maximal quotient of | D53×#1439, D53×#1442, D53×#1446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 7708);