Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | #350×D53 |
| Fitting | C53×#350 ⋊ C2 |
| Sylow | C53 ⋊ C2×#350 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D53 |
| commutator | C4×C53 | C22×C8 |
| Frattini | C2×C8 | C22×D53 |
| Fitting | C53×#350 | C2 |
| socle | C2×C53 | C2×C22⋊C8 |
| hypercenter | #350 | D53 |
| hypocenter | C53 | C2×#350 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #350 | |
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
784 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#350×D53, D53×#2117, #27536796, … |
| maximal normal subgroup of | C2×#350×D53, D53×#2117, #27536796, … |
| maximal quotient of | D53×#1315, #27293165, D53×#1323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6132);