Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | #346×D53 |
| Fitting | C53×#346 ⋊ C2 |
| Sylow | C53 ⋊ C2×#346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D53 |
| commutator | C2×C53 | C2×C4×C8 |
| Fitting | C53×#346 | C2 |
| socle | C22×C53 | C22×C8 |
| hypercenter | #346 | D53 |
| hypocenter | C53 | C2×#346 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ #346 | |
200 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1313, #27293095, #27293099, … |
| maximal normal subgroup of | D53×#1313, #27293095, #27293099, … |
| maximal quotient of | D53×#1311, D53×#1312, #27293108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6098);