Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16811622 |
| Fitting | C22×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#421 |
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306629, #28306637, #28306652, … |
| maximal normal subgroup of | #28306629, #28306637, #28306652, … |
| maximal quotient of | C2×#20290016, C2×#20290017, C2×#20290013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21139);