Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16811053 |
| Fitting | C2×#135×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27301139, #27301140, #27301142, … |
| maximal normal subgroup of | #27301139, #27301140, #27301142, … |
| maximal quotient of | C2×#20276420, C2×#20276422, C2×#20276497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17626);