Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×D4⋊#88324 |
| Sylow | C53 ⋊ C2×D4⋊C8 |
344 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
316 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D4⋊#88324, #28301628, #28301634, … |
| maximal normal subgroup of | C4×D4⋊#88324, #28301628, #28301634, … |
| maximal quotient of | C2×#20289531, C2×#20289533, #28299410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19795);