Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×D212 |
| Fitting | C4×D8×C53 ⋊ C2 |
| Sylow | C53 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
763 conjugacy classes — view the full character table.
| maximal subgroup of | #27297515, #27297519, #27297543, … |
| maximal normal subgroup of | #27297515, #27297519, #27297543, … |
| maximal quotient of | #27373444, #27373459, #27373474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16186);