Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16811020 |
| Sylow | C53 ⋊ C2×#498 |
424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #27302648, #27302650, #27303198, … |
| maximal normal subgroup of | #27302648, #27302650, #27303198, … |
| maximal quotient of | C2×#20274870, C2×#20275441, C2×#20275442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15008);