Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16811001 |
| Sylow | C53 ⋊ C2×#494 |
552 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 552 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 | #27302308, #27302326, #27302346, … |
| maximal normal subgroup of | #27302308, #27302326, #27302346, … |
| maximal quotient of | C2×#20274309, C2×#20274311, C2×#20274313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14924);