Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#16810924 |
| Fitting | C2×C4⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#478 |
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27280440, #27280442, #27391693, … |
| maximal normal subgroup of | #27280440, #27280442, #27391693, … |
| maximal quotient of | C2×#20274726, C2×#20274965, C2×#20274979, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14268);