Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16811007 |
| Fitting | C2×C4×C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#495 |
592 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 592 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.
1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27283633, #27283635, #27283657, … |
| maximal normal subgroup of | #27283633, #27283635, #27283657, … |
| maximal quotient of | C2×#20274307, C2×#20274312, C2×#20274316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14931);