Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16811440 |
| Fitting | C2×#131×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#578 |
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299782, #27299785, #27299792, … |
| maximal normal subgroup of | #27299782, #27299785, #27299792, … |
| maximal quotient of | C2×#20283249, C2×#20283315, C2×#20283560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19277);