Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810840 |
| Fitting | C22×SD16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#463 |
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 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.
766 conjugacy classes — view the full character table.
| maximal subgroup of | #27390309, C4×#16810840, #27390383, … |
| maximal normal subgroup of | #27390309, C4×#16810840, #27390383, … |
| maximal quotient of | C2×#20274126, C2×#20274140, C2×#20274154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13936);