Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16811663 |
| unambiguous semidirect product | D53⋊#441 |
| Fitting | C2×Q16×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#441 |
480 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
226 conjugacy classes — view the full character table.
| maximal subgroup of | #28310707, #28310708, #28310709, … |
| maximal normal subgroup of | #28310707, #28310708, #28310709, … |
| maximal quotient of | C2×#20290308, C2×#20290309, D53⋊#1579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21262);