Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810741 |
| Fitting | C2×C4×C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#443 |
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20272687, C2×#20272689, #27293878, … |
| maximal normal subgroup of | C2×#20272687, C2×#20272689, #27293878, … |
| maximal quotient of | C2×C8×D424, C2×C8×#11719913, C2×C8×Dic212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13401);