Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D848 |
| Fitting | C4×C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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 | #27271541, #27271543, #27271547, … |
| maximal normal subgroup of | #27271541, #27271543, #27271547, … |
| maximal quotient of | C8×D848, #27295989, #27296072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6358);