Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16810970 |
| Fitting | C2×C4×C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#486 |
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #27279340, #27279342, #27279373, … |
| maximal normal subgroup of | #27279340, #27279342, #27279373, … |
| maximal quotient of | C2×#20274843, C2×#20275398, C2×#20275521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14816);