Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#16811025 |
| Sylow | C53 ⋊ C2×#499 |
360 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 360 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 | #27283638, #27283640, #27283662, … |
| maximal normal subgroup of | #27283638, #27283640, #27283662, … |
| maximal quotient of | C2×#20274879, C2×#20275443, C2×#20275448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15014);