Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810834 |
| Sylow | C53 ⋊ C2×#462 |
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27278915, #27278917, #27278922, … |
| maximal normal subgroup of | #27278915, #27278917, #27278922, … |
| maximal quotient of | C2×#20274098, C2×#20274110, C2×#20274120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13949);