Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16810596 |
| Fitting | C2×#117×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#410 |
788 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289418, #27289421, #27289423, … |
| maximal normal subgroup of | #27289418, #27289421, #27289423, … |
| maximal quotient of | C2×#20273027, C2×#20273035, C2×#20273038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12966);