Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16811620 |
| Fitting | C2×#41×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#421 |
772 conjugacy classes of subgroups.
304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306622, #28306624, #28306639, … |
| maximal normal subgroup of | #28306622, #28306624, #28306639, … |
| maximal quotient of | C2×#20290015, C2×#20290018, C2×#20290010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21138);