Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16811436 |
| Fitting | C22×Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#578 |
1408 conjugacy classes of subgroups.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27299781, #27299793, #27299822, … |
| maximal normal subgroup of | #27299781, #27299793, #27299822, … |
| maximal quotient of | C2×#20283243, C2×#20283311, C2×#20283552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19273);