Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#16810460 |
| Fitting | C2×Q32×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×SD64 |
112 conjugacy classes of subgroups.
610 conjugacy classes — view the full character table.
| maximal subgroup of | #27304668, C4×#16810460, #27304681, … |
| maximal normal subgroup of | #27304668, C4×#16810460, #27304681, … |
| maximal quotient of | C2×#20272892, C2×#20272896, C2×#20272916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6810);