Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#16810461 |
| Sylow | C53 ⋊ C2×SD64 |
112 conjugacy classes of subgroups.
610 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16810461, #27304674, #27304680, … |
| maximal normal subgroup of | C4×#16810461, #27304674, #27304680, … |
| maximal quotient of | C2×#20272893, C2×#20272895, C2×#20272916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6811);