Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16811434 |
| Fitting | C2×H(5,𝔽2)×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#577 |
1460 conjugacy classes of subgroups.
928 conjugacy classes — view the full character table.
| maximal subgroup of | #27400002, #27400008, #27400029, … |
| maximal normal subgroup of | #27400002, #27400008, #27400029, … |
| maximal quotient of | C2×#20283241, C2×#20283245, C2×#20283308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19270);