Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810743 |
| Fitting | C2×#131×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#444 |
464 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27300998, #27300999, #27301001, … |
| maximal normal subgroup of | #27300998, #27300999, #27301001, … |
| maximal quotient of | C2×#20273525, C2×#20273527, C2×#20273532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13404);