Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #137×#6157 |
| Fitting | #137×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
187 conjugacy classes — view the full character table.
| maximal subgroup of | #455×#6157, #456×#6157, #28320987, … |
| maximal normal subgroup of | #455×#6157, #456×#6157, #28320987, … |
| maximal quotient of | #137×#88324, #28316389, #28316390, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21266);