Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#16811496 |
| Fitting | C2×C4⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#340 |
512 conjugacy classes of subgroups.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #340×#6157, C4×#16811496, #28306385, … |
| maximal normal subgroup of | #340×#6157, C4×#16811496, #28306385, … |
| maximal quotient of | C2×#20289544, #28300175, #28300185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20193);