Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4⋊C4×#6157 |
| Fitting | C2×C4⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×C4×C4⋊C4 |
928 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | #324×#6157, #28301541, #340×#6157, … |
| maximal normal subgroup of | #324×#6157, #28301541, #340×#6157, … |
| maximal quotient of | C2×#95×#6157, C4×C4⋊C4×#6157, C2×#20289890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20941);