Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#13133243 |
| Fitting | C2×C4×D4×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27278713, #27278719, #27278727, … |
| maximal normal subgroup of | #27278713, #27278719, #27278727, … |
| maximal quotient of | C8×#13133243, #27353675, #27353695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13318);