Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#13133248 |
| Fitting | C2×C4×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27278706, #27278712, #27278720, … |
| maximal normal subgroup of | #27278706, #27278712, #27278720, … |
| maximal quotient of | C8×#13133248, #27353686, #27353706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13329);