Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C26×D53 |
| unambiguous semidirect product | C53⋊C27 |
| unambiguous semidirect product | (C2×C53)⋊C26 |
| Fitting, socle | C26×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D53 |
| commutator, hypocenter | C53 | C27 |
| Frattini | C1 | G |
| Fitting, socle | C26×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C26 | |
58424 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27315247, C2×#379×D53, C22×#16810478, … |
| maximal normal subgroup of | #27315247, C2×#379×D53, C22×#16810478, … |
| maximal quotient of | C25×C4×D53, C26×Dic53, C24×D4×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19324);