Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×#11719908 |
| derived, Sylow | C53 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D53 |
| commutator, hypocenter | C53 | C23×C16 |
| Frattini | C8 | C23×D53 |
| Fitting | C23×C8×C53 | C2 |
| socle | C24×C53 | C8 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23×C8 | |
440 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17603);