Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C8×#11719908 |
| derived, Sylow | C53 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | D53 |
| commutator, hypocenter | C53 | C8×C16 |
| Frattini | C4×C8 | C2×D53 |
| Fitting | C82×C53 | C2 |
| socle | C22×C53 | C4×C8 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C82 | |
104 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#11719908, #27270706, #27270707, … |
| maximal normal subgroup of | C16×#11719908, #27270706, #27270707, … |
| maximal quotient of | C16×#11719908, #27270706, #27270920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2425);