Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#16811337 |
| Fitting | C2×#121×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D53 |
| commutator | C22×C53 | C25 |
| Frattini | C22 | C24×D53 |
| Fitting | C2×#121×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C2×#121 | D53 |
| hypocenter | C53 | C2×#555 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
1240 conjugacy classes of subgroups.
778 conjugacy classes — view the full character table.
| maximal subgroup of | #27275677, #27350335, #27400285, … |
| maximal normal subgroup of | #27275677, #27350335, #27400285, … |
| maximal quotient of | C2×#20277597, C2×#20277599, C2×#20277602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 18049);