Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #472×D53 |
| Fitting | C53×#472 ⋊ C2 |
| Sylow | C53 ⋊ C2×#472 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #121×D53 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#472 | C2 |
| socle | C2×C53 | C2×#121 |
| hypercenter | #472 | D53 |
| hypocenter | C53 | C2×#472 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
488 conjugacy classes of subgroups.
448 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2192, D53×#2193, #27538072, … |
| maximal normal subgroup of | D53×#2192, D53×#2193, #27538072, … |
| maximal quotient of | D53×#1667, D53×#1675, D53×#1677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14213);