Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #398×D53 |
| Fitting | C53×#398 ⋊ C2 |
| Sylow | C53 ⋊ C2×#398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C53×#398 | C2 |
| hypercenter | #398 | D53 |
| hypocenter | C53 | C2×#398 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #398 | |
692 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1346, #27294776, D53×#1609, … |
| maximal normal subgroup of | D53×#1346, #27294776, D53×#1609, … |
| maximal quotient of | D53×#1441, D53×#1442, D53×#1444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 7739);