Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #575×D53 |
| Fitting | C53×#575 ⋊ C2 |
| Sylow | C53 ⋊ C2×#575 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D53 |
| commutator | C4×C53 | C25 |
| Frattini | C4 | C24×D53 |
| Fitting | C53×#575 | C2 |
| socle | C2×C53 | C23×D4 |
| hypercenter | #575 | D53 |
| hypocenter | C53 | C2×#575 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
1484 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1881, #27385570, D53×#1906, … |
| maximal normal subgroup of | D53×#1881, #27385570, D53×#1906, … |
| maximal quotient of | D53×#2896, D53×#2911, D53×#2943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19252);