Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #536×D53 |
| Fitting | C53×#536 ⋊ C2 |
| Sylow | C53 ⋊ C2×#536 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D53 |
| commutator, socle | C22×C53 | C25 |
| Fitting | C53×#536 | C2 |
| hypercenter | #536 | D53 |
| hypocenter | C53 | C2×#536 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #536 | |
1512 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1909, D53×#1912, D53×#1915, … |
| maximal normal subgroup of | D53×#1909, D53×#1912, D53×#1915, … |
| maximal quotient of | D53×#2310, D53×#2311, D53×#2317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17822);