Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #529×D53 |
| Fitting | C53×#529 ⋊ C2 |
| Sylow | C53 ⋊ C2×#529 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C25 |
| Frattini | C22 | C24×D53 |
| Fitting | C53×#529 | C2 |
| hypercenter | #529 | D53 |
| hypocenter | C53 | C2×#529 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #529 | |
1232 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1482, D53×#1483, #27350642, … |
| maximal normal subgroup of | D53×#1482, D53×#1483, #27350642, … |
| maximal quotient of | D53×#2283, D53×#2290, D53×#2293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17768);