Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #532×D53 |
| Fitting | C53×#532 ⋊ C2 |
| Sylow | C53 ⋊ C2×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C25 |
| Frattini | C22 | C24×D53 |
| Fitting | C53×#532 | C2 |
| hypercenter | #532 | D53 |
| hypocenter | C53 | C2×#532 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
1728 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1480, D53×#1484, #27350630, … |
| maximal normal subgroup of | D53×#1480, D53×#1484, #27350630, … |
| maximal quotient of | D53×#2285, D53×#2293, D53×#2297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17787);