Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | #131×#6157 |
| Fitting | #131×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22×#6157 |
| commutator, socle | C2×C53 | C22×C42 |
| Frattini | C4 | C23×#6157 |
| Fitting | #131×C53 | C4 |
| hypercenter | #131 | #6157 |
| hypocenter | C53 | C4×#131 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C8 ◁ #131 | |
572 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | #350×#6157, #28310491, #443×#6157, … |
| maximal normal subgroup of | #350×#6157, #28310491, #443×#6157, … |
| maximal quotient of | #131×#88324, #28313763, C8×#13133304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21077);