Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #557×D53 |
| Fitting | C53×#557 ⋊ C2 |
| Sylow | C53 ⋊ C2×#557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D53 |
| commutator, socle | C22×C53 | C25 |
| Fitting | C53×#557 | C2 |
| hypercenter | #557 | D53 |
| hypocenter | C53 | C2×#557 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #557 | |
1048 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1626, D53×#1636, D53×#1648, … |
| maximal normal subgroup of | D53×#1626, D53×#1636, D53×#1648, … |
| maximal quotient of | Q8×C4⋊C4×D53, D53×#2351, D53×#2355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 18078);