Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×D53⋊C32 |
| unambiguous semidirect product | D53⋊(C2×C32) |
| derived, Sylow | C53 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #6157 |
| commutator, hypocenter | C53 | C22×C32 |
| Frattini | C8 | C22×#6157 |
| Fitting | C2×C16×C53 | C4 |
| socle | C22×C53 | C2×C16 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C16 | |
120 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#6157)⋊C32, #28299177, #28299178, … |
| maximal normal subgroup of | (C2×#6157)⋊C32, #28299177, #28299178, … |
| maximal quotient of | C4×D53⋊C32, C2×#20289820, D53⋊(C22⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20929);