Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×D53⋊M16 |
| Sylow | C53 ⋊ C2×C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×#6157 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C22 | C23×#6157 |
| Fitting | C2×C42×C53 | C4 |
| socle | C22×C53 | C23×C4 |
| hypercenter | C2×C42 | #6157 |
| hypocenter | C53 | C2×C4×M16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C42 ◁ C2×C42 | |
656 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | #28300113, #28300114, #28300121, … |
| maximal normal subgroup of | #28300113, #28300114, #28300121, … |
| maximal quotient of | C8×D53⋊M16, #28313774, #28313802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21066);