Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16811586 |
| Fitting | C22×C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×#6157 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C4 | C23×#6157 |
| Fitting | C22×C8×C53 | C4 |
| socle | C22×C53 | C2×C42 |
| hypercenter | C22×C8 | #6157 |
| hypocenter | C53 | C2×#405 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
592 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | #28306371, #28306372, #28306395, … |
| maximal normal subgroup of | #28306371, #28306372, #28306395, … |
| maximal quotient of | C2×C8×#11719940, C8×D53⋊M16, C2×C8×#11719936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21068);