Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#41×#6157 |
| unambiguous semidirect product | D53⋊(C4×#41) |
| Fitting | C2×#41×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6157 |
| commutator | C2×C53 | C24×C4 |
| Frattini | C2 | C24×#6157 |
| Fitting | C2×#41×C53 | C4 |
| socle | C22×C53 | C23×C4 |
| hypercenter | C2×#41 | #6157 |
| hypocenter | C53 | C2×C4×#41 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
1728 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | #28306575, #28306578, #28306620, … |
| maximal normal subgroup of | #28306575, #28306578, #28306620, … |
| maximal quotient of | C2×#117×#6157, C2×C4×D4×#6157, C2×C4×Q8×#6157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21486);