Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×#6157 |
| unambiguous semidirect product | D53⋊(C22×C42) |
| Fitting | C23×C4×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #6157 |
| commutator, hypocenter | C53 | C23×C42 |
| Frattini | C2 | C24×#6157 |
| Fitting | C23×C4×C53 | C4 |
| socle | C24×C53 | C2×C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23×C4 | |
3000 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#6157)⋊#95, #28306423, #28306447, … |
| maximal normal subgroup of | (C2×#6157)⋊#95, #28306423, #28306447, … |
| maximal quotient of | C22×C42×#6157, C23×(C2×#6157)⋊C4, C22×#16811559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21480);