Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×#88324 |
| derived, Sylow | C53 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #6157 |
| commutator, hypocenter | C53 | C42×C8 |
| Frattini | C23 | C22×#6157 |
| Fitting | C2×C42×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C42 | |
408 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | #28297999, C4×C8×#88324, C4×#16811464, … |
| maximal normal subgroup of | #28297999, C4×C8×#88324, C4×#16811464, … |
| maximal quotient of | C4×C8×#88324, C4×#16811464, #97×#88324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20162);