Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#88324 |
| derived, Sylow | C53 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #6157 |
| commutator, hypocenter | C53 | C24×C8 |
| Frattini | C2 | C24×#6157 |
| Fitting, socle | C25×C53 | C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C25 | |
1976 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | #28306431, C22×#16811489, C2×#20290381, … |
| maximal normal subgroup of | #28306431, C22×#16811489, C2×#20290381, … |
| maximal quotient of | C23×C4×#88324, C23×C22⋊#88324, C23×C4⋊#88324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21493);