Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C32×#6157 |
| Fitting | C32×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #6157 |
| commutator, hypocenter | C53 | C4×C32 |
| Frattini | C16 | C2×#6157 |
| Fitting | C32×C53 | C4 |
| socle | C2×C53 | C4×C16 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | C64×#6157, #28299311, C2×C32×#6157, … |
| maximal normal subgroup of | C64×#6157, #28299311, C2×C32×#6157, … |
| maximal quotient of | C32×#88324, #88324⋊C32, (C2×#6157)⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19613);