Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810605 |
| Fitting | C22×M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#413 |
756 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289428, #27289431, #27289438, … |
| maximal normal subgroup of | #27289428, #27289431, #27289438, … |
| maximal quotient of | C2×#20273027, C2×#20273031, #27349903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12983);