Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#16810394 |
| Sylow | C53 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #344×Dic53, C4×#16810394, #27289305, … |
| maximal normal subgroup of | #344×Dic53, C4×#16810394, #27289305, … |
| maximal quotient of | C2×#20272560, #27273723, #27273726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4252);