Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16810597 |
| Sylow | C53 ⋊ C2×#410 |
788 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289419, #27289420, #27289424, … |
| maximal normal subgroup of | #27289419, #27289420, #27289424, … |
| maximal quotient of | C2×#20273029, C2×#20273036, C2×#20273039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12967);