Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16811435 |
| Fitting | C2×#131×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#577 |
1460 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27400003, #27400009, #27400030, … |
| maximal normal subgroup of | #27400003, #27400009, #27400030, … |
| maximal quotient of | C2×#20283242, C2×#20283249, C2×#20283310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19271);