Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16810673 |
| Sylow | C53 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27273681, #27273687, #27273706, … |
| maximal normal subgroup of | #27273681, #27273687, #27273706, … |
| maximal quotient of | C2×#20274459, C2×C22⋊C8×Dic53, C2×#20274563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13123);