Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810740 |
| Sylow | C53 ⋊ C2×#443 |
472 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | #27299329, #27299331, #27299336, … |
| maximal normal subgroup of | #27299329, #27299331, #27299336, … |
| maximal quotient of | C2×D8×#88322, C2×SD16×#88322, C2×Q16×#88322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13400);