Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C2×C22⋊C8×D53 |
| Fitting | C2×C22⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×C22⋊C8 |
1072 conjugacy classes of subgroups.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1280, #27273684, #27273702, … |
| maximal normal subgroup of | D53×#1280, #27273684, #27273702, … |
| maximal quotient of | C2×#323×D53, C2×#324×D53, D53×#1458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12940);