Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810686 |
| Fitting | C2×C22⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27274632, #27274637, #27276985, … |
| maximal normal subgroup of | #27274632, #27274637, #27276985, … |
| maximal quotient of | C2×#20273507, C2×#20273512, C2×#20273518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13180);