Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#108×D53 |
| Fitting | C2×#108×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×#108 |
480 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1381, #27298980, D53×#1382, … |
| maximal normal subgroup of | D53×#1381, #27298980, D53×#1382, … |
| maximal quotient of | C2×#334×D53, C2×#335×D53, D53×#1564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13111);