Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊#10587739 |
| unambiguous semidirect product | D137⋊(C2×C4⋊C4) |
| Fitting | C22×C4×C137 ⋊ C4 |
| Sylow | C137 ⋊ C22×C4⋊C4 |
418 conjugacy classes of subgroups.
584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795966, #31795967, #31795969, … |
| maximal normal subgroup of | #31795966, #31795967, #31795969, … |
| maximal quotient of | C22×(C2×#10587739)⋊C4, C2×C4×C4⋊#10587739, C2×#22578345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1611);