Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C22×#5745 |
| Fitting | C23×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C22×#568 |
11118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#87200, C22×#87192, C22×D3×#568 |
| maximal normal subgroup of | C22×#87200, C22×#87192, C22×D3×#568 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083332);