Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#5835 |
| Fitting | C22×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C22×#576 |
11462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#576, C22×#87207, C22×#87204, … |
| maximal normal subgroup of | C22×D3×#576, C22×#87207, C22×#87204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083378);