Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
| direct product | C2×D3×#338 |
| Fitting | C2×C3×#338 ⋊ C2 |
| Sylow | C3 ⋊ C22×#338 |
2110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1903, C2×D3×#2091, D3×#11014, … |
| maximal normal subgroup of | C2×D3×#1903, C2×D3×#2091, D3×#11014, … |
| maximal quotient of | D3×C22⋊#338 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 166944);