Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#82329 |
| Fitting | C22×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2328 |
4430 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72253467, #72253490, C2×D3×#2328, … |
| maximal normal subgroup of | #72253467, #72253490, C2×D3×#2328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 328368);