Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#74153 |
| Fitting | C2×C3×#382 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2328 |
4430 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72253463, #72253493, C2×D3×#2328, … |
| maximal normal subgroup of | #72253463, #72253493, C2×D3×#2328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 328369);