Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×C22⋊C4×#67 |
| Fitting | C23×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×D4×C22⋊C4 |
8774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67×#120, C2×#10990482, C2×D3×D4×C22⋊C4, … |
| maximal normal subgroup of | C2×#67×#120, C2×#10990482, C2×D3×D4×C22⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 328739);