Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#74659 |
| Fitting | C2×C3×#386 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×#120 |
8582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D3×#120, C2×#10990476, #72270930, … |
| maximal normal subgroup of | C2×C4×D3×#120, C2×#10990476, #72270930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 327985);