Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#78535 |
| Fitting | C2×C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3184 |
2514 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3184, C2×#10784426, C2×#10784428 |
| maximal normal subgroup of | C2×D3×#3184, C2×#10784426, C2×#10784428 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1039532);