Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#78044 |
| Fitting | C2×C3×#399 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2598 |
3502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #72254612, C2×D3×#2598, #72254826, … |
| maximal normal subgroup of | #72254612, C2×D3×#2598, #72254826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 340197);