Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D3×#1911 |
| Fitting | C3×#1911 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1911 |
1974 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
87 conjugacy classes — view the full character table.
| maximal subgroup of | #72214881, D3×#12753, D3×#23897, … |
| maximal normal subgroup of | D3×#12753, D3×#23897, C2×D3×#1911, … |
| maximal quotient of | #72214881, C2×D3×#1911, #72252287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171556);