Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D3×#2127 |
| Fitting | C3×#2127 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2127 |
1510 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12753, D3×#12707, D3×#12754, … |
| maximal normal subgroup of | D3×#12753, D3×#33551, D3×#12707, … |
| maximal quotient of | C2×D3×#2127, #72252359, D3×#12696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322349);