Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | D3×#2879 |
| Fitting | C3×#2879 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2879 |
5150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23439, D3×#11014, D3×#10987, … |
| maximal normal subgroup of | D3×#23439, D3×#11014, D3×#10987, … |
| maximal quotient of | D3×#21379 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033005);