Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D3×#2956 |
| Fitting | C3×#2956 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2956 |
2674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #72214070, #72214973, D3×#61110, … |
| maximal normal subgroup of | D3×#61110, D3×#33688, D3×#11669, … |
| maximal quotient of | #72214070, #72214973, D3×#20512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033875);