Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25 |
| direct product | D3×#2110 |
| Fitting | C3×#2110 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2110 |
738 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #72222743, #72222774, D3×#33329, … |
| maximal normal subgroup of | D3×#33329, D3×#33469, D3×#33471, … |
| maximal quotient of | #72222743, #72222774, D3×#11405 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322223);