Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×D3×#418 |
| Fitting | C2×C3×#418 ⋊ C2 |
| Sylow | C3 ⋊ C22×#418 |
7214 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3003, C22×D3×#418, C2×D3×#2002, … |
| maximal normal subgroup of | C2×D3×#3003, C22×D3×#418, C2×D3×#2002, … |
| maximal quotient of | C22×D3×#418, D3×#20598, D3×#20739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033088);