Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×#443 |
| Fitting | C2×C3×#443 ⋊ C2 |
| Sylow | C3 ⋊ C22×#443 |
2750 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12823, C2×D3×#2213, D3×#20512, … |
| maximal normal subgroup of | D3×#12823, C2×D3×#2213, D3×#20512, … |
| maximal quotient of | C2×D3×C8×D8, C2×C3⋊D3×#443 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033855);