Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×#334 |
| Fitting | C2×C3×#334 ⋊ C2 |
| Sylow | C3 ⋊ C22×#334 |
942 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1368, C2×D3×#1580, C2×D3×#1333, … |
| maximal normal subgroup of | C2×D3×#1368, C2×D3×#1580, C2×D3×#1333 |
| maximal quotient of | C2×D3×#1368, C2×D3×#1369, C2×C3⋊D3×#334 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 138532);