Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C2×D3×C8×D4 |
| Fitting | C2×C3×C8×D4 ⋊ C2 |
| Sylow | C3 ⋊ C22×C8×D4 |
3694 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×C8×D8, C2×D3×#1580, C2×C8×D4×C3⋊D3 |
| maximal normal subgroup of | C2×D3×C8×D8, C2×D3×#1580 |
| maximal quotient of | D3×#33443, C2×D3×C8×D8, C2×D3×#1580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033396);