Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×D3×#518 |
| Fitting | C2×C3×#518 ⋊ C2 |
| Sylow | C3 ⋊ C22×#518 |
14590 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3484, C2×D3×#1889, D3×#10745, … |
| maximal normal subgroup of | C2×D3×#3484, C2×D3×#1889, D3×#10745, … |
| maximal quotient of | C2×D3×D4×C22⋊C4, D3×#34415, D3×#34468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076145);