Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D3×#455 |
| Fitting | C2×C3×#455 ⋊ C2 |
| Sylow | C3 ⋊ C22×#455 |
5110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3019, D3×#13349, D3×#13348, … |
| maximal normal subgroup of | C2×D3×#3019, D3×#13349, D3×#13348, … |
| maximal quotient of | D3×#23907, D3×#32891 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036173);