Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C2×D3×#393 |
| Fitting | C2×C3×#393 ⋊ C2 |
| Sylow | C3 ⋊ C22×#393 |
7118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#14885, C2×D3×#2404, D3×#15323, … |
| maximal normal subgroup of | D3×#14885, C2×D3×#2404, D3×#15323, … |
| maximal quotient of | C2×D3×#2032 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 335746);