Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8 |
| direct product | C2×#69849 |
| Sylow | C3 ⋊ C2×#1455 |
994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10784426, C2×D3×#1455, C2×#10784430 |
| maximal normal subgroup of | C2×#10784426, C2×D3×#1455, C2×#10784430 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 135274);