Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8 |
| direct product | C2×#68050 |
| Fitting | C2×C3×C82 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1455 |
994 conjugacy classes of subgroups; only the 475 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 475 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10784425, C2×#10784429, C2×D3×#1455 |
| maximal normal subgroup of | C2×#10784425, C2×#10784429, C2×D3×#1455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 135273);