Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#5401 |
| Fitting | C24×C8 ⋊ D3 |
1669 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1669 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#5401, C22×#85440, C22×SD16×S4, … |
| maximal normal subgroup of | A4×#5401, C22×#85440, C22×SD16×S4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1089133);