Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C28 |
| direct product | C22×A4×C22⋊C4 |
| Fitting, Sylow | C24×C22⋊C4 ⋊ C3 |
8403 conjugacy classes of subgroups; only the 507 normal subgroups are shown.
This group has 8403 conjugacy classes of subgroups — too many to draw. Only its 507 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | A42×C22⋊C4, #72259025, C22⋊C4×GL(2,ℤ/4), … |
| maximal normal subgroup of | A42×C22⋊C4, #72259025, C22⋊C4×GL(2,ℤ/4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084957);