Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C24 |
| direct product | SD16×C22⋊A4 |
| Fitting, Sylow | C24×SD16 ⋊ C3 |
2335 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 2335 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | A42×SD16, SD16×#1020, AGL(1,ℤ/8)×C22⋊A4, … |
| maximal normal subgroup of | A42×SD16, SD16×#1020, AGL(1,ℤ/8)×C22⋊A4, … |
| maximal quotient of | SD16×#997, #106×C22⋊A4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085257);