Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×M16×S4 |
| Fitting | C23×M16 ⋊ D3 |
1643 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 1643 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #72226192, M16×GL(2,ℤ/4), C2×S4×AGL(1,ℤ/8), … |
| maximal normal subgroup of | #72226192, M16×GL(2,ℤ/4), C2×S4×AGL(1,ℤ/8), … |
| maximal quotient of | #72226192, M16×GL(2,ℤ/4), D3×M16×S4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1089000);