Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×GO+(4,𝔽2) |
| Fitting | C32×D8 ⋊ D4 |
| Sylow | C32 ⋊ D4×D8 |
958 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | D8×AΓL(1,𝔽9), AGL(1,ℤ/8)×GO+(4,𝔽2), #72220229 |
| maximal normal subgroup of | D8×AΓL(1,𝔽9), AGL(1,ℤ/8)×GO+(4,𝔽2), #72220229 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 119790);