Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | M16×PSU(3,𝔽2) |
| Fitting | C32×M16 ⋊ Q8 |
| Sylow | C32 ⋊ Q8×M16 |
422 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | M16×PSU(3,𝔽2)⋊C3, M16×AΓL(1,𝔽9), AGL(1,ℤ/8)×PSU(3,𝔽2), … |
| maximal normal subgroup of | M16×PSU(3,𝔽2)⋊C3, M16×AΓL(1,𝔽9), AGL(1,ℤ/8)×PSU(3,𝔽2), … |
| maximal quotient of | #97×PSU(3,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 95542);