Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22×C3 |
| direct product | C16×PSU(3,𝔽2) |
| Fitting | C32×C16 ⋊ Q8 |
| Sylow | C32 ⋊ Q8×C16 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C16×PSU(3,𝔽2)⋊C3, C3×C16×PSU(3,𝔽2), C16×AΓL(1,𝔽9), … |
| maximal normal subgroup of | C16×PSU(3,𝔽2)⋊C3, C3×C16×PSU(3,𝔽2), C16×AΓL(1,𝔽9), … |
| maximal quotient of | C3×C16×PSU(3,𝔽2), C32×PSU(3,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 32019);