Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | C8×PSU(3,𝔽2) |
| Fitting | C32×C8 ⋊ Q8 |
| Sylow | C32 ⋊ C8×Q8 |
113 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | PSU(3,𝔽2)⋊C16, C8×AΓL(1,𝔽9), #11777508, … |
| maximal normal subgroup of | PSU(3,𝔽2)⋊C16, C8×AΓL(1,𝔽9), #11777508, … |
| maximal quotient of | C8×#3777, #11788980, #11790050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5413);