Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C3 |
| direct product | C24×PSU(3,𝔽2) |
| Fitting, socle | C24×C32 ⋊ Q8 |
| Sylow | C32 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | PSU(3,𝔽2) |
| commutator, cosocle | C3⋊D3 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | Q8 |
| prime radical | C24×C3⋊D3 | C22 |
| hypocenter | C32 | C24×Q8 |
| LCS | G ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C24 | |
6638 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C24×PSU(3,𝔽2)⋊C3, #120×PSU(3,𝔽2), C24×AΓL(1,𝔽9), … |
| maximal normal subgroup of | C24×PSU(3,𝔽2)⋊C3, #120×PSU(3,𝔽2), C24×AΓL(1,𝔽9), … |
| maximal quotient of | H(5,𝔽2)×PSU(3,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153193);