Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of C11⋊PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×C11⋊PSU(3,𝔽2) |
| unambiguous semidirect product | (C2×C11)⋊PSU(3,𝔽2) |
| Fitting, socle | C2×C32×C11 ⋊ Q8 |
| Hall | C32×C11 ⋊ C2×Q8 |
| Sylow | C11 ⋊ C2×PSU(3,𝔽2) |
| Sylow | C32 ⋊ C2×Dic22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊PSU(3,𝔽2) |
| commutator, cosocle | C11×C3⋊D3 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C11 | Q8 |
| prime radical | C2×C11×C3⋊D3 | C22 |
| hypocenter | C32×C11 | C2×Q8 |
| LCS | G ▷ C11×C3⋊D3 ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 674);