Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×AGL(1,𝔽9) |
| Fitting | C32×C42 ⋊ C8 |
| derived, Sylow | C32 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C42×C8 |
| Frattini | C22 | C22×AGL(1,𝔽9) |
| Fitting | C32×C42 | C8 |
| socle | C22×C32 | C22×C8 |
| prime radical | C22×C3⋊D3 | C22×C4 |
| cosocle | C22×#157 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C42 | |
462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C42×AΓL(1,𝔽9), #127×AGL(1,𝔽9), #72220538, … |
| maximal normal subgroup of | C42×AΓL(1,𝔽9), #127×AGL(1,𝔽9), #72220538, … |
| maximal quotient of | #97×AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17026);