Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×AGL(1,𝔽9) |
| Fitting, socle | C24×C32 ⋊ C8 |
| derived, Sylow | C32 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C24×C8 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | C8 |
| prime radical | C24×C3⋊D3 | C4 |
| cosocle | #157 | C25 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C24 | |
2350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C24×AΓL(1,𝔽9), #120×AGL(1,𝔽9), #72220546 |
| maximal normal subgroup of | C24×AΓL(1,𝔽9), #120×AGL(1,𝔽9), #72220546 |
| maximal quotient of | H(5,𝔽2)×AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152440);