Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C16 · Schur multiplier (H2) = C3 |
| direct product | C32×#3771 |
| derived | C32 ⋊ C32×C16 |
| Sylow | C34 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C32×C16 |
| Frattini | C2 | C32×AGL(1,𝔽9) |
| Fitting, socle, prime radical | C2×C34 | C8 |
| cosocle | #622 | C2×C32 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C32 | |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #72252860, C32×#64218, #72252867 |
| maximal normal subgroup of | #72252860, C32×#64218, #72252867 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3093);