Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C8 · Schur multiplier (H2) = C33 |
| direct product | C33×AGL(1,𝔽9) |
| Fitting, socle, Sylow | C35 ⋊ C8 |
| derived | C32 ⋊ C33×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C33×C8 |
| Frattini | C1 | G |
| Fitting, socle | C35 | C8 |
| prime radical | C33×C3⋊D3 | C4 |
| cosocle | #157 | C2×C33 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C33 | |
592 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3884);