Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×C3⋊AGL(1,𝔽9) |
| unambiguous semidirect product | C3⋊(C32×AGL(1,𝔽9)) |
| Fitting, socle, Sylow | C35 ⋊ C8 |
| derived | C33 ⋊ C32×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊AGL(1,𝔽9) |
| commutator, hypocenter | C33 | C32×C8 |
| Frattini | C1 | G |
| Fitting, socle | C35 | C8 |
| prime radical | C33×C3⋊D3 | C4 |
| cosocle | C3×#157 | C2×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C32 | |
512 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3885);