Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×(C9⋊C8)⋊C9 |
| unambiguous semidirect product | (C3×C9⋊C8)⋊C9 |
| derived | C9 ⋊ C3×C8×C9 |
| Sylow | C3×C9⋊C9 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C4 | AGL(1,ℤ/9) |
| commutator, hypocenter | C9 | C3×C8×C9 |
| Frattini | C32×C4 | C32×D3 |
| Fitting | C3×C4×C9⋊C9 | C2 |
| socle, prime radical | C2×C33 | C3×Dic3 |
| cosocle | C3×C4×C9 | C2×C32 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C32×C4 | |
210 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 678);