Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×C27×Dic9 |
| derived | C9 ⋊ C2×C4×C27 |
| Sylow | C9×C27 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C27 | D9 |
| commutator, hypocenter | C9 | C2×C4×C27 |
| Frattini | C2×C3×C9 | C2×C3×D3 |
| Fitting | C22×C9×C27 | C2 |
| socle, prime radical | C22×C32 | D3×C9 |
| cosocle | C2×C92 | C22×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C27 | |
156 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 429);