Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9×C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | D9×C3⋊Dic9 |
| unambiguous semidirect product | (C3×D9)⋊Dic9 |
| unambiguous semidirect product | (C9×D9)⋊Dic3 |
| derived, Sylow | C3×C92 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C3⋊D9 |
| commutator, hypocenter | C3×C92 | C2×C4 |
| Frattini | C2×C32 | D3×C3⋊D3 |
| Fitting, cosocle | C2×C3×C92 | C22 |
| socle | C2×C33 | D32 |
| prime radical | C2×C32×D9 | D3 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 ◁ C2 | |
384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1328);