Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D9×#157 |
| Fitting, Sylow | C33×C9 ⋊ C2×C4 |
| derived | C32×C9 ⋊ C2×C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D9×#157 |
| commutator, hypocenter | C32×C9 | C2×C3×C4 |
| Frattini | C3 | C3×D3×#157 |
| Fitting | C33×C9 | C2×C4 |
| socle | C34 | C4×D3 |
| prime radical | C3×D9×C3⋊D3 | C2 |
| cosocle | C9×C3⋊D3 | C22×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
260 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3480);