Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | D33×C9 |
| Fitting, Sylow | C33×C9 ⋊ C23 |
| derived | C33 ⋊ C23×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D33 |
| commutator, hypocenter | C33 | C23×C9 |
| Frattini | C3 | C3×D33 |
| Fitting | C33×C9 | C23 |
| socle, cosocle | C34 | C23×C3 |
| prime radical | C3×D33 | C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C9 | |
684 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D9⋊C9, D32×C9×D9, D33×3−1+2, … |
| maximal normal subgroup of | D33×3−1+2, D33×D9 |
| maximal quotient of | D32×D9⋊C9, D32×C9×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3563);