| order | 1944 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C8 · Schur multiplier (H2) = C33 |
| direct product | C33×C9⋊C8 |
| derived | C9 ⋊ C33×C8 |
| Sylow | C33×C9 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33×C4 | D9 |
| commutator, hypocenter | C9 | C33×C8 |
| Frattini | C3×C4 | C33×D3 |
| Fitting | C33×C4×C9 | C2 |
| socle, prime radical | C2×C34 | Dic3 |
| cosocle | C4×C9 | C2×C33 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C33×C4 | |
804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2253);