Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C27 · Schur multiplier (H2) = C1 |
| direct product | C27×C9⋊C8 |
| derived | C9 ⋊ C8×C27 |
| Sylow | C9×C27 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C27 | D9 |
| commutator, hypocenter | C9 | C8×C27 |
| Frattini | C3×C4×C9 | C3×D3 |
| Fitting | C4×C9×C27 | C2 |
| socle, prime radical | C2×C32 | C9×Dic3 |
| cosocle | C4×C92 | C2×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C4×C27 | |
84 conjugacy classes of subgroups.
| 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, 23);