Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×C27⋊C8 |
| derived | C27 ⋊ C32×C8 |
| Sylow | C32×C27 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C4 | D27 |
| commutator, hypocenter | C27 | C32×C8 |
| Frattini | C4×C9 | C32×D3 |
| Fitting | C32×C4×C27 | C2 |
| socle, prime radical | C2×C33 | Dic9 |
| cosocle | C4×C27 | C2×C32 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C32×C4 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 693);