Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C8 · Schur multiplier (H2) = C34 |
| direct product | C33×C3⋊(C3⋊C8) |
| unambiguous semidirect product | C3⋊(C33×C3⋊C8) |
| derived | C32 ⋊ C33×C8 |
| Sylow | C35 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33×C4 | C3⋊D3 |
| commutator, hypocenter | C32 | C33×C8 |
| Frattini | C4 | C33×C3⋊D3 |
| Fitting | C35×C4 | C2 |
| socle, prime radical | C2×C35 | C4 |
| cosocle | C32×C4 | C2×C33 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C33×C4 | |
4416 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, 3435);