Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C3⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C33 |
| direct product | C3×C3⋊(C3⋊(C9⋊C8)) |
| unambiguous semidirect product | C3⋊(C3×C3⋊(C9⋊C8)) |
| derived | C32×C9 ⋊ C3×C8 |
| Sylow | C33×C9 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C3⋊(C3⋊D9) |
| commutator, hypocenter | C32×C9 | C3×C8 |
| Frattini | C3×C4 | C3×C3⋊(C3⋊D3) |
| Fitting | C33×C4×C9 | C2 |
| socle, prime radical | C2×C34 | Dic3 |
| cosocle | C32×C4×C9 | C2×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3×C4 | |
844 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2273);