Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9×C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×D9×C3⋊(C3⋊D3) |
| Fitting | C2×C33×C9 ⋊ C22 |
| derived, Sylow | C33×C9 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C33×C9 | C23 |
| Frattini | C3 | C2×D3×C3⋊(C3⋊D3) |
| Fitting | C2×C33×C9 | C22 |
| socle | C2×C34 | C2×D3 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
2124 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 2124 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3716);