Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (C3⋊S4)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×(C3⋊S4)⋊C9 |
| unambiguous semidirect product | (C3×C3⋊S4)⋊C9 |
| Fitting | C22×C32×C9 ⋊ D3 |
| derived | C3×A4 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | (C3⋊S4)⋊C3 |
| commutator, hypocenter | C3×A4 | C2×C3×C9 |
| Frattini | C32 | C32×S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3×D3 |
| prime radical | C32×C3⋊S4 | C3 |
| cosocle | C32×A4 | C2×C32 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C32 | |
327 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2364);