Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C92 · Schur multiplier (H2) = C2×C32×C9 |
| direct product | C2×C3×C9×C22⋊C9 |
| unambiguous semidirect product | (C23×C3)⋊C92 |
| derived | C22 ⋊ C2×C3×C92 |
| Sylow | C23 ⋊ C3×C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C9 | A4 |
| commutator, hypocenter | C22 | C2×C3×C92 |
| Frattini | C32 | C2×C32×A4 |
| Fitting | C23×C32×C9 | C3 |
| socle, prime radical | C23×C33 | C32 |
| cosocle | C22×C32 | C2×C33 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C32×C9 | |
704 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 352 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 486 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2796);