Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C27 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3×A4×C27 |
| Fitting | C23×C3×C27 ⋊ C3 |
| derived | C22 ⋊ C2×C32×C27 |
| Sylow | C23 ⋊ C32×C27 |
344 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 172 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, 2773);