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×C32×C22⋊C27 |
| derived | C22 ⋊ C2×C32×C27 |
| Sylow | C23 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C9 | A4 |
| commutator, hypocenter | C22 | C2×C32×C27 |
| Frattini | C9 | C2×C32×A4 |
| Fitting | C23×C32×C9 | C3 |
| socle, prime radical | C23×C33 | C9 |
| cosocle | C22×C9 | C2×C33 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C32×C9 | |
488 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 244 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, 2794);