Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C243 · Schur multiplier (H2) = C2 |
| direct product | C2×C22⋊C243 |
| unambiguous semidirect product | C23⋊C243 |
| derived | C22 ⋊ C2×C243 |
| Sylow | C23 ⋊ C243 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C81 | A4 |
| commutator, hypocenter | C22 | C2×C243 |
| Frattini | C81 | C2×A4 |
| Fitting | C23×C81 | C3 |
| socle, prime radical | C23×C3 | C81 |
| cosocle | C22×C81 | C2×C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C81 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 249 |
| 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, 101);