Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C4×C52×A4 |
| unambiguous semidirect product | (C22×C4)⋊(C3×C52) |
| unambiguous semidirect product | (C22×C4×C5)⋊(C3×C5) |
| Fitting, Hall | C22×C4×C52 ⋊ C3 |
| derived | C22 ⋊ C3×C4×C52 |
| Sylow | C22×C4 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C52 | A4 |
| commutator, hypocenter | C22 | C3×C4×C52 |
| Frattini | C2 | C2×C52×A4 |
| Fitting | C22×C4×C52 | C3 |
| socle | C23×C52 | C2×C3 |
| prime radical | C2×C52×A4 | C2 |
| cosocle | C23 | C2×C3×C52 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C4×C52 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 879);