Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C2 |
| direct product | C4×A4×C25 |
| unambiguous semidirect product | (C22×C4)⋊(C3×C25) |
| unambiguous semidirect product | (C22×C4×C25)⋊C3 |
| Fitting, Hall | C22×C4×C25 ⋊ C3 |
| derived | C22 ⋊ C3×C4×C25 |
| Sylow | C22×C4 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C25 | A4 |
| commutator, hypocenter | C22 | C3×C4×C25 |
| Frattini | C2×C5 | C2×C5×A4 |
| Fitting | C22×C4×C25 | C3 |
| socle, cosocle | C23×C5 | C2×C3×C5 |
| prime radical | C2×C5×A4 | C2×C5 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C4×C25 | |
57 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| 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, 146);