Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25×C49 · Schur multiplier (H2) = C2 |
| direct product | A4×C25×C49 |
| unambiguous semidirect product | C22⋊(C3×C25×C49) |
| unambiguous semidirect product | (C22×C25)⋊(C3×C49) |
| Fitting, Hall | C22×C25×C49 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C25×C49 |
| Hall | C22×C49 ⋊ C3×C25 |
| Hall | C22×C25 ⋊ C3×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C49 | A4 |
| commutator, hypocenter | C22 | C3×C25×C49 |
| Frattini | C5×C7 | C5×C7×A4 |
| Fitting | C22×C25×C49 | C3 |
| socle, cosocle | C22×C5×C7 | C3×C5×C7 |
| prime radical | C5×C7×A4 | C5×C7 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C25×C49 | |
45 conjugacy classes of subgroups.
4900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 32);