Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9×C31 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×C31×C22⋊C9 |
| unambiguous semidirect product | C22⋊(C52×C9×C31) |
| unambiguous semidirect product | (C22×C5)⋊(C5×C9×C31) |
| derived, Sylow | C22 ⋊ C52×C9×C31 |
| Hall | C22×C52×C31 ⋊ C9 |
| Hall | C22×C31 ⋊ C52×C9 |
| Hall | C22×C52 ⋊ C9×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52×C31 | A4 |
| commutator, hypocenter | C22 | C52×C9×C31 |
| Frattini | C3 | C52×A4×C31 |
| Fitting, socle, prime radical | C22×C3×C52×C31 | C3 |
| cosocle | C22×C3 | C3×C52×C31 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C52×C31 | |
128 conjugacy classes of subgroups.
9300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 325);