Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C25 · Schur multiplier (H2) = C2×C3 |
| derived, Hall | C22×C31 ⋊ C32×C25 |
| Hall | C22×C31⋊C25 ⋊ C32 |
| Hall | A4×C31⋊C3 ⋊ C25 |
| Hall | C31⋊C25 ⋊ C3×A4 |
| Sylow | C31 ⋊ C3×A4×C25 |
| Sylow | C22 ⋊ C3×(C31⋊C3)⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | A4×(C31⋊C3)⋊C5 |
| commutator, hypocenter | C22×C31 | C32×C25 |
| Fitting, socle, cosocle | C22×C5×C31 | C32×C5 |
| prime radical | C5×A4×C31⋊C3 | C5 |
| LCS | G ▷ C22×C31 | |
| UCS | C1 ◁ C5 | |
84 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 128);