Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C3 |
| direct product | #157×C31⋊C25 |
| unambiguous semidirect product | (C31×#157)⋊C25 |
| derived, Hall | C32×C31 ⋊ C4×C25 |
| Hall | C32×C31⋊C25 ⋊ C4 |
| Hall | C31×#157 ⋊ C25 |
| Sylow | C31 ⋊ C25×#157 |
| Sylow | C32 ⋊ C4×C31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #157×ΓL(1,𝔽32) |
| commutator, hypocenter | C32×C31 | C4×C25 |
| Fitting, socle | C32×C5×C31 | C4×C5 |
| prime radical, cosocle | C5×C3⋊D3×C31 | C2×C5 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 138);