Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×A5×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C3×C31)⋊(C5×A5) |
| unambiguous semidirect product | (C3×C31×A5)⋊C5 |
| Fitting | C3×C31 ⋊ C5×A5 |
| socle | C3×C31×A5 ⋊ C5 |
| derived | C31×A5 ⋊ C3×C5 |
| Sylow | C31 ⋊ C3×C5×A5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A5×ΓL(1,𝔽32) |
| commutator, hypocenter | C31×A5 | C3×C5 |
| Frattini | C1 | G |
| Fitting | C3×C31 | C5×A5 |
| socle | C3×C31×A5 | C5 |
| cosocle | C31 | C3×C5×A5 |
| LCS | G ▷ C31×A5 | |
| UCS | C1 ◁ C3 | |
92 conjugacy classes of subgroups.
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 746);