Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D5×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D9 |
| unambiguous semidirect product | (C5×D9)⋊(C2×C5) |
| unambiguous semidirect product | (C9×D5)⋊(C2×C5) |
| unambiguous semidirect product | D45⋊(C2×C5) |
| Fitting, Hall | C52×C9 ⋊ C22 |
| derived | C5×C9 ⋊ C22×C5 |
| Sylow | C52 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D9 |
| commutator, cosocle, hypocenter | C5×C9 | C22×C5 |
| Frattini | C3 | C5×D3×D5 |
| Fitting | C52×C9 | C22 |
| socle | C3×C52 | C2×D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C5 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D9×AGL(1,𝔽5), D9×#1042, D52×D9, … |
| maximal normal subgroup of | C5×D9×AGL(1,𝔽5), D9×#1042, D52×D9, … |
| maximal quotient of | C5×#67077, C5×D9×Dic5, C5×#67079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 60);