Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D5×D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D45 |
| unambiguous semidirect product | (C5×D5)⋊D9 |
| unambiguous semidirect product | (C9×D5)⋊D5 |
| Fitting, derived, Hall | C52×C9 ⋊ C22 |
| Sylow | C52 ⋊ C2×D9 |
| Sylow | C9 ⋊ D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9 | C22 |
| Frattini | C3 | D5×D15 |
| socle | C3×C52 | C2×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×D45, #1042⋊D9, D52×D9, … |
| maximal normal subgroup of | AGL(1,𝔽5)×D45, #1042⋊D9, D52×D9, … |
| maximal quotient of | #14267976, Dic5×D45, #14267978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 62);