Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic25 |
| derived, Sylow | C25 ⋊ C4×C9 |
| Hall | C9×C25 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D25 |
| commutator, hypocenter | C25 | C4×C9 |
| Frattini, socle, prime radical | C2×C3×C5 | C3×D5 |
| Fitting | C2×C9×C25 | C2 |
| cosocle | C2×C3×C25 | C2×C3 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C9 | |
27 conjugacy classes of subgroups.
| transitive degree | μt(G) = 900 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#6016, C9⋊#6016, D9×Dic25, … |
| maximal normal subgroup of | C9×#6016, C9⋊#6016, D9×Dic25, … |
| maximal quotient of | C9×#6014, C2×C9×Dic25, Dic25×C13⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 2);