Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C9×C5⋊D5 |
| unambiguous semidirect product | (C2×C5)⋊(C9×D5) |
| Fitting | C2×C52×C9 ⋊ C2 |
| derived, Sylow | C52 ⋊ C22×C9 |
| Hall | C52×C9 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C5⋊D5 |
| commutator, hypocenter | C52 | C22×C9 |
| Frattini | C3 | C2×C3×C5⋊D5 |
| Fitting | C2×C52×C9 | C2 |
| socle | C2×C3×C52 | C2×C3 |
| prime radical | C2×C3×C5⋊D5 | C3 |
| cosocle | C3×C52 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C9 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 450 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#6036, C9×#6038, Dic9×C5⋊D5, … |
| maximal normal subgroup of | C9×#6036, C9×#6038, Dic9×C5⋊D5, … |
| maximal quotient of | C9×#6045, C4×C9×C5⋊D5, C9×C4⋊(C5⋊D5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 68);