Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×D9 |
| unambiguous semidirect product | C9⋊(C22×C52) |
| unambiguous semidirect product | (C2×C9)⋊(C2×C52) |
| Fitting | C2×C52×C9 ⋊ C2 |
| derived, Sylow | C9 ⋊ C22×C52 |
| Hall | C52×C9 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D9 |
| commutator, cosocle, hypocenter | C9 | C22×C52 |
| Frattini | C3 | C2×C52×D3 |
| Fitting | C2×C52×C9 | C2 |
| socle | C2×C3×C52 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C52 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 450 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×Dic5, C5×#67080, C5×#67082, … |
| maximal normal subgroup of | C5×D9×Dic5, C5×#67080, C5×#67082, … |
| maximal quotient of | C52×Dic18, C4×C52×D9, C52×D36, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 69);