Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D25 |
| unambiguous semidirect product | C25⋊(C22×C32) |
| unambiguous semidirect product | (C2×C25)⋊(C2×C32) |
| Fitting | C2×C32×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C22×C32 |
| Hall | C32×C25 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D25 |
| commutator, cosocle, hypocenter | C25 | C22×C32 |
| Frattini | C5 | C2×C32×D5 |
| Fitting | C2×C32×C25 | C2 |
| socle | C2×C32×C5 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C32 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 450 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×D25, C3×#10597029, C3×#10597031, … |
| maximal normal subgroup of | C3×Dic3×D25, C3×#10597029, C3×#10597031, … |
| maximal quotient of | C32×Dic50, C32×C4×D25, C32×D100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 40);