Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D32×C25 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C25) |
| unambiguous semidirect product | (C3⋊D3)⋊(C2×C25) |
| Fitting, Hall | C32×C25 ⋊ C22 |
| derived, Sylow | C32 ⋊ C22×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D32 |
| commutator, hypocenter | C32 | C22×C25 |
| Frattini | C5 | C5×D32 |
| Fitting | C32×C25 | C22 |
| socle, cosocle | C32×C5 | C22×C5 |
| prime radical | C5×D32 | C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C25 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C25×GO+(4,𝔽2), D32⋊D25, D32×D25, … |
| maximal normal subgroup of | C25×GO+(4,𝔽2), D32⋊D25, D32×D25, … |
| maximal quotient of | D3×Dic3×C25, C25×#624, C25×#625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 36);