Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3×C25 |
| unambiguous semidirect product | C3⋊(C3×C4×C25) |
| derived | C3 ⋊ C3×C4×C25 |
| Hall | C32×C25 ⋊ C4 |
| Sylow | C32 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C25 | D3 |
| commutator, hypocenter | C3 | C3×C4×C25 |
| Frattini | C2×C5 | C3×C5×D3 |
| Fitting | C2×C32×C25 | C2 |
| socle, prime radical | C2×C32×C5 | C2×C5 |
| cosocle | C2×C3×C5 | C2×C3×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C3×C25 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10597026, C3×Dic3×D25, C3×#10597028, … |
| maximal normal subgroup of | C3×#10597026, C3×Dic3×D25, C3×#10597028, … |
| maximal quotient of | C3×C3⋊C8×C25, C2×C3×Dic3×C25, Dic3×C25×C13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 14);