Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D75 |
| unambiguous semidirect product | (C2×C3)⋊(C3×D25) |
| unambiguous semidirect product | (C2×C25)⋊(C3×D3) |
| Fitting | C2×C32×C25 ⋊ C2 |
| derived | C3×C25 ⋊ C22×C3 |
| Hall | C32×C25 ⋊ C22 |
| Sylow | C25 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ C2×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C22×C3 |
| Frattini | C5 | C2×C3×D15 |
| Fitting | C2×C32×C25 | C2 |
| socle | C2×C32×C5 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2×C3 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10597028, C3×#10597029, C3×#10597032, … |
| maximal normal subgroup of | C3×#10597028, C3×#10597029, C3×#10597032, … |
| maximal quotient of | C3×Dic150, C3×C4×D75, C3×D300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 42);