Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D3×D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D75 |
| unambiguous semidirect product | (C3×D3)⋊D25 |
| unambiguous semidirect product | (D3×C25)⋊D3 |
| Fitting, derived, Hall | C32×C25 ⋊ C22 |
| Sylow | C25 ⋊ D32 |
| Sylow | C32 ⋊ C2×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C25 | C22 |
| Frattini | C5 | D3×D15 |
| socle | C32×C5 | C2×D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D25, C2×D3×D75, D3×C13×D75, … |
| maximal normal subgroup of | D32×D25, C2×D3×D75, D3×C13×D75, … |
| maximal quotient of | #14267891, Dic3×D75, #14267893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 37);