Finite Group DatabasebetaFinite Group Databasebeta| order | 9075 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C121⋊C25 |
| unambiguous semidirect product | C121⋊(C3×C25) |
| unambiguous semidirect product | (C3×C121)⋊C25 |
| derived, Sylow | C121 ⋊ C3×C25 |
| Hall | C3×C121 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C121⋊C5 |
| commutator, hypocenter | C121 | C3×C25 |
| Frattini | C5×C11 | C3×C11⋊C5 |
| Fitting | C3×C5×C121 | C5 |
| socle | C3×C5×C11 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C3×C5 | |
18 conjugacy classes of subgroups.
435 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D121⋊C25, D3×C121⋊C25, C3⋊(D121⋊C25), … |
| maximal normal subgroup of | C3×D121⋊C25, D3×C121⋊C25, C3⋊(D121⋊C25), … |
| maximal quotient of | C2×C3×C121⋊C25, C9×C121⋊C25, C32×C121⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9075, 2);