Finite Group DatabasebetaFinite Group Databasebeta| order | 9225 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C25 · Schur multiplier (H2) = C3 |
| direct product | C32×C41⋊C25 |
| unambiguous semidirect product | C41⋊(C32×C25) |
| unambiguous semidirect product | (C3×C41)⋊(C3×C25) |
| unambiguous semidirect product | (C32×C41)⋊C25 |
| derived, Sylow | C41 ⋊ C32×C25 |
| Hall | C32×C41 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | C41⋊C5 |
| commutator, hypocenter | C41 | C32×C25 |
| Frattini | C5 | C32×C41⋊C5 |
| Fitting, socle | C32×C5×C41 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C32×C5 | |
36 conjugacy classes of subgroups.
585 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D41⋊C25, C3×C3⋊(D41⋊C25), C3×D3×C41⋊C25, … |
| maximal normal subgroup of | C32×D41⋊C25, C3×C3⋊(D41⋊C25), C3×D3×C41⋊C25, … |
| maximal quotient of | C2×C32×C41⋊C25, C3×A4×C41⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9225, 4);