Finite Group DatabasebetaFinite Group Databasebeta| order | 9225 |
| isoclinism | isoclinic class of C41⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5 |
| Fitting, socle | C32×C5×C41 ⋊ C5 |
| derived, Sylow | C41 ⋊ C32×C52 |
| Hall | C32×C41 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | C41⋊C5 |
| commutator, hypocenter | C41 | C32×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C41 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C32×C5 | |
96 conjugacy classes of subgroups.
585 conjugacy classes — view the full character table.
| maximal subgroup of | C32×C5×D41⋊C5, C32×C5⋊(D41⋊C5), C32×D5×C41⋊C5, … |
| maximal normal subgroup of | C32×C5×D41⋊C5, C32×C5⋊(D41⋊C5), C32×D5×C41⋊C5, … |
| maximal quotient of | C2×C32×C5×C41⋊C5, C3×C5×A4×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9225, 9);