Finite Group DatabasebetaFinite Group Databasebeta| order | 9405 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×#4296 |
| Fitting, socle, Hall | C5×C11×C19 ⋊ C9 |
| derived, Sylow | C19 ⋊ C5×C9×C11 |
| Hall | C11×C19 ⋊ C5×C9 |
| Hall | C5×C19 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | #4296 |
| commutator, hypocenter | C19 | C5×C9×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C19 | C9 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C5×C11 | |
24 conjugacy classes of subgroups.
605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9405, 8);