Finite Group DatabasebetaFinite Group Databasebeta| order | 4895 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C89 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×C89 |
| unambiguous semidirect product | C11⋊(C5×C89) |
| unambiguous semidirect product | (C11×C89)⋊C5 |
| Fitting, socle, Hall | C11×C89 ⋊ C5 |
| derived, Sylow | C11 ⋊ C5×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | C11⋊C5 |
| commutator, hypocenter | C11 | C5×C89 |
| Frattini | C1 | G |
| Fitting, socle | C11×C89 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C89 | |
8 conjugacy classes of subgroups.
623 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11⋊C5×C89, C5×C11⋊C5×C89, C7×C11⋊C5×C89 |
| maximal normal subgroup of | C3×C11⋊C5×C89, C5×C11⋊C5×C89, C7×C11⋊C5×C89 |
| maximal quotient of | C3×C11⋊C5×C89, C89×C11⋊C25, C5×C11⋊C5×C89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4895, 2);