Finite Group DatabasebetaFinite Group Databasebeta| order | 15895 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C289 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×C289 |
| unambiguous semidirect product | C11⋊(C5×C289) |
| unambiguous semidirect product | (C11×C289)⋊C5 |
| Fitting, Hall | C11×C289 ⋊ C5 |
| derived, Sylow | C11 ⋊ C5×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | C11⋊C5 |
| commutator, hypocenter | C11 | C5×C289 |
| Frattini | C17 | C17×C11⋊C5 |
| Fitting | C11×C289 | C5 |
| socle, cosocle | C11×C17 | C5×C17 |
| prime radical | C17×C11⋊C5 | C17 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C289 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3179 |
2023 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11⋊C5×D289, AGL(1,𝔽11)×C289, (C11⋊C5)⋊D289, … |
| maximal normal subgroup of | C11⋊C5×D289, AGL(1,𝔽11)×C289, (C11⋊C5)⋊D289, … |
| maximal quotient of | C2×C11⋊C5×C289 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15895, 2);