Finite Group DatabasebetaFinite Group Databasebeta| order | 15345 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×C31⋊C9 |
| unambiguous semidirect product | C11⋊(C5×C31⋊C9) |
| unambiguous semidirect product | (C31×C11⋊C5)⋊C9 |
| derived, Hall | C11×C31 ⋊ C5×C9 |
| Hall | C11×C31⋊C9 ⋊ C5 |
| Hall | C31×C11⋊C5 ⋊ C9 |
| Sylow | C31 ⋊ C9×C11⋊C5 |
| Sylow | C11 ⋊ C5×C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊C5×C31⋊C3 |
| commutator, hypocenter | C11×C31 | C5×C9 |
| Fitting, socle, cosocle | C3×C11×C31 | C3×C5 |
| prime radical | C3×C31×C11⋊C5 | C3 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
273 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11⋊C5×C31⋊C9, C11⋊C5×D31⋊C9, AGL(1,𝔽11)×C31⋊C9, … |
| maximal normal subgroup of | C2×C11⋊C5×C31⋊C9, C11⋊C5×D31⋊C9, AGL(1,𝔽11)×C31⋊C9, … |
| maximal quotient of | C2×C11⋊C5×C31⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15345, 10);