Finite Group DatabasebetaFinite Group Databasebeta| order | 15939 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| derived, Hall | C7×C23 ⋊ C9×C11 |
| Hall | C7×C23⋊C11 ⋊ C9 |
| Hall | C23×C7⋊C9 ⋊ C11 |
| Sylow | C23 ⋊ C11×C7⋊C9 |
| Sylow | C7 ⋊ C9×C23⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×C23⋊C11 |
| commutator, hypocenter | C7×C23 | C9×C11 |
| Fitting, socle, cosocle | C3×C7×C23 | C3×C11 |
| prime radical | C3×C7×C23⋊C11 | C3 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1449 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C7⋊C9×C23⋊C11, C7⋊C9×AGL(1,𝔽23), D7⋊C9×C23⋊C11, … |
| maximal normal subgroup of | C2×C7⋊C9×C23⋊C11, C7⋊C9×AGL(1,𝔽23), D7⋊C9×C23⋊C11, … |
| maximal quotient of | C2×C7⋊C9×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15939, 4);