Finite Group DatabasebetaFinite Group Databasebeta| order | 15327 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C1 |
| direct product | C9×C131⋊C13 |
| unambiguous semidirect product | C131⋊(C9×C13) |
| unambiguous semidirect product | (C9×C131)⋊C13 |
| Fitting, Hall | C9×C131 ⋊ C13 |
| derived, Sylow | C131 ⋊ C9×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C131⋊C13 |
| commutator, hypocenter | C131 | C9×C13 |
| Frattini | C3 | C3×C131⋊C13 |
| Fitting | C9×C131 | C13 |
| socle, cosocle | C3×C131 | C3×C13 |
| prime radical | C3×C131⋊C13 | C3 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1179 |
207 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9×C131⋊C13, C9×D131⋊C13, D9×C131⋊C13, … |
| maximal normal subgroup of | C2×C9×C131⋊C13, C9×D131⋊C13, D9×C131⋊C13, … |
| maximal quotient of | C2×C9×C131⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15327, 2);