Finite Group DatabasebetaFinite Group Databasebeta| order | 15318 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D851 |
| unambiguous semidirect product | C23⋊(C9×D37) |
| Fitting, Hall | C9×C23×C37 ⋊ C2 |
| derived, Hall | C23×C37 ⋊ C2×C9 |
| Hall | C9×C37 ⋊ D23 |
| Hall | C9×C23 ⋊ D37 |
| Sylow | C37 ⋊ C9×D23 |
| Sylow | C23 ⋊ C9×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D851 |
| commutator, hypocenter | C23×C37 | C2×C9 |
| Frattini | C3 | C3×D851 |
| Fitting | C9×C23×C37 | C2 |
| socle, cosocle | C3×C23×C37 | C2×C3 |
| prime radical | C3×D851 | C3 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7659 |
3843 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D23×D37, D9×D851, D207⋊D37, … |
| maximal normal subgroup of | C9×D23×D37, D9×D851, D207⋊D37, … |
| maximal quotient of | C9×Dic851, C2×C9×D851 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15318, 5);