Finite Group DatabasebetaFinite Group Databasebeta| order | 10860 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic181⋊C5) |
| unambiguous semidirect product | Dic543⋊C5 |
| derived, Hall | C3×C181 ⋊ C4×C5 |
| Hall | C3×C181⋊C5 ⋊ C4 |
| Hall | Dic543 ⋊ C5 |
| Hall | C181⋊C5 ⋊ Dic3 |
| Sylow | C181 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ Dic181⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D181⋊C5) |
| commutator, hypocenter | C3×C181 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C181 | C2×C5 |
| prime radical | C2×C3×C181⋊C5 | C2 |
| LCS | G ▷ C3×C181 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,181,2|a^2=e,b^a=b^2,d^a=d^180,d^c=d^59138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10860, 14);