Finite Group DatabasebetaFinite Group Databasebeta| order | 10860 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (#10624382⋊C3)⋊C5 |
| unambiguous semidirect product | (#10624382⋊C5)⋊C3 |
| Fitting, socle, derived, Sylow | C181 ⋊ C3×C4×C5 |
| Hall | #10624382⋊C5 ⋊ C3 |
| Hall | (C181⋊C3)⋊C5 ⋊ C4 |
| Hall | #10624382⋊C3 ⋊ C5 |
| Hall | C181⋊C5 ⋊ C3×C4 |
| Hall | #10624382 ⋊ C3×C5 |
| Hall | C181⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C181 | C3×C4×C5 |
| prime radical | (D181⋊C3)⋊C5 | C2 |
| cosocle | D181 | C2×C3×C5 |
| LCS | G ▷ C181 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,2,181|a^2=d,e^a=e^162,e^b=e^132,e^c=e^59,e^d=e^18063 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10860, 20);