Finite Group DatabasebetaFinite Group Databasebeta| order | 18180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(#87938⋊C5) |
| unambiguous semidirect product | (C9⋊#87938)⋊C5 |
| Fitting, derived, Hall | C9×C101 ⋊ C4×C5 |
| Hall | C9×C101⋊C5 ⋊ C4 |
| Hall | C9⋊#87938 ⋊ C5 |
| Hall | C101⋊C5 ⋊ Dic9 |
| Sylow | C101 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ #87938⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C101 | C4×C5 |
| Frattini | C3 | C3⋊(#87938⋊C5) |
| socle | C3×C101 | C5×Dic3 |
| prime radical | C3×D101⋊C5 | D3 |
| cosocle | C9×D101 | C2×C5 |
| LCS | G ▷ C9×C101 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 909 |
Polycyclic presentation:
2,5,2,3,101,3|a^2=c,d^3=f^2,d^a=d^2f,e^a=e^10,f^a=f^2,e^b=e^95,e^c=e^100105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18180, 15);