Finite Group DatabasebetaFinite Group Databasebeta| order | 18180 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊(#87938⋊C5) |
| unambiguous semidirect product | C3⋊(C3×#87938⋊C5) |
| unambiguous semidirect product | (C3⋊#87938)⋊(C3×C5) |
| unambiguous semidirect product | (C3×C3⋊#87938)⋊C5 |
| Fitting, socle, Hall | C32×C101 ⋊ C4×C5 |
| derived | C3×C101 ⋊ C3×C4×C5 |
| Hall | C32×C101⋊C5 ⋊ C4 |
| Hall | C3×C3⋊#87938 ⋊ C5 |
| Hall | C101⋊C5 ⋊ C3×Dic3 |
| Sylow | C101 ⋊ C3×C5×Dic3 |
| Sylow | C32 ⋊ #87938⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(#87938⋊C5) |
| commutator, hypocenter | C3×C101 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C101 | C4×C5 |
| prime radical | C32×D101⋊C5 | C2 |
| cosocle | C3×D101 | C2×C3×C5 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 606 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18180, 69);