Finite Group DatabasebetaFinite Group Databasebeta| order | 18180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C101 · Schur multiplier (H2) = C2 |
| direct product | D3×D15×C101 |
| unambiguous semidirect product | (C3×D3)⋊(D5×C101) |
| unambiguous semidirect product | (C5×D3)⋊(D3×C101) |
| Fitting, socle, Hall | C32×C5×C101 ⋊ C22 |
| derived, Hall | C32×C5 ⋊ C22×C101 |
| Hall | C32×C101 ⋊ C2×D5 |
| Hall | C5×C101 ⋊ D32 |
| Sylow | C32 ⋊ C2×D5×C101 |
| Sylow | C5 ⋊ D32×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | D3×D15 |
| commutator, cosocle, hypocenter | C32×C5 | C22×C101 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C101 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C101 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3030 |
2727 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18180, 120);