Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of D3×D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D55 |
| unambiguous semidirect product | (C5×D3)⋊D11 |
| unambiguous semidirect product | (D3×C11)⋊D5 |
| Fitting, socle, derived, Hall | C3×C5×C11 ⋊ C22 |
| Hall | C5×C11 ⋊ C2×D3 |
| Hall | C3×C11 ⋊ C2×D5 |
| Hall | C3×C5 ⋊ C2×D11 |
| Sylow | C11 ⋊ D3×D5 |
| Sylow | C5 ⋊ D3×D11 |
| Sylow | C3 ⋊ C2×D55 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C11 | C22 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 165 |
87 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×D11, C2×D3×D55, D9×D55, … |
| maximal normal subgroup of | D3×D5×D11, C2×D3×D55, C3×D3×D55, … |
| maximal quotient of | Dic3×D55, D3×Dic55, #13050378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 30);