Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of D5×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D11 |
| unambiguous semidirect product | (D5×C11)⋊(C2×C3) |
| unambiguous semidirect product | (C5×D11)⋊(C2×C3) |
| unambiguous semidirect product | D55⋊(C2×C3) |
| Fitting, socle, Hall | C3×C5×C11 ⋊ C22 |
| derived, Hall | C5×C11 ⋊ C22×C3 |
| Hall | C3×C11 ⋊ C2×D5 |
| Hall | C3×C5 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×C3×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D11 |
| commutator, cosocle, hypocenter | C5×C11 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11 | C22 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 165 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×D11, D11×ΓL(1,𝔽16), D3×D5×D11, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×D11, D11×ΓL(1,𝔽16), D3×D5×D11, … |
| maximal quotient of | C3×Dic5×D11, C3×D5×Dic11, C3×#89166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 25);