Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5×D11 |
| Fitting, socle | C2×C3×C5×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C22×C3×C5 |
| Hall | C3×C5×C11 ⋊ C22 |
| Hall | C5×C11 ⋊ C22×C3 |
| Hall | C3×C11 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D11 |
| commutator, cosocle, hypocenter | C11 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C11 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C3×C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic5×D11, C3×#89167, C3×#89168, … |
| maximal normal subgroup of | C3×Dic5×D11, C3×#89167, C3×#89168, … |
| maximal quotient of | C3×C5×Dic22, C3×C4×C5×D11, C3×C5×D44, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 33);