Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic11 |
| derived, Sylow | C11 ⋊ C3×C4×C5 |
| Hall | C3×C5×C11 ⋊ C4 |
| Hall | C5×C11 ⋊ C3×C4 |
| Hall | C3×C11 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D11 |
| commutator, hypocenter | C11 | C3×C4×C5 |
| Frattini | C2 | C3×C5×D11 |
| Fitting, socle, prime radical | C2×C3×C5×C11 | C2 |
| cosocle | C2×C11 | C2×C3×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 660 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×Dic11, C3×#89166, C3×#89169, … |
| maximal normal subgroup of | C3×D5×Dic11, C3×#89166, C3×#89169, … |
| maximal quotient of | C3×C5×C11⋊C8, C2×C3×C5×Dic11, C5×C9×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 5);