Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic33 |
| unambiguous semidirect product | C3⋊(C5×Dic11) |
| derived, Hall | C3×C11 ⋊ C4×C5 |
| Hall | C3×C5×C11 ⋊ C4 |
| Hall | C5×C11 ⋊ Dic3 |
| Hall | C3×C5 ⋊ Dic11 |
| Sylow | C11 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ C5×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D33 |
| commutator, hypocenter | C3×C11 | C4×C5 |
| Frattini | C2 | C5×D33 |
| Fitting, socle, prime radical | C2×C3×C5×C11 | C2 |
| cosocle | C2×C3×C11 | C2×C5 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 660 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic3×D11, C5×D3×Dic11, C5×#63140, … |
| maximal normal subgroup of | C5×Dic3×D11, C5×D3×Dic11, C5×#63140, … |
| maximal quotient of | C5×C3⋊(C11⋊C8), C2×C5×Dic33, C5×Dic99, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 9);