Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of D3×C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C11⋊C5 |
| unambiguous semidirect product | C3⋊(C4×C11⋊C5) |
| unambiguous semidirect product | (C11×Dic3)⋊C5 |
| derived, Hall | C3×C11 ⋊ C4×C5 |
| Hall | C3×C11⋊C5 ⋊ C4 |
| Hall | C11×Dic3 ⋊ C5 |
| Sylow | C11 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ C4×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C11⋊C5 |
| commutator, hypocenter | C3×C11 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C11 | C2×C5 |
| prime radical | C2×C3×C11⋊C5 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×AGL(1,𝔽11), (D33⋊C4)⋊C5, #63141⋊C5, … |
| maximal normal subgroup of | Dic3×AGL(1,𝔽11), (D33⋊C4)⋊C5, #63141⋊C5, … |
| maximal quotient of | C3⋊C8×C11⋊C5, C2×Dic3×C11⋊C5, Dic9×C11⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 2);