Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of D15⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D11 |
| unambiguous semidirect product | D33⋊D5 |
| unambiguous semidirect product | D55⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C11 ⋊ C22 |
| Hall | C5×C11 ⋊ C2×D3 |
| Hall | C3×C11 ⋊ C2×D5 |
| Hall | C3×C5 ⋊ C2×D11 |
| Sylow | C11 ⋊ D3×D5 |
| Sylow | C5 ⋊ D3×D11 |
| Sylow | C3 ⋊ D5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C11 | C22 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 165 |
Polycyclic presentation:
2^2,3,5,11|c^a=c^2,e^a=e^10,c^b=c^2,d^b=d^457 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×D11, C2×D15⋊D11, D45⋊D11, … |
| maximal normal subgroup of | D3×D5×D11, C2×D15⋊D11, C3×D15⋊D11, … |
| maximal quotient of | #13050383, #13050384, D33⋊Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 31);