Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C3×C11 ⋊ C2×C5 |
| derived, Sylow | C11 ⋊ C22×C3×C5 |
| Hall | C3×C11⋊C5 ⋊ C22 |
| Hall | C2×C3×D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C22×C3 |
| Hall | C2×D11 ⋊ C3×C5 |
| Hall | C3×C11 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C11 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 66 |
66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 17);