Finite Group DatabasebetaFinite Group Databasebeta| order | 11660 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C53 · Schur multiplier (H2) = C2 |
| direct product | C22×C53×C11⋊C5 |
| unambiguous semidirect product | (C22×C11)⋊(C5×C53) |
| unambiguous semidirect product | (C22×C11×C53)⋊C5 |
| Fitting, socle, Hall | C22×C11×C53 ⋊ C5 |
| derived, Sylow | C11 ⋊ C22×C5×C53 |
| Hall | C11×C53 ⋊ C22×C5 |
| Hall | C22×C11 ⋊ C5×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C53 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C22×C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C22×C11×C53 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C22×C53 | |
40 conjugacy classes of subgroups.
1484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C53×C11⋊C5, C2×D3×C53×C11⋊C5, C22×C3×C53×C11⋊C5 |
| maximal normal subgroup of | A4×C53×C11⋊C5, C22×C3×C53×C11⋊C5 |
| maximal quotient of | C2×D3×C53×C11⋊C5, C22×C3×C53×C11⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11660, 20);