Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of A4×C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2 |
| direct product | A4×C11⋊C5 |
| unambiguous semidirect product | C22⋊(C3×C11⋊C5) |
| unambiguous semidirect product | C11⋊(C5×A4) |
| unambiguous semidirect product | (C11×A4)⋊C5 |
| unambiguous semidirect product | (C22×C11⋊C5)⋊C3 |
| Fitting, socle, derived, Hall | C22×C11 ⋊ C3×C5 |
| Hall | C22×C11⋊C5 ⋊ C3 |
| Hall | C11×A4 ⋊ C5 |
| Sylow | C11 ⋊ C5×A4 |
| Sylow | C22 ⋊ C3×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C11 | C3×C5 |
| LCS | G ▷ C22×C11 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 44 |
28 conjugacy classes — view the full character table.
| maximal subgroup of | S4×C11⋊C5, A4⋊AGL(1,𝔽11), A4×AGL(1,𝔽11), … |
| maximal normal subgroup of | S4×C11⋊C5, A4⋊AGL(1,𝔽11), A4×AGL(1,𝔽11), … |
| maximal quotient of | SL(2,𝔽3)×C11⋊C5, C2×A4×C11⋊C5, C22⋊C9×C11⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 16);