Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D5×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | D5×C11×A4 |
| unambiguous semidirect product | C5⋊(C2×C11×A4) |
| unambiguous semidirect product | (C22×D5)⋊(C3×C11) |
| unambiguous semidirect product | (C22×D5×C11)⋊C3 |
| Fitting, socle | C22×C5×C11 ⋊ C2×C3 |
| derived | C22×C5 ⋊ C2×C3×C11 |
| Hall | C22×D5×C11 ⋊ C3 |
| Hall | C5×C11 ⋊ C2×A4 |
| Hall | C22×D5 ⋊ C3×C11 |
| Sylow | C5 ⋊ C2×C11×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D5×A4 |
| commutator, cosocle, hypocenter | C22×C5 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C11 | C2×C3 |
| LCS | G ▷ C22×C5 | |
| UCS | C1 ◁ C11 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 220 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | D5×A4×C11⋊C5, D5×A4×D11, C11×A4×AGL(1,𝔽5), … |
| maximal normal subgroup of | D5×A4×C11⋊C5, D5×A4×D11, C11×A4×AGL(1,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 159);