Finite Group DatabasebetaFinite Group Databasebeta| order | 2820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×D47 |
| unambiguous semidirect product | (D3×C47)⋊(C2×C5) |
| unambiguous semidirect product | (C3×D47)⋊(C2×C5) |
| unambiguous semidirect product | D141⋊(C2×C5) |
| Fitting, socle, Hall | C3×C5×C47 ⋊ C22 |
| derived, Hall | C3×C47 ⋊ C22×C5 |
| Hall | C5×C47 ⋊ C2×D3 |
| Sylow | C47 ⋊ C2×C5×D3 |
| Hall | C3×C5 ⋊ C2×D47 |
| Sylow | C3 ⋊ C2×C5×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×D47 |
| commutator, cosocle, hypocenter | C3×C47 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C47 | C22 |
| LCS | G ▷ C3×C47 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 705 |
375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C25×D47, C52×D3×D47, C5×D15×D47, … |
| maximal normal subgroup of | D3×C25×D47, C52×D3×D47, C5×D3×C7×D47, … |
| maximal quotient of | D3×C25×D47, C52×D3×D47, C5×D15×D47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2820, 13);