Finite Group DatabasebetaFinite Group Databasebeta| order | 820 |
| isoclinism | isoclinic class of D5×D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D41 |
| unambiguous semidirect product | (D5×C41)⋊C2 |
| unambiguous semidirect product | (C5×D41)⋊C2 |
| unambiguous semidirect product | D205⋊C2 |
| Fitting, socle, derived, Hall | C5×C41 ⋊ C22 |
| Sylow | C41 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C41 | C22 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 205 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#4223, AGL(1,𝔽5)×D41, D5×#4223, … |
| maximal normal subgroup of | D5⋊#4223, AGL(1,𝔽5)×D41, D5×#4223, … |
| maximal quotient of | Dic5×D41, D5×Dic41, #13109988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(820, 16);