Finite Group DatabasebetaFinite Group Databasebeta| order | 820 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#4223 |
| Fitting, socle, Hall | C5×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #4223 |
| commutator, hypocenter | C41 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C41 | C4 |
| prime radical | C5×D41 | C2 |
| cosocle | D41 | C2×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 205 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#66502, #13110017, D5×#4223, … |
| maximal normal subgroup of | C5×#66502, #13110017, D5×#4223, … |
| maximal quotient of | C5×#66493, C2×C5×#4223, C3×C5×#4223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(820, 10);