Finite Group DatabasebetaFinite Group Databasebeta| order | 820 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C41 |
| derived, Sylow | C5 ⋊ C4×C41 |
| Hall | C5×C41 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D5 |
| commutator, hypocenter | C5 | C4×C41 |
| Frattini | C2 | D5×C41 |
| Fitting, socle, prime radical | C2×C5×C41 | C2 |
| cosocle | C2×C5 | C2×C41 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C41 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 820 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #170×C41, #13109984, Dic5×D41, … |
| maximal normal subgroup of | #170×C41, #13109984, Dic5×D41, … |
| maximal quotient of | #168×C41, C2×Dic5×C41, C3×Dic5×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(820, 3);