Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C49 · Schur multiplier (H2) = C2 |
| direct product | C4×D5×C49 |
| Fitting | C4×C5×C49 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C4×C49 |
| Hall | C5×C49 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C49 | D5 |
| commutator, hypocenter | C5 | C2×C4×C49 |
| Frattini | C2×C7 | C2×C7×D5 |
| Fitting | C4×C5×C49 | C2 |
| socle, cosocle | C2×C5×C7 | C22×C7 |
| prime radical | C2×C7×D5 | C2×C7 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C4×C49 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 980 |
784 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 20);