Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D5×D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic5×D49 |
| derived, Hall | C5×C49 ⋊ C2×C4 |
| Sylow | C49 ⋊ C2×Dic5 |
| Sylow | C5 ⋊ C4×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×D49 |
| commutator, hypocenter | C5×C49 | C2×C4 |
| Frattini | C2×C7 | D5×D7 |
| Fitting, cosocle | C2×C5×C49 | C22 |
| socle | C2×C5×C7 | C2×D7 |
| prime radical | C2×C5×D49 | C2 |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 980 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 8);