Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D5×D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×D49 |
| unambiguous semidirect product | (D5×C49)⋊C22 |
| unambiguous semidirect product | (C5×D49)⋊C22 |
| unambiguous semidirect product | D245⋊C22 |
| Fitting | C2×C5×C49 ⋊ C22 |
| derived, Hall | C5×C49 ⋊ C23 |
| Sylow | C49 ⋊ C22×D5 |
| Sylow | C5 ⋊ C22×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×D49 |
| commutator, cosocle, hypocenter | C5×C49 | C23 |
| Frattini | C7 | C2×D5×D7 |
| Fitting | C2×C5×C49 | C22 |
| socle | C2×C5×C7 | C2×D7 |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 490 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 36);