Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D245 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic245 |
| unambiguous semidirect product | (C2×C49)⋊Dic5 |
| derived, Hall | C5×C49 ⋊ C2×C4 |
| Sylow | C49 ⋊ C2×Dic5 |
| Sylow | C5 ⋊ C2×Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D245 |
| commutator, hypocenter | C5×C49 | C2×C4 |
| Frattini | C2×C7 | C2×D35 |
| Fitting | C22×C5×C49 | C2 |
| socle, prime radical | C22×C5×C7 | D7 |
| cosocle | C2×C5×C49 | C22 |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C22 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1960 |
496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 27);