Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D245 |
| Fitting | C22×C5×C49 ⋊ C2 |
| Hall | C5×C49 ⋊ D4 |
| Sylow | C49 ⋊ C22⋊D5 |
| Sylow | C5 ⋊ C22⋊D49 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D245 |
| commutator, cosocle | C2×C5×C49 | C22 |
| Frattini | C2×C7 | C2×D35 |
| Fitting | C22×C5×C49 | C2 |
| socle | C2×C5×C7 | C2×D7 |
| hypercenter | C22 | D245 |
| hypocenter | C5×C49 | D4 |
| LCS | G ▷ C2×C5×C49 ▷ C5×C49 | |
| UCS | C1 ◁ C2 ◁ C22 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 980 |
Polycyclic presentation:
2^3,5,7^2|e^7=f,b^a=bc,d^a=d^4,e^a=e^6f^6,f^a=f^6493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 28);