Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of C11⋊(C24⋊C5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C11⋊(C24⋊C5) |
| unambiguous semidirect product | (C2×C11)⋊(C24⋊C5) |
| unambiguous semidirect product | C25⋊(C11⋊C5) |
| Fitting, socle, Hall | C25×C11 ⋊ C5 |
| derived | C24×C11 ⋊ C2×C5 |
| Sylow | C25 ⋊ C11⋊C5 |
| Sylow | C11 ⋊ C2×C24⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊(C24⋊C5) |
| commutator, cosocle, hypocenter | C24×C11 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C25×C11 | C5 |
| LCS | G ▷ C24×C11 | |
| UCS | C1 ◁ C2 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 110 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1278);