Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #564⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×#564⋊C5 |
| unambiguous semidirect product | (C2×#564)⋊C5 |
| Fitting, Sylow | C2×#564 ⋊ C5 |
| derived | #564 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23 | C24⋊C5 |
| commutator, cosocle, hypocenter | #564 | C2×C5 |
| Frattini | C22 | C2×C24⋊C5 |
| Fitting | C2×#564 | C5 |
| LCS | G ▷ #564 | |
| UCS | C1 ◁ C23 | |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
46 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#564⋊C5, C22×#564⋊C5, C2×#3531⋊C5, … |
| maximal normal subgroup of | C4×#564⋊C5, C22×#564⋊C5, C2×#3531⋊C5, … |
| maximal quotient of | C4×#564⋊C5, C22×#564⋊C5, C2×C3×#564⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19101);