Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #41×C22⋊D5 |
| Fitting | C22×C5×#41 ⋊ C2 |
| Sylow | C5 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Frattini | C22 | C24×D5 |
| Fitting | C22×C5×#41 | C2 |
| hypercenter | C22×#41 | D5 |
| hypocenter | C5 | D4×#41 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
1648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #12114967, #104×C22⋊D5, #12114978, … |
| maximal normal subgroup of | #12114967, #104×C22⋊D5, #12114978, … |
| maximal quotient of | #41×#685, #41×C22⋊Dic5, #41×#683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21255);