Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D5×#407 |
| Fitting | C5×#407 ⋊ C2 |
| Sylow | C5 ⋊ C2×#407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D5 |
| commutator, socle | C22×C5 | C23×C4 |
| Fitting | C5×#407 | C2 |
| prime radical | C24×D5 | C4 |
| cosocle | C2×C4×C5 | C24 |
| hypercenter | #407 | D5 |
| hypocenter | C5 | C2×#407 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
1008 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1284, #11989022, #11989026, … |
| maximal normal subgroup of | D5×#1284, #11989022, #11989026, … |
| maximal quotient of | D5×#1462, D5×#1463, D5×#1464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12442);