Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | D5×#386 |
| Fitting | C5×#386 ⋊ C2 |
| Sylow | C5 ⋊ C2×#386 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D5 |
| commutator | C22×C5 | C23×C4 |
| Fitting | C5×#386 | C2 |
| socle, cosocle | C23×C5 | C24 |
| prime radical | C22×D4×D5 | C2 |
| hypercenter | #386 | D5 |
| hypocenter | C5 | C2×#386 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #386 | |
1576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1390, #12015537, D5×#1790, … |
| maximal normal subgroup of | D5×#1390, #12015537, D5×#1790, … |
| maximal quotient of | D5×C22⋊#95, D5×#1436, D5×#1437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 8686);