Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | D5×#433 |
| Fitting | C5×#433 ⋊ C2 |
| Sylow | C5 ⋊ C2×#433 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D5 |
| commutator, socle | C22×C5 | C23×C4 |
| Fitting | C5×#433 | C2 |
| prime radical | C23×D5 | C2×C4 |
| cosocle | C2×C4×C5 | C24 |
| hypercenter | #433 | D5 |
| hypocenter | C5 | C2×#433 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
412 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#433, D5×#2921, D5×#2922, … |
| maximal normal subgroup of | C2×D5×#433, D5×#2921, D5×#2922, … |
| maximal quotient of | D5×#1746, D5×#1750, D5×#1768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13183);