Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D5×D32 |
| Fitting | C5×D32 ⋊ C2 |
| Sylow | C5 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D5×D16 |
| commutator, cosocle | C5×C16 | C23 |
| Frattini | C16 | C22×D5 |
| Fitting | C5×D32 | C2 |
| socle | C2×C5 | C2×D16 |
| hypercenter | D32 | D5 |
| hypocenter | C5 | C2×D32 |
| LCS | G ▷ C5×C16 ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D64, D5×SD128, #12020356, … |
| maximal normal subgroup of | D5×D64, D5×SD128, #12020356, … |
| maximal quotient of | D5×#1415, D5×#1423, #12019871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2250);