Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D160 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic80 |
| Sylow | C5 ⋊ C2×Q64 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D80 |
| commutator, cosocle | C5×C16 | C23 |
| Frattini | C16 | C22×D5 |
| Fitting | C2×C5×C32 | C2 |
| socle, prime radical | C22×C5 | D16 |
| hypercenter | C2×C32 | D5 |
| hypocenter | C5 | C2×Q64 |
| LCS | G ▷ C5×C16 ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
166 conjugacy classes — view the full character table.
| maximal subgroup of | #11987180, #11987182, #11987192, … |
| maximal normal subgroup of | #11987180, #11987182, #11987192, … |
| maximal quotient of | C2×#10598088, C2×#10598082, C4×Dic80, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2245);