Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#3926 |
| derived, Sylow | C5 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D5 |
| commutator, hypocenter | C5 | C22×C32 |
| Frattini | C16 | C22×D5 |
| Fitting | C22×C5×C16 | C2 |
| socle, prime radical | C23×C5 | C16 |
| cosocle | C5×C16 | C23 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #11986986, #11986987, #11986998, … |
| maximal normal subgroup of | #11986986, #11986987, #11986998, … |
| maximal quotient of | C2×C4×#3926, C2×C22⋊#3926, C2×C4⋊#3926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4270);