Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×Dic5 |
| derived, Sylow | C5 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D5 |
| commutator, hypocenter | C5 | C42×C8 |
| Frattini | C22×C4 | C22×D5 |
| Fitting | C2×C4×C5×C8 | C2 |
| socle, prime radical | C23×C5 | C22×C4 |
| cosocle | C22×C4×C5 | C23 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C4×C8 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #11986155, C82×Dic5, Dic5×#322, … |
| maximal normal subgroup of | #11986155, C82×Dic5, Dic5×#322, … |
| maximal quotient of | C82×Dic5, C4×C8×#168, Dic5×#322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2622);