Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C8×Dic5 |
| derived, Sylow | C5 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D5 |
| commutator, hypocenter | C5 | C22×C4×C8 |
| Frattini | C2×C4 | C23×D5 |
| Fitting | C23×C5×C8 | C2 |
| socle, prime radical | C24×C5 | C2×C4 |
| cosocle | C2×C4×C5 | C24 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C8 | |
760 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×#336, #12004451, #12004455, … |
| maximal normal subgroup of | Dic5×#336, #12004451, #12004455, … |
| maximal quotient of | C22×C8×#168, C22×#64674, C2×C8×#681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17537);