Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C26×D5 |
| unambiguous semidirect product | C5⋊C27 |
| unambiguous semidirect product | (C2×C5)⋊C26 |
| Fitting, socle | C26×C5 ⋊ C2 |
| derived, Sylow | C5 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D5 |
| commutator, cosocle, hypocenter | C5 | C27 |
| Frattini | C1 | G |
| Fitting, socle | C26×C5 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C26 | |
58424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #12030455, C2×D5×#379, C22×#65244, … |
| maximal normal subgroup of | #12030455, C2×D5×#379, C22×#65244, … |
| maximal quotient of | C25×C4×D5, C26×Dic5, C24×D4×D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21540);