Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×C22⋊D5 |
| Fitting | C26×C5 ⋊ C2 |
| Sylow | C5 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D5 |
| commutator, cosocle | C2×C5 | C26 |
| Frattini | C2 | C25×D5 |
| Fitting | C26×C5 | C2 |
| socle | C25×C5 | C22 |
| hypercenter | C26 | D5 |
| hypocenter | C5 | C24×D4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C25 ◁ C26 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10602343, #12021166, #12021167, … |
| maximal normal subgroup of | C2×#10602343, #12021166, #12021167, … |
| maximal quotient of | C24×#685, C24×C22⋊Dic5, C24×#683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21526);