Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#4150 |
| Fitting | C4×C5×#41 ⋊ C2 |
| Sylow | C5 ⋊ C4×2−1+4 |
1492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #11990702, #11990705, #12065685, … |
| maximal normal subgroup of | #11990702, #11990705, #12065685, … |
| maximal quotient of | C4×#65857, C4×#65880, C4×#66161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19805);