Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ #2297 |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=eg,d^2=f,b^a=be,c^a=cf,h^a=h^2,h^b=h^3,h^g=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13021745, #13021746, #13021761, … |
| maximal normal subgroup of | #13021745, #13021746, #13021761, … |
| maximal quotient of | #13027906, #13027916, C4×#65779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19637);