Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×C5×#41 ⋊ C2 |
| Sylow | C5 ⋊ #3428 |
1540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^d=h^4148 conjugacy classes — view the full character table.
| maximal subgroup of | #12097027, #12097030, #12098845, … |
| maximal normal subgroup of | #12097027, #12097030, #12098845, … |
| maximal quotient of | #12257512, #12257527, #12257529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19817);