Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ #2933 |
502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=f,f^2=g,b^a=be,h^a=h^4,d^c=dg130 conjugacy classes — view the full character table.
| maximal subgroup of | #12120030, #12120037, #12120045, … |
| maximal normal subgroup of | #12120030, #12120037, #12120045, … |
| maximal quotient of | #12070186, #12070197, #12070210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17570);