Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1830 |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^4,f^b=fg,e^c=eg97 conjugacy classes — view the full character table.
| maximal subgroup of | #12014933, #12014935, #12014937, … |
| maximal normal subgroup of | #12014933, #12014935, #12014937, … |
| maximal quotient of | #11992762, #11992768, #11992822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4534);