Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#416 ⋊ C2 |
| Sylow | C5 ⋊ #2898 |
726 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=g,e^2=g,b^a=be,e^a=eg,h^a=h^4,e^b=eg,h^b=h^4,d^c=dg,h^c=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #12115289, #12115298, #12115304, … |
| maximal normal subgroup of | #12115289, #12115298, #12115304, … |
| maximal quotient of | #12065685, #12065783, #12065791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12645);