Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #2880 |
774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=be,d^c=dg,h^c=h^4130 conjugacy classes — view the full character table.
| maximal subgroup of | #11995606, #11995610, #11995620, … |
| maximal normal subgroup of | #11995606, #11995610, #11995620, … |
| maximal quotient of | #12065480, #12065481, #12065488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12413);