Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C5×#41 ⋊ C2 |
| Sylow | C5 ⋊ #3115 |
430 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4,d^c=dg,f^c=fg112 conjugacy classes — view the full character table.
| maximal subgroup of | #11995107, #11995109, #11995114, … |
| maximal normal subgroup of | #11995107, #11995109, #11995114, … |
| maximal quotient of | #12099383, #12102331, #12102361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16344);