Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #2360 |
620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,h^a=h^4,d^b=de130 conjugacy classes — view the full character table.
| maximal subgroup of | #12119550, #12119557, #12119625, … |
| maximal normal subgroup of | #12119550, #12119557, #12119625, … |
| maximal quotient of | C4⋊C4×C22⋊Dic5, #12020804, #12020841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15975);