Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2245 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ceg,d^a=df,e^a=efg,f^a=fg,h^a=h^4,c^b=cg,h^b=h^4,h^c=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #12012962, #12012963, #12012969, … |
| maximal normal subgroup of | #12012962, #12012963, #12012969, … |
| maximal quotient of | #12015685, #12017236, #12017535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4228);