Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1307 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^4,c^b=cg,d^b=df,h^b=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | #11986846, #11986847, #11986924, … |
| maximal normal subgroup of | #11986846, #11986847, #11986924, … |
| maximal quotient of | #11985874, #11985876, #11985892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 289);