Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1710 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=dg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^4,h^c=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | #12013609, #12013610, #12013613, … |
| maximal normal subgroup of | #12013609, #12013610, #12013613, … |
| maximal quotient of | #11993076, #11999044, #11999048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4236);