Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1849 |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=d,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^4,c^b=cg112 conjugacy classes — view the full character table.
| maximal subgroup of | #11993692, #11993693, #12003437, … |
| maximal normal subgroup of | #11993692, #11993693, #12003437, … |
| maximal quotient of | #11993049, #11993053, #11993056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2717);