Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×#135 ⋊ C2 |
| Sylow | C5 ⋊ #3284 |
494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^4,d^b=de,e^b=eg,e^d=eg91 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3284, C2×#10615658, #12974589, … |
| maximal normal subgroup of | D5×#3284, C2×#10615658, #12974589, … |
| maximal quotient of | #12090083, #12090088, #12090098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17740);