Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×C82 ⋊ C2 |
| Sylow | C5 ⋊ #1335 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^4,c^b=ce,e^b=eg,h^b=h^4172 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1335, C2×#10597932, #12009085, … |
| maximal normal subgroup of | D5×#1335, C2×#10597932, #12009085, … |
| maximal quotient of | #11985950, #11985953, #11985968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 14);