Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#473 ⋊ C2 |
| Sylow | C5 ⋊ #3069 |
446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^4,d^b=dg,f^c=fg,h^d=h^461 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3069, C2×#10612675, #12966719, … |
| maximal normal subgroup of | D5×#3069, C2×#10612675, #12966719, … |
| maximal quotient of | #12082076, #12082078, #12082087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 14757);