Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#489 ⋊ C2 |
| Sylow | C5 ⋊ #3137 |
372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^c=h^4,h^d=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3137, C2×#10613412, #12968554, … |
| maximal normal subgroup of | D5×#3137, C2×#10613412, #12968554, … |
| maximal quotient of | #12099505, #12101949, #12101956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15494);