Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1313 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^4,c^b=cg124 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1313, C2×#10597933, #12008299, … |
| maximal normal subgroup of | D5×#1313, C2×#10597933, #12008299, … |
| maximal quotient of | #11985917, #11986130, #11986636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15);