Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #3035 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4,f^c=fg,h^c=h^4118 conjugacy classes — view the full character table.
| maximal subgroup of | #11994186, #11994188, #11994193, … |
| maximal normal subgroup of | #11994186, #11994188, #11994193, … |
| maximal quotient of | #12081724, #12081739, #12081750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12834);