Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×2−1+4 ⋊ C2 |
| Sylow | C5 ⋊ #3013 |
712 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^4,e^b=eg,d^c=dg100 conjugacy classes — view the full character table.
| maximal subgroup of | #12130759, #12130763, #12130768, … |
| maximal normal subgroup of | #12130759, #12130763, #12130768, … |
| maximal quotient of | #12072515, #12072526, #12072603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17927);