Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×M64 ⋊ C2 |
| Sylow | C5 ⋊ #2264 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^4,d^b=de,e^b=ef,f^b=fg,h^b=h^4106 conjugacy classes — view the full character table.
| maximal subgroup of | #12019917, #12019920, #12019979, … |
| maximal normal subgroup of | #12019917, #12019920, #12019979, … |
| maximal quotient of | #12019740, #12019748, #12019807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2249);