Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ #2873 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,e^2=g,d^a=dg,c^b=cg,h^b=h^2,h^f=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13021939, #13021941, #13021942, … |
| maximal normal subgroup of | #13021939, #13021941, #13021942, … |
| maximal quotient of | #13028963, #13028964, #13028965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19489);