Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#123 ⋊ C4 |
| Sylow | C5 ⋊ #2322 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^2,c^b=ce,h^b=h^3,h^g=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #13025798, #13036208, C2×#10617304, … |
| maximal normal subgroup of | #13025798, #13036208, C2×#10617304, … |
| maximal quotient of | #13027945, #13027960, #13027964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19386);