Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ #2339 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=g,c^2=e,b^a=be,c^a=cf,h^a=h^2,d^b=de,h^g=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13020220, #13020221, #13020228, … |
| maximal normal subgroup of | #13020220, #13020221, #13020228, … |
| maximal quotient of | #13027994, #13028000, D4×(C2×AGL(1,𝔽5))⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19639);