Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2352 |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=f,c^2=f,b^a=be,c^a=cf,h^a=h^4,d^b=de,h^b=h^4,h^d=h^4130 conjugacy classes — view the full character table.
| maximal subgroup of | #12114722, #12114724, #12114748, … |
| maximal normal subgroup of | #12114722, #12114724, #12114748, … |
| maximal quotient of | C4⋊C4×#685, #12020721, #12020746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7584);