Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #2988 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^b=h^4148 conjugacy classes — view the full character table.
| maximal subgroup of | #11993182, #11993186, #11993189, … |
| maximal normal subgroup of | #11993182, #11993186, #11993189, … |
| maximal quotient of | #12098088, #12098090, #12098182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12826);