Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×C8×Q8 ⋊ C2 |
| Sylow | C5 ⋊ #2985 |
322 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,d^b=dg,h^d=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #12069398, #12069402, #12069406, … |
| maximal normal subgroup of | #12069398, #12069402, #12069406, … |
| maximal quotient of | #12098049, #12098075, #12098376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13735);