Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C5 ⋊ #3006 |
806 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #12136560, #12136564, #12136593, … |
| maximal normal subgroup of | #12136560, #12136564, #12136593, … |
| maximal quotient of | #12071691, #12071730, #12071769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17759);