Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C5 ⋊ #2884 |
716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,h^a=h^4,f^b=fg,d^c=dg109 conjugacy classes — view the full character table.
| maximal subgroup of | #12016892, #12016896, #12016906, … |
| maximal normal subgroup of | #12016892, #12016896, #12016906, … |
| maximal quotient of | #12065129, #12065133, #12065233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17932);