Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C5 ⋊ #3428 |
1540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,e^2=f,b^a=bf,d^a=df,h^a=h^4,c^b=cf148 conjugacy classes — view the full character table.
| maximal subgroup of | #12004632, #12004635, #12004652, … |
| maximal normal subgroup of | #12004632, #12004635, #12004652, … |
| maximal quotient of | #12257514, #12257529, C4×#66132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21243);