Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2247 |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^c=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | #12020088, #12020089, #12020093, … |
| maximal normal subgroup of | #12020088, #12020089, #12020093, … |
| maximal quotient of | #12013955, #12013957, #12013959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4374);