Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1544 |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=g,d^2=g,e^2=fg,b^a=bd,d^a=df,h^a=h^4,d^b=dg,e^b=efg94 conjugacy classes — view the full character table.
| maximal subgroup of | #11990308, #11990310, #11990318, … |
| maximal normal subgroup of | #11990308, #11990310, #11990318, … |
| maximal quotient of | #11987255, #11987272, #11987601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4704);