Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2875 |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,e^2=g,b^a=bg,h^a=h^2,d^c=dg,h^e=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13020092, #13020094, #13020096, … |
| maximal normal subgroup of | #13020092, #13020094, #13020096, … |
| maximal quotient of | #13028976, #13029004, #13029077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19218);