Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2973 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^4,c^b=ce124 conjugacy classes — view the full character table.
| maximal subgroup of | #11993270, #11993273, #11993309, … |
| maximal normal subgroup of | #11993270, #11993273, #11993309, … |
| maximal quotient of | #12097978, #12097990, #12098036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16115);