Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2994 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,h^a=h^2,c^b=ceg,d^b=dg,h^b=h^4,h^c=h^4,h^d=h^4,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13032557, #13032559, #13032577, … |
| maximal normal subgroup of | #13032557, #13032559, #13032577, … |
| maximal quotient of | #13033963, #13034003, #13034027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19423);