Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #3223 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^4,f^c=fg,h^c=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3223, C2×#10612002, #12970708, … |
| maximal normal subgroup of | D5×#3223, C2×#10612002, #12970708, … |
| maximal quotient of | #12108683, #12109092, #12109895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 14084);