Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #3310 |
450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4,c^b=cg,d^b=de,f^c=fg79 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3310, C2×#10615215, #12976073, … |
| maximal normal subgroup of | D5×#3310, C2×#10615215, #12976073, … |
| maximal quotient of | #12114840, #12115582, #12116349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17297);