Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1452 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^b=cf,h^b=h^2,h^e=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13013655, #13013657, #13016683, … |
| maximal normal subgroup of | #13013655, #13013657, #13016683, … |
| maximal quotient of | #13015256, #13015277, #13016668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6771);