Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2110 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,h^a=h^4,c^b=cg,d^b=dg124 conjugacy classes — view the full character table.
| maximal subgroup of | #12010482, #12010483, #12010486, … |
| maximal normal subgroup of | #12010482, #12010483, #12010486, … |
| maximal quotient of | #12008305, #12008309, #12008342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2759);