Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#427 ⋊ C2 |
| Sylow | C5 ⋊ #2912 |
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,e^2=g,b^a=be,e^a=eg,h^a=h^4,d^c=dg,h^c=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #12015616, #12015622, #12015882, … |
| maximal normal subgroup of | #12015616, #12015622, #12015882, … |
| maximal quotient of | #12068286, #12068339, #12068344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12991);